Chapter 01 - Why Are Financial Institutions Special?
Solutions for End-of-Chapter Questions and Problems: Chapter One
1.
What are five risks common to all financial institutions?
Default or credit risk of assets, interest rate risk caused by maturity mismatches between assets
and liabilities, liability withdrawal or liquidity risk, underwriting risk, and operating risks.
2.
Explain how economic transactions between household savers of funds and corporate users
of funds would occur in a world without financial institutions.
In a world without FIs the users of corporate funds in the economy would have to directly
approach the household savers of funds in order to satisfy their borrowing needs. This process
would be extremely costly because of the up-front information costs faced by potential lenders.
Cost inefficiencies would arise with the identification of potential borrowers, the pooling of
small savings into loans of sufficient size to finance corporate activities, and the assessment of
risk and investment opportunities. Moreover, lenders would have to monitor the activities of
borrowers over each loan's life span. The net result would be an imperfect allocation of resources
in an economy.
3.
Identify and explain three economic disincentives that would dampen the flow of funds
between household savers of funds and corporate users of funds in an economic world
without financial institutions.
Investors generally are averse to directly purchasing securities because of (a) monitoring costs,
(b) liquidity costs, and (c) price risk. Monitoring the activities of borrowers requires extensive
time, expense, and expertise. As a result, households would prefer to leave this activity to others,
and by definition, the resulting lack of monitoring would increase the riskiness of investing in
corporate debt and equity markets. The long-term nature of corporate equity and debt securities
would likely eliminate at least a portion of those households willing to lend money, as the
preference of many for near-cash liquidity would dominate the extra returns which may be
available. Finally, the price risk of transactions on the secondary markets would increase without
the information flows and services generated by high volume.
4.
Identify and explain the two functions FIs perform that would enable the smooth flow of
funds from household savers to corporate users.
FIs serve as conduits between users and savers of funds by providing a brokerage function and
by engaging in an asset transformation function. The brokerage function can benefit both savers
and users of funds and can vary according to the firm. FIs may provide only transaction services,
such as discount brokerages, or they also may offer advisory services which help reduce
information costs, such as full-line firms like Merrill Lynch. The asset transformation function is
accomplished by issuing their own securities, such as deposits and insurance policies that are
more attractive to household savers, and using the proceeds to purchase the primary securities of
corporations. Thus, FIs take on the costs associated with the purchase of securities.
1-1
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
5.
In what sense are the financial claims of FIs considered secondary securities, while the
financial claims of commercial corporations are considered primary securities? How does
the transformation process, or intermediation, reduce the risk, or economic disincentives, to
the savers?
Funds raised by the financial claims issued by commercial corporations are used to invest in real
assets. These financial claims, which are considered primary securities, are purchased by FIs
whose financial claims therefore are considered secondary securities. Savers who invest in the
financial claims of FIs are indirectly investing in the primary securities of commercial
corporations. However, the information gathering and evaluation expenses, monitoring expenses,
liquidity costs, and price risk of placing the investments directly with the commercial corporation
are reduced because of the efficiencies of the FI.
6.
Explain how financial institutions act as delegated monitors. What secondary benefits often
accrue to the entire financial system because of this monitoring process?
By putting excess funds into financial institutions, individual investors give to the FIs the
responsibility of deciding who should receive the money and of ensuring that the money is
utilized properly by the borrower. In this sense, depositors have delegated the FI to act as a
monitor on their behalf. Further, the FI can collect information more efficiently than individual
investors. The FI can utilize this information to create new products, such as commercial loans,
that continually update the information pool. This more frequent monitoring process sends
important informational signals to other participants in the market, a process that reduces
information imperfection and asymmetry between the ultimate providers and users of funds in
the economy.
7.
What are five general areas of FI specialness that are caused by providing various services
to sectors of the economy?
First, FIs collect and process information more efficiently than individual savers. Second, FIs
provide secondary claims to household savers which often have better liquidity characteristics
than primary securities such as equities and bonds. Third, by diversifying the asset base FIs
provide secondary securities with lower price risk conditions than primary securities. Fourth, FIs
provide economies of scale in transaction costs because assets are purchased in larger amounts.
Finally, FIs provide maturity intermediation to the economy which allows the introduction of
additional types of investment contracts, such as mortgage loans, that are financed with shortterm deposits.
8.
What are agency costs? How do FIs solve the information and related agency costs
experienced when household savers invest directly in securities issued by corporations?
Agency costs occur when owners or managers take actions that are not in the best interests of the
equity investor or lender. These costs typically result from the failure to adequately monitor the
activities of the borrower. If no other lender performs these tasks, the lender is subject to agency
costs as the firm may not satisfy the covenants in the lending agreement. Because the FI invests
1-2
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
the funds of many small savers, the FI has a greater incentive to collect information and monitor
the activities of the borrower.
9.
How do large financial institutions solve the problem of high information collection costs
for lenders, borrowers, and financial markets?
One way financial institutions solve this problem is that they develop of secondary securities that
allow for improvements in the monitoring process. An example is the bank loan that is renewed
more quickly than long-term debt. The renewal process updates the financial and operating
information of the firm more frequently, thereby reducing the need for restrictive bond covenants
that may be difficult and costly to implement.
10.
How do FIs alleviate the problem of liquidity risk faced by investors who wish to buy
securities issued by corporations?
Liquidity risk occurs when savers are not able to sell their securities on demand. Commercial
banks, for example, offer deposits that can be withdrawn at any time. Yet, the banks make longterm loans or invest in illiquid assets because they are able to diversify their portfolios and better
monitor the performance of firms that have borrowed or issued securities. Thus, individual
investors are able to realize the benefits of investing in primary assets without accepting the
liquidity risk of direct investment.
11.
How do financial institutions help individual savers diversify their portfolio risks? Which
type of financial institution is best able to achieve this goal?
Money placed in any financial institution will result in a claim on a more diversified portfolio.
Banks lend money to many different types of corporate, consumer, and government customers.
Insurance companies have investments in many different types of assets. Investments in a mutual
fund may generate the greatest diversification benefit because of the fund’s investment in a wide
array of stocks and fixed income securities.
12.
How can financial institutions invest in high-risk assets with funding provided by low-risk
liabilities from savers?
Diversification of risk occurs with investments in assets whose returns are not perfectly
positively correlated. One result of extensive diversification is that the average risk of the asset
base of an FI will be less than the average risk of the assets in which the individual has invested.
Thus, individual investors realize some of the returns of high-risk assets without accepting the
corresponding risk characteristics.
13.
How can individual savers use financial institutions to reduce the transaction costs of
investing in financial assets?
By pooling the assets of many small investors, FIs can gain economies of scale in transaction
costs. This benefit occurs whether the FI is lending to a corporate or retail customer, or
purchasing assets in the money and capital markets. In either case, operating activities that are
1-3
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
designed to deal in large volumes typically are more efficient than those activities designed for
small volumes.
14.
What is maturity intermediation? What are some of the ways in which the risks of maturity
intermediation are managed by financial institutions?
If net borrowers and net lenders have different optimal time horizons, FIs can service both
sectors by matching their asset and liability maturities through on- and off-balance sheet hedging
activities and flexible access to the financial markets. For example, the FI can offer the relatively
short-term liabilities desired by households and also satisfy the demand for long-term loans such
as home mortgages. By investing in a portfolio of long- and short-term assets that have variableand fixed-rate components, the FI can reduce maturity risk exposure by utilizing liabilities that
have similar variable- and fixed-rate characteristics, or by using futures, options, swaps, and
other derivative products.
15.
What are five areas of institution-specific FI specialness and which types of institutions are
most likely to be the service providers?
First, commercial banks and other depository institutions are key players for the transmission of
monetary policy from the central bank to the rest of the economy. Second, specific FIs often are
identified as the major source of financing for certain sectors of the economy. For example,
savings institutions traditionally serve the credit needs of the residential real estate market.
Third, life insurance companies and pension funds commonly are encouraged to provide
mechanisms to transfer wealth across generations. Fourth, depository institutions efficiently
provide payment services to benefit the economy. Finally, mutual funds provide denomination
intermediation by allowing small investors to purchase pieces of assets with large minimum sizes
such as negotiable CDs and commercial paper issues.
16.
How do depository institutions such as commercial banks assist in the implementation and
transmission of monetary policy?
The Federal Reserve Board can directly involve commercial banks in the implementation of
monetary policy through changes in the reserve requirements and the discount rate. The open
market sale and purchase of Treasury securities by the Fed involves banks in the implementation
of monetary policy in a less direct manner.
17.
What is meant by credit allocation regulation? What social benefit is this type of regulation
intended to provide?
Credit allocation regulation refers to the requirement faced by FIs to lend to certain sectors of the
economy which are considered to be socially important. These may include housing and farming.
Presumably the provision of credit to make houses more affordable or farms more viable leads to
a more stable and productive society.
1-4
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
18.
Which intermediaries best fulfill the intergenerational wealth transfer function? What is
this wealth transfer process?
Life insurance companies and pension funds often receive special taxation relief and other
subsidies to assist in the transfer of wealth from one generation to another. In effect, the wealth
transfer process allows for the accumulation of wealth by one generation to be transferred
directly to one or more younger generations by establishing life insurance policies and trust
provisions in pension plans. Often this wealth transfer process avoids the full marginal tax
treatment that a direct payment would incur.
19.
What are two of the most important payment services provided by financial institutions? To
what extent do these services efficiently provide benefits to the economy?
The two most important payment services are check clearing and wire transfer services. Any
breakdown in these systems would produce gridlock in the payment system with resulting
harmful effects to the economy at both the domestic and potentially the international level.
20.
What is denomination intermediation? How do FIs assist in this process?
Denomination intermediation is the process whereby small investors are able to purchase pieces
of assets that normally are sold only in large denominations. Individual savers often invest small
amounts in mutual funds. The mutual funds pool these small amounts and purchase a well
diversified portfolio of assets. Therefore, small investors can benefit in the returns and low risk
which these assets typically offer.
21.
What is negative externality? In what ways do the existence of negative externalities justify
the extra regulatory attention received by financial institutions?
A negative externality refers to the action by one party that has an adverse effect on another
party who is not part of the original transaction. For example, in an industrial setting, smoke
from a factory that lowers surrounding property values may be viewed as a negative externality.
For financial institutions, one concern is the contagion effect that can arise when the failure of
one FI can cast doubt on the solvency of other FIs.
22.
If financial markets operated perfectly and costlessly, would there be a need for financial
institutions?
To a certain extent, financial institutions exist because of financial market imperfections. If
information is available costlessly to all participants, savers would not need FIs to act as either
their brokers or their delegated monitors. However, if there are social benefits to intermediation,
such as the transmission of monetary policy or credit allocation, then FIs would exist even in the
absence of financial market imperfections.
1-5
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
23.
Why are FIs among the most regulated sectors in the world? When is the net regulatory
burden positive?
FIs are required to enhance the efficient operation of the economy. Successful financial
institutions provide sources of financing that fund economic growth opportunities that ultimately
raise the overall level of economic activity. Moreover, successful financial institutions provide
transaction services to the economy that facilitate trade and wealth accumulation.
Conversely, distressed FIs create negative externalities for the entire economy. That is, the
adverse impact of an FI failure is greater than just the loss to shareholders and other private
claimants on the FI's assets. For example, the local market suffers if an FI fails and other FIs also
may be thrown into financial distress by a contagion effect. Therefore, since some of the costs of
the failure of an FI are generally borne by society at large, the government intervenes in the
management of these institutions to protect society's interests. This intervention takes the form of
regulation.
However, the need for regulation to minimize social costs may impose private costs to the FIs
that would not exist without regulation. This additional private cost is defined as a net regulatory
burden. Examples include the cost of holding excess capital and/or excess reserves and the extra
costs of providing information. Although they may be socially beneficial, these costs add to
private operating costs. To the extent that these additional costs help to avoid negative
externalities and to ensure the smooth and efficient operation of the economy, the net regulatory
burden is positive.
24.
What forms of protection and regulation do regulators of FIs impose to ensure their safety
and soundness?
Regulators have issued several guidelines to insure the safety and soundness of FIs:
a.
b.
c.
d.
25.
FIs are required to diversify their assets. For example, banks cannot lend more than 10
percent of their equity to a single borrower.
FIs are required to maintain minimum amounts of capital to cushion any unexpected losses.
In the case of banks, the Basle standards require a minimum core and supplementary
capital based on the size of an FIs’ risk-adjusted assets.
Regulators have set up guaranty funds such as DIF for commercial banks, SIPC for
securities firms, and state guaranty funds for insurance firms to protect individual investors.
Regulators also engage in periodic monitoring and surveillance, such as on-site
examinations, and request periodic information from the FIs.
In the transmission of monetary policy, what is the difference between inside money and
outside money? How does the Federal Reserve try to control the amount of inside money?
How can this regulatory position create a cost for the depository institutions?
1-6
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Outside money is that part of the money supply directly produced and controlled by the Fed, for
example, coins and currency. Inside money refers to bank deposits not directly controlled by the
Fed. The Fed can influence this amount of money by adjusting reserve requirement and discount
rate policies. In cases where the level of required reserves exceeds the level considered optimal
by the FI, the inability to use the excess reserves to generate revenue may be considered a tax or
cost of providing intermediation.
26.
What are some examples of credit allocation regulation? How can this attempt to create
social benefits create costs to a private institution?
The qualified thrift lender test (QTL) requires thrifts to hold 65 percent of their assets in
residential mortgage-related assets to retain the thrift charter. Some states have enacted usury
laws that place maximum restrictions on the interest rates that can be charged on mortgages
and/or consumer loans. These types of restrictions often create additional operating costs to the
FI and almost certainly reduce the amount of profit that could be realized without such
regulation.
27.
What is the purpose of the Home Mortgage Disclosure Act? What are the social benefits
desired from the legislation? How does the implementation of this legislation create a net
regulatory burden on financial institutions?
The HMDA was passed by Congress to prevent discrimination in mortgage lending. The social
benefit is to ensure that everyone who qualifies financially is provided the opportunity to
purchase a house should they so desire. The regulatory burden has been to require a written
statement indicating the reasons why credit was or was not granted.
28.
What legislation has been passed specifically to protect investors who use investment
banks directly or indirectly to purchase securities? Give some examples of the types of
abuses for which protection is provided.
The Securities Acts of 1933 and 1934 and the Investment Company Act of 1940 were passed by
Congress to protect investors against possible abuses such as insider trading, lack of disclosure,
outright malfeasance, and breach of fiduciary responsibilities.
29.
How do regulations regarding barriers to entry and the scope of permitted activities affect
the charter value of financial institutions?
The profitability of existing firms will be increased as the direct and indirect costs of establishing
competition increase. Direct costs include the actual physical and financial costs of establishing a
business. In the case of FIs, the financial costs include raising the necessary minimum capital to
receive a charter. Indirect costs include permission from regulatory authorities to receive a
charter. Again in the case of FIs this cost involves acceptable leadership to regulators. As these
barriers to entry are stronger, the charter value for existing firms is higher.
1-7
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
30.
What reasons have been given for the growth of investment companies at the expense of
“traditional” banks and insurance companies?
The recent growth of investment companies can be attributed to two major factors:
a.
Investors have demanded increased access to direct investment in securities markets.
Investment companies allow investors to take positions in securities markets while still
obtaining the risk diversification, monitoring, and transactional efficiency benefits of
financial intermediation. Some experts would argue that this growth is the result of
increased sophistication on the part of investors. Others would argue that the ability to use
these markets has caused the increased investor awareness. The growth in these assets is
inarguable.
b.
Recent episodes of financial distress in both the banking and insurance industries have led
to an increase in regulation and governmental oversight, thereby increasing the net
regulatory burden of “traditional” companies. As such, the costs of intermediation have
increased, which increases the cost of providing services to customers.
31.
What events resulted in banks’ shift from the traditional banking model of “originate and
hold” to a model of “originate and distribute?”
As FIs adjusted to regulatory changes brought about by the likes of the FSM Act, one result was
a dramatic increase in systemic risk of the financial system, caused in large part by a shift in the
banking model from that of “originate and hold” to “originate to distribute.” In the traditional
model, banks take short term deposits and other sources of funds and use them to fund longer
term loans to businesses and consumers. Banks typically hold these loans to maturity, and thus
have an incentive to screen and monitor borrower activities even after a loan is made. However,
the traditional banking model exposes the institution to potential liquidity, interest rate, and
credit risk. In attempts to avoid these risk exposures and generate improved return-risk tradeoffs,
banks shifted to an underwriting model in which they originated or warehoused loans, and then
quickly sold them. Indeed, most large banks organized as financial service holding companies to
facilitate these new activities. More recently activities of shadow banks, nonfinancial service
firms that perform banking services, have facilitated the change from the originate and hold
model of commercial banking to the originate and distribute banking model. These innovations
removed risk from the balance sheet of financial institutions and shifted risk off the balance sheet
and to other parts of the financial system. Since the FIs, acting as underwriters, were not exposed
to the credit, liquidity, and interest rate risks of traditional banking, they had little incentive to
screen and monitor activities of borrowers to whom they originated loans. Thus, FIs failed to act
as specialists in risk measurement and management.
1-8
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
32.
How did the boom in the housing market in the early and mid-2000s exacerbate FI’s
transition away from their role as specialists in risk measurement and management?
The boom (“bubble”) in the housing markets began building in 2001, particularly after the
terrorist attacks of 9/11. The immediate response by regulators to the terrorist attacks was to
create stability in the financial markets by providing liquidity to FIs. For example, the Federal
Reserve lowered the short-term money market rate that banks and other financial institutions pay
in the Federal funds market and even made lender of last resort funds available to non-bank FIs
such as investment banks. Perhaps not surprisingly, low interest rates and the increased liquidity
provided by Central banks resulted in a rapid expansion in consumer, mortgage, and corporate
debt financing. Demand for residential mortgages and credit card debt rose dramatically. As the
demand for mortgage debt grew, especially among those who had previously been excluded from
participating in the market because of their poor credit ratings, FIs began lowering their credit
quality cut-off points. Moreover, to boost their earnings, in the market now popularly known as
the “subprime market,” banks and other mortgage-supplying institutions often offered relatively
low “teaser” rates on adjustable rate mortgages (ARMs) at exceptionally low initial interest rates,
but with substantial step-up in rates after the initial rate period expired two or three year later and
if market rates rose in the future. Under the traditional banking structure, banks might have been
reluctant to so aggressively pursue low credit quality borrowers for fear that the loans would
default. However, under the originate-to-distribute model of banking, asset securitization and
loan syndication allowed banks to retain little or no part of the loans, and hence the default risk
on loans that they originated. Thus, as long as the borrower did not default within the first
months after a loan’s issuance and the loans were sold or securitized without recourse back to the
bank, the issuing bank could ignore longer term credit risk concerns. The result was deterioration
in credit quality, at the same time as there was a dramatic increase in consumer and corporate
leverage.
The following questions and problems are based on material in Appendix 1B to the Chapter.
33. What are the tools used by the Federal Reserve to implement monetary policy?
The tools used by the Federal Reserve to implement its monetary policy include open market
operations, the discount rate, and reserve requirements. Open market operations are the Federal
Reserves’ purchases or sales of securities in the U.S. Treasury securities market. The discount
rate is the rate of interest Federal Reserve Banks charge on “emergency” or “lender of last
resort” loans to depository institutions in their district. Reserve requirements determine the
minimum amount of reserve assets (vault cash plus bank deposits at Federal Reserve Banks) that
depository institutions must maintain by law to back transaction deposits held as liabilities on
their balance sheets. This requirement is usually set as a ratio of transaction accounts, e.g., 10
percent.
34.
Suppose the Federal Reserve instructs the Trading Desk to purchase $1 billion of securities.
Show the result of this transaction on the balance sheets of the Federal Reserve System and
commercial banks.
1-9
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
For the purchase of $1 billion in securities, the balance sheet of the Federal Reserve System and
commercial banks is shown below.
Change in Federal Reserve’s Balance Sheet
Assets
Treasury securities
Liabilities
Reserve account of
+ $1 b
securities dealers’ banks
---------------------------------------------------------------------------------------------------Change in Commercial Bank Balance Sheets
Assets
Reserve accounts
at Federal Reserve
35.
+ $1 b
Liabilities
Securities dealers’ demand
deposit accounts
+ $1 b
+ $1 b
Explain how a decrease in the discount rate affects credit availability and the money
supply.
Changing the discount rate signals to the market and the economy that the Federal Reserve
would like to see higher or lower rates in the economy. Thus, the discount rate is like a signal of
the FOMC’s intention regarding the tenor of monetary policy. For example, raising the discount
rate “signals” that the Fed would like to see a tightening of monetary conditions and higher
interest rates in general (and a relatively lower amount of borrowing). Lowering the discount rate
“signals” a desire to see more expansionary monetary conditions and lower interest rates in
general.
36.
What changes did the Fed implement to its discount window lending policy in the early
2000s?
In January 2003, the Fed implemented changes to its discount window lending that increased the cost of borrowing
but eased the terms. Specifically, three lending programs are now offered through the Feds discount window.
Primary credit is available to generally sound depository institutions on a very short-term basis,
typically overnight, at a rate above the Federal Open Market Committee's (FOMC) target rate for
federal funds. Primary credit may be used for any purpose, including financing the sale of fed funds. Primary credit
may be extended for periods of up to a few weeks to depository institutions in generally sound financial condition that
cannot obtain temporary funds in the financial markets at reasonable terms. Secondary credit is available to
depository institutions that are not eligible for primary credit. It is extended on a very short-term
basis, typically overnight, at a rate that is above the primary credit rate. Secondary credit is
available to meet backup liquidity needs when its use is consistent with a timely return to a
reliance on market sources of funding or the orderly resolution of a troubled institution.
Secondary credit may not be used to fund an expansion of the borrower’s assets. The Federal
Reserve's seasonal credit program is designed to assist small depository institutions in managing
significant seasonal swings in their loans and deposits. Seasonal credit is available to depository
institutions that can demonstrate a clear pattern of recurring intra-yearly swings in funding needs.
1-10
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Eligible institutions are usually located in agricultural or tourist areas. Under the seasonal
program, borrowers may obtain longer term funds from the discount window during periods of
seasonal need so that they can carry fewer liquid assets during the rest of the year and make more
funds available for local lending.
With the change, discount window loans to healthy banks would be priced at 1 percent
above the fed funds rate rather than below as it generally was in the period preceding January
2003. Loans to troubled banks would cost 1.5 percent above the fed funds rate. The changes
were not intended to change the Fed’s use of the discount window to implement monetary
policy, but significantly increase the discount rate while making it easier to get a discount
window loan. By increasing banks= use of the discount window as a source of funding, the Fed
hopes to reduce volatility in the fed funds market as well. The change also allows healthy banks
to borrow from the Fed regardless of the availability of private funds. Previously, the Fed
required borrowers to prove they could not get funds from the private sector, which put a stigma
on discount window borrowing. With the changes, the Fed will lend to all banks, but the subsidy
of below fed fund rate borrowing will be gone.
37.
Bank Three currently has $600 million in transaction deposits on its balance sheet. The
Federal Reserve has currently set the reserve requirement at 10 percent of transaction
deposits.
a.
Suppose the Federal Reserve decreases the reserve requirement to 8 percent. Show the
balance sheet of Bank Three and the Federal Reserve System just before and after the full
effect of the reserve requirement change. Assume Bank Three withdraws all excess
reserves and gives out loans, and that borrowers eventually return all of these funds to
Bank Three in the form of transaction deposits.
Panel A: Initial Balance Sheets
Federal Reserve Bank
Assets
Liabilities
Securities
$60m
Reserve accounts
$60m
--------------------------------------------------------------------------------------------Bank Three
Assets
Liabilities
Loans
$540m
Transaction deposits $600m
Reserve deposits
60m
at Fed
1-11
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Panel B: Balance Sheet after All Changes Resulting from Decrease in Reserve Requirement
Federal Reserve Bank
Assets
Liabilities
Securities
$60m
Reserve accounts
$60m
--------------------------------------------------------------------------------------------------Bank Three
Assets
Liabilities
Loans
$690m
Transaction deposits
$750m
($750m - $60m)
($60m x 0.08)
Reserve deposits
60m
at Fed
b.
Redo part (a) using a 12 percent reserve requirement.
Panel A: Initial Balance Sheets
Federal Reserve Bank
Assets
Liabilities
Securities
$60m
Reserve accounts
$60m
--------------------------------------------------------------------------------------------Bank Three
Assets
Liabilities
Loans
$540m
Transaction deposits $600m
Reserve deposits
60m
at Fed
Panel B: Balance Sheet after All Changes Resulting from Decrease in Reserve Requirement
Federal Reserve Bank
Assets
Liabilities
Securities
$60m
Reserve accounts
$60m
--------------------------------------------------------------------------------------------------Bank Three
Assets
Liabilities
Loans
$440m
Transaction deposits
$500m
($500m - $60m)
($60m x 0.12)
Reserve deposits
60m
at Fed
1-12
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
38.
Which of the monetary tools available to the Federal Reserve is most often used? Why?
The Federal Reserve uses mainly open market operations to implement its monetary policy.
Adjustments to the discount rate are rarely used because it is difficult for the Fed to predict
changes in bank discount window borrowing when the discount rate changes and because in
addition to their effect on the money supply, discount rate changes often have great effects on the
financial markets. Further, because changes in the reserve requirements can result in
unpredictable changes in the money base (depending on the amount of excess reserves held by
banks and the willingness of the public to redeposit funds at banks instead of holding cash (i.e.,
they have a preferred cash-deposit ratio)), the reserve requirement is rarely used by the Federal
Reserve as a monetary policy tool. The unpredictability comes from at least two sources. First,
there is uncertainty about whether banks will actually convert excess reserves (created from a
decrease in the reserve requirement) into new loans. Second, there is uncertainty about what
portion of the new loans will be returned to depository institutions in the form of transaction
deposits. Thus, like the discount window rate, the use of the reserve requirement as a monetary
policy tool increases the probability that a money base or interest rate target set by the FOMC
will not be achieved.
39.
Describe how expansionary activities conducted by the Federal Reserve impact credit
availability, the money supply, interest rates, and security prices. Do the same for
contractionary activities.
Expansionary Activities: We described three monetary policy tools that the Fed can use to
increase the money supply. These include open market purchases of securities, discount rate
decreases, and reserve requirement decreases. All else constant, when the Federal Reserve
purchases securities in the open market, reserve accounts of banks (and thus, the money base)
increase. When the Fed lowers the discount rate, this generally results in a lowering of interest
rates in the economy. Finally, a decrease in the reserve requirements, all else constant, results in
an increase in reserves for all banks. In two of the three cases (open market operations and
reserve requirement changes), an increase in reserves results in an increase in bank deposits and
assets. One immediate effect of this is that interest rates fall and security prices to rise. In the
third case (a discount rate change), the impact of a lowering of interest rates is more direct.
Lower interest rates encourage borrowing. Economic agents spend more when they can get
cheaper funds. Households, business, and governments are more likely to invest in fixed assets
(e.g., housing, plant, and equipment). Households increase their purchases of durable goods (e.g.,
automobiles, appliances). State and local government spending increases (e.g., new road
construction, school improvements). Finally, lower domestic interest rates relative to foreign
rates can result in a drop in the (foreign) exchange value of the dollar relative to other currencies.
As the dollar’s (foreign) exchange value drops, U.S. goods become relatively cheaper compared
to foreign goods. Eventually, U.S. exports increase. The increase in spending from all of these
market participants results in economic expansion, stimulates additional real production, and
may cause inflation to rise. Ideally, the expansionary policies of the Fed are meant to be
conducive to real economic expansion (economic growth, full employment, sustainable
international trade) without price inflation. Indeed, price stabilization can be viewed as the
primary objective of the Fed.
1-13
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Contractionary Activities: We also described three monetary policy tools that the Fed can use to
decrease the money supply. These include open market sales, discount rate increases, and reserve
requirement increases. All else constant, when the Federal Reserve sells securities in the open
market, reserve accounts of banks (and the money base) decrease. When the Fed raises the
discount rate, interest rates generally increase in the open market. Finally, an increase in the
reserve requirement, all else constant, results in a decrease in excess reserves for all banks. In all
three cases, interest rates will tend to rise. Higher interest rates discourage credit availability and
borrowing. Economic participants spend less when funds are expensive. Households, business,
and governments are less likely to invest in fixed assets. Households decrease their purchases of
durable goods. State and local government spending decreases. Finally, a decrease in domestic
interest rates relative to foreign rates may result in an increase in the (foreign) exchange value
(rate) of the dollar. As the dollar’s exchange rate increases, U.S. goods become relatively
expensive compared to foreign goods. Eventually, U.S. exports decrease. The decrease in
spending from all of these market participants results in economic contraction, (depressing
additional real production) and causes prices to fall (causing the rate of inflation to fall).
1-14
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Solutions for End-of-Chapter Questions and Problems: Chapter Seven
1.
What is the process of asset transformation performed by a financial institution? Why does
this process often lead to the creation of interest rate risk? What is interest rate risk?
Asset transformation by an FI involves purchasing primary assets and issuing secondary assets as
a source of funds. The primary securities purchased by the FI often have maturity and liquidity
characteristics that are different from the secondary securities issued by the FI. For example, a
bank buys medium- to long-term bonds and makes medium-term loans with funds raised by
issuing short-term deposits.
Interest rate risk occurs because the prices and reinvestment income characteristics of long-term
assets react differently to changes in market interest rates than the prices and interest expense
characteristics of short-term deposits. Interest rate risk is the risk incurred by an FI when the
maturities of its assets and liabilities are mismatched.
2.
What is refinancing risk? How is refinancing risk part of interest rate risk? If an FI funds
long-term fixed-rate assets with short-term liabilities, what will be the impact on earnings
of an increase in the rate of interest? A decrease in the rate of interest?
Refinancing risk is the risk that the cost of rolling over or reborrowing funds will rise above the
returns being earned on asset investments. This risk occurs when an FI is holding assets with
maturities greater than the maturities of its liabilities. For example, if a bank has a ten-year fixedrate loan funded by a 2-year time deposit, the bank faces a risk in that new deposits may only be
obtained, and the loans refinanced, at a higher rate in two years. These interest rate increases
would reduce net interest income. The bank would benefit if interest rates fall as the cost of
renewing the deposits would decrease, while the interest rate earned on the loan would not
change. In this case, net interest income would increase.
3.
What is reinvestment risk? How is reinvestment risk part of interest rate risk? If an FI funds
short-term assets with long-term liabilities, what will be the impact on earnings of a
decrease in the rate of interest? An increase in the rate of interest?
Reinvestment risk is the risk that the return on funds to be reinvested will fall below the cost of
funds. This risk occurs when an FI holds assets with maturities that are shorter than the
maturities of its liabilities. For example, if a bank has a two-year loan funded by a ten-year fixedrate time deposit, the bank faces the risk that it might be forced to lend or reinvest the money at
lower rates after two years, perhaps even below the deposit rates. Also, if the bank receives
periodic cash flows, such as coupon payments from a bond or monthly payments on a loan, these
periodic cash flows will also be reinvested at the new lower (or higher) interest rates. Besides the
effect on the income statement, reinvestment risk may cause realized yields on assets to differ
from the a priori expected yields.
1-15
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
4.
The sales literature of a mutual fund claims that the fund has no risk exposure since it
invests exclusively in federal government securities which are free of default risk. Is
this claim true? Explain why or why not.
Although the fund's asset portfolio is comprised of securities with no default risk, the securities
are exposed to interest rate risk. For example, if interest rates increase, the market value of the
fund's Treasury security portfolio will decrease. Further, if interest rates decrease, the realized
yield on these securities will be less than the expected rate of return because of reinvestment risk.
In either case, investors who liquidate their positions in the fund may sell at a Net Asset Value
(NAV) that is lower than the purchase price.
5.
How can interest rate risk adversely affect the economic or market value of an FI?
When interest rates increase (or decrease), the values of fixed-rate assets decrease (or increase)
because of the discounted present value of the cash flows. To the extent that the change in
market value of the assets differs from the change in market value of the liabilities, the difference
is realized in the economic or market value of the equity of the FI. For example, for most
depository institutions, an increase in interest rates will cause asset values to decrease more than
liability values. The difference will cause the market value, or share price, of equity to decrease.
6.
Consider an FI that issues $100 million of liabilities with one year to maturity to finance the
purchase of $100 million of assets with a two year maturity. Suppose that the cost of funds
(liabilities) for the FI is 5 percent per year and the interest return on the assets is 8 percent
per year.
a.
Calculate the FI’s profit spread and dollar value of profit in year 1.
Over the first year, the FI can lock in a profit spread of 3 percent (8 percent - 5 percent) by
borrowing short term (for one year) and lending long term (for two years). Thus, its profit is $3
million (0.03 x $100m.). Its profit for the second year, however, is uncertain. The risk always
exists, however, that interest rates will change between years 1 and 2.
b.
Calculate the profit spread and dollar value of profit in year 2, if the FI can refinance its
liabilities at 5 percent.
If the level of interest rates does not change, the FI will, receive a profit spread of 3 percent or $3
million profit for the second year as well.
c.
If interest rates rise and the FI can borrow new one-year liabilities at 9 percent in the
second year, calculate the FI’s profit spread and dollar value of profit in year 2.
1-16
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
In this case the FI’s profit spread in the second year is negative: 8 percent -9 percent = -1
percent, or the FI loses $1 million (-0.01 x 100m.). The positive spread earned in the first year by
the FI from holding assets with a longer maturity than its liabilities is offset by a negative spread
in the second year. As a result, when an FI holds longer-term assets relative to liabilities, it
potentially exposes itself to the interest rate risk that the cost of refinancing can be more than the
return earned on asset investments.
d.
If interest rates fall and the FI can borrow new one-year liabilities at 3 percent in the
second year, calculate the FI’s profit spread and dollar value of profit in year 2.
If interest rates rise and the FI can borrow new one-year liabilities at 3 percent in the second
year, its profit spread in the second year is positive: 8 percent - 3 percent = 5 percent, or the FI
gains $5 million (0.05 x 100m.). The positive spread earned in the first year by the FI from
holding assets with a longer maturity than its liabilities is even greater in the second year.
7.
Consider an FI that issues $200 million of liabilities with two years to maturity to finance
the purchase of $200 million of assets with a one year maturity. Suppose that the cost of
funds (liabilities) for the FI is 5 percent per year and the interest return on the assets is 9
percent per year.
a.
Calculate the FI’s profit spread and dollar value of profit in year 1.
Over the first year, the FI can lock in a profit spread of 4 percent (9 percent - 5 percent) by
borrowing long term (for two years) and lending short term (for one year). Thus, its profit is $8
million (0.04 x $200m.). In this case, the FI is also exposed to an interest rate risk; by holding
shorter term assets relative to liabilities, it faces uncertainty about the interest rate at which it can
reinvest funds in the second period.
b.
Calculate the profit spread and dollar value of profit in year 2, if the FI can reinvest its
assets at 9 percent.
If the level of interest rates does not change, the FI will receive a profit spread of 4 percent or $8
million profit for the second year as well.
c.
If interest rates fall and the FI can invest in one-year assets at 6 percent in the second
year, calculate the FI’s profit spread and dollar value of profit in year 2.
If in the second year interest rates on $200 million invested in new one-year assets decreases to 6
percent, the FI’s profit spread falls to 1 percent (6 percent - 5 percent), or the FI profit falls to $2
million (0.01 x $200m.). As a result, when an FI holds longer term liabilities relative to assets, it
potentially exposes itself to the interest rate risk that borrowed funds can only be reinvested at a
rate lower than their cost.
1-17
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
d.
If interest rates rise and the FI can invest in one-year assets at 11 percent in the second
year, calculate the FI’s profit spread and dollar value of profit in year 2.
If in the second year interest rates on $200 million invested in new one-year assets increases to
11 percent, the FI’s profit spread rises to 6 percent (11 percent - 5 percent), or the FI profit
increases to $12 million (0.06 x $200m.).
8.
A financial institution has the following market value balance sheet structure:
Assets
Cash
Bond
Total assets
Liabilities and Equity
Certificate of deposit
Equity
Total liabilities and equity
$1,000
$10,000
$11,000
$10,000
$1,000
$11,000
a. The bond has a 10-year maturity, a fixed-rate coupon of 10 percent paid at the end of
each year, and a par value of $10,000. The certificate of deposit has a 1-year maturity
and a 6 percent fixed rate of interest. The FI expects no additional asset growth. What
will be the net interest income (NII) at the end of the first year? Note: Net interest
income equals interest income minus interest expense.
Interest income
Interest expense
Net interest income (NII)
$1,000
600
$400
$10,000 x 0.10
$10,000 x 0.06
b.
If at the end of year 1 market interest rates have increased 100 basis points (1
percent), what will be the net interest income for the second year? Is the change in NII
caused by reinvestment risk or refinancing risk?
Interest income
Interest expense
Net interest income (NII)
$1,000
700
$300
$10,000 x 0.10
$10,000 x 0.07
The decrease in net interest income is caused by the increase in financing cost without a
corresponding increase in the earnings rate. Thus, the change in NII is caused by refinancing
risk. The increase in market interest rates does not affect the interest income because the bond
has a fixed-rate coupon for ten years. Note: this answer makes no assumption about reinvesting
the first year’s interest income at the new higher rate.
c. Assuming that market interest rates increase 1 percent, the bond will have a value of
$9,446 at the end of year 1. What will be the market value of the equity for the FI? Assume
that all of the NII in part (a) is used to cover operating expenses or is distributed as
dividends.
1-18
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Cash
Bond
Total assets
$1,000
$9,446
$10,446
Certificate of deposit
$10,000
Equity
$ 446
Total liabilities and equity $10,446
d.If market interest rates had decreased 100 basis points by the end of year 1, would the
market value of equity be higher or lower than $1,000? Why?
The market value of the equity would be higher ($1,600) because the value of the bond
would be higher ($10,600) and the value of the CD would remain unchanged.
e. What factors have caused the changes in operating performance and market value for this
firm?
The operating performance has been affected by changes in market interest rates that
have caused corresponding changes in interest income, interest expense, and net interest income.
These specific changes have occurred because of the unique maturities of the fixed-rate assets
and variable-rate liabilities. Similarly, the economic or market value of the firm has changed
because of the effect of the changing rates on the market value of the bond.
9.
How does a policy of matching the maturities of assets and liabilities work (a) to minimize
interest rate risk and (b) against the asset-transformation function of FIs?
A policy of maturity matching will allow changes in market interest rates to have approximately
the same effect on both interest income and interest expense. An increase in rates will tend to
increase both income and expense, and a decrease in rates will tend to decrease both income and
expense. The changes in income and expense may not be equal because of different cash flow
characteristics of the assets and liabilities. The asset-transformation function of an FI involves
investing short-term liabilities in long-term assets. Maturity matching clearly works against
successful implementation of this process.
10.
Corporate bonds usually pay interest semiannually. If a company decided to change from
semiannual to annual interest payments, how would this affect the bond’s interest rate
risk?
The interest rate risk would increase as the bonds are being paid back more slowly and therefore
the cash flows would be exposed to interest rate changes for a longer period of time. Thus, any
change in interest rates would cause a larger inverse change in the value of the bonds.
11.
Two 10-year bonds are being considered for an investment that may have to be liquidated
before the maturity of the bonds. The first bond is a 10-year premium bond with a coupon
rate higher than its required rate of return, and the second bond is a zero-coupon bond that
pays only a lump-sum payment after 10 years with no interest over its life. Which bond
would have more interest rate risk? That is, which bond’s price would change by a larger
amount for a given change in interest rates? Explain your answer.
1-19
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
The zero-coupon bond would have more interest rate risk. Because the entire cash flow is not
received until the bond matures, the entire cash flow is exposed to interest rate changes over the
entire life of the bond. The cash flows of the coupon-paying bond are returned with periodic
regularity, thus allowing less exposure to interest rate changes. In effect, some of the cash flows
may be received before interest rates change.
12.
Consider again the two bonds in problem 11. If the investment goal is to leave the assets
untouched until maturity, such as for a child’s education or for one’s retirement, which
of the two bonds has more interest rate risk? What is the source of this risk?
In this case the coupon-paying bond has more interest rate risk. The zero-coupon bond will
generate exactly the expected return at the time of purchase because no interim cash flows will
be realized. Thus, the zero-coupon bond has no reinvestment risk. The coupon-paying bond faces
reinvestment risk each time a coupon payment is received. The results of reinvestment will be
beneficial if interest rates rise, but decreases in interest rate will cause the realized return to be
less than the expected return.
13.
A money market mutual fund bought $1 million of two-year Treasury notes six months
ago. During this time, the value of the securities has increased, but for tax reasons the
mutual fund wants to postpone any sale for two more months. What type of risk does
the mutual fund face for the next two months?
The mutual fund faces the risk of interest rates rising and the value of the securities falling.
14.
A bank invested $50 million in a two-year asset paying 10 percent interest per year and
simultaneously issued a $50 million, one-year liability paying 8 percent interest per
year. The liability will be rolled over after one year at the current market rate. What
will be the bank’s net interest income if at the end of the first year all interest rates have
increased by 1 percent (100 basis points)?
Net interest income is not affected in the first year, but NII will decrease in the second year.
Interest income
Interest expense
Net interest income
Year 1
$5,000,000
$4,000,000
$1,000,000
Year 2
$5,000,000
$4,500,000
$500,000
The bank’s net interest income decreases in year 2 by $500,000 as the result of refinancing risk.
1-20
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
15.
What is credit risk? Which types of FIs are more susceptible to this type of risk? Why?
Credit risk is the risk that promised cash flows from loans and securities held by FIs may not be
paid in full. FIs that lend money for long periods of time, whether as loans or by buying bonds,
are more susceptible to this risk than those FIs that have short investment horizons. For example,
life insurance companies and depository institutions generally must wait a longer time for returns
to be realized than money market mutual funds and property-casualty insurance companies.
16.
What is the difference between firm-specific credit risk and systematic credit risk? How
can an FI alleviate firm-specific credit risk?
Firm-specific credit risk refers to the likelihood that a single asset may deteriorate in quality,
while systematic credit risk involves macroeconomic factors that may increase the default risk of
all firms in the economy. Thus, if S&P lowers its rating on IBM stock and if an investor is
holding only this particular stock, he may face significant losses as a result of this downgrading.
However, portfolio theory in finance has shown that firm-specific credit risk can be diversified
away if a portfolio of well-diversified stocks is held. Similarly, if an FI holds a well-diversified
portfolio of assets, the FI will face only systematic credit risk that will be affected by the general
condition of the economy. The risks specific to any one customer will not be a significant portion
of the FIs overall credit risk.
17.
Many banks and savings institutions that failed in the 1980s had made loans to oil
companies in Louisiana, Texas, and Oklahoma. When oil prices fell, these companies,
the regional economy, and the banks and savings institutions all experienced financial
problems. What types of risk were inherent in the loans that were made by these banks
and savings institutions?
The loans in question involved credit risk. Although the geographic area covered a large region
of the United States, the risk more closely characterized firm-specific risk than systematic risk.
More extensive diversification by the FIs to other types of industries would have decreased the
amount of financial hardship these institutions had to endure.
18.
What is liquidity risk? What routine operating factors allow FIs to deal with this risk in
times of normal economic activity? What market reality can create severe financial
difficulty for an FI in times of extreme liquidity crises?
Liquidity risk is the risk that a sudden surge in liability withdrawals may require an FI to
liquidate assets in a very short period of time and at less than fair market prices. In times of
normal economic activity, depository institutions meet cash withdrawals by accepting new
deposits and borrowing funds in the short-term money markets. However, in times of harsh
liquidity crises, the FI may need to sell assets at significant losses in order to generate cash
quickly.
1-21
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
19.
Consider the simple FI balance sheet below (in millions of dollars).
Before the Withdrawal
Assets
Liabilities/Equity
Cash assets
$ 20 Deposit
$150
Nonliquid
assets
155 Equity
25
$175
$175
Suppose that depositors unexpectedly withdraw $50 million in deposits and the FI receives
no new deposits to replace them. Assume that the FI cannot borrow any more funds in the
short-term money markets, and because it cannot wait to get better prices for its assets in
the future (as it needs the cash now to meet immediate depositor withdrawals), the FI has to
sell any nonliquid assets at 75 cents on the dollar. Show the FI’s balance sheet after
adjustments are made for the $50 million of deposit withdrawals.
.
Before the Withdrawal
Assets
Liabilities/Equity
Cash assets $ 20 Deposit
$150
Nonliquid
assets
155
Equity
25
$175
$175
After the Withdrawal
Assets
Liabilities/Equity
Cash assets $ 0 Deposits
$100
Nonliquid
assets
115 Equity
15
$115
$115
To meet these deposit withdrawals, the FI first uses the $20 million it has in cash assets and then
seeks to sell some of its nonliquid assets to raise an additional $30 million in cash. To cover the
remaining $30 million in deposit withdrawals, the FI must sell $40 million in nonliquid assets,
incurring a loss of $10million from the face value of those assets. The FI must then write off any
such losses against its capital or equity funds. Since its capital was only $10 million before the
deposit withdrawal, the loss on the fire-sale of assets of $5 million leaves the FI with $5 million.
20.
What two factors provide potential benefits to FIs that expand their asset holdings and
liability funding sources beyond their domestic borders?
FIs can realize operational and financial benefits from direct foreign investment and foreign
portfolio investments in two ways. First, the technologies and firms across various economies
differ from each other in terms of growth rates, extent of development, etc. Second, exchange
rate changes may not be perfectly correlated across various economies.
1-22
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
21.
What is foreign exchange risk? What does it mean for an FI to be net long in foreign
assets? What does it mean for an FI to be net short in foreign assets? In each case, what
must happen to the foreign exchange rate to cause the FI to suffer losses?
Foreign exchange risk is the risk that exchange rate changes can affect the value of an FI’s assets
and liabilities denominated in non-domestic currencies. An FI is net long in foreign assets when
the foreign currency-denominated assets exceed the foreign currency-denominated liabilities. In
this case, an FI will suffer potential losses if the domestic currency strengthens relative to the
foreign currency when repayment of the assets will occur in the foreign currency. An FI is net
short in foreign assets when the foreign currency-denominated liabilities exceed the foreign
currency-denominated assets. In this case, an FI will suffer potential losses if the domestic
currency weakens relative to the foreign currency when repayment of the liabilities will occur in
the domestic currency.
22.
If the Swiss franc is expected to depreciate in the near future, would a U.S.-based FI in
Bern City prefer to be net long or net short in its asset positions? Discuss.
The U.S. FI would prefer to be net short (liabilities greater than assets) in its asset position. The
depreciation of the Swiss franc relative to the dollar means that the U.S. FI would pay back the
net liability position with fewer dollars. In other words, the decrease in the foreign assets in
dollar value after conversion will be less than the decrease in the value of the foreign liabilities in
dollar value after conversion.
23.
If international capital markets are well integrated and operate efficiently, will FIs be
exposed to foreign exchange risk? What are the sources of foreign exchange risk for
FIs?
If there are no real or financial barriers to international capital and goods flows, FIs can eliminate
all foreign exchange rate risk exposure. Sources of foreign exchange risk exposure include
international differentials in real prices, cross-country differences in the real rate of interest
(perhaps, as a result of differential rates of time preference), regulatory and government
intervention, and restrictions on capital movements, trade barriers, and tariffs.
24.
If an FI has the same amount of foreign assets and foreign liabilities in the same currency,
has that FI necessarily reduced the risk involved in these international transactions to
zero? Explain.
Matching the size of the foreign currency book will not eliminate the risk of the international
transactions if the maturities of the assets and liabilities are mismatched. To the extent that the
assets and liabilities are mismatched in terms of maturities, or more importantly durations, the FI
will be exposed to foreign interest rate risk.
1-23
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
25.
A U.S. insurance company invests $1,000,000 in a private placement of British bonds.
Each bond pays £300 in interest per year for 20 years. If the current exchange rate is
£1.564/$, what is the nature of the insurance company’s exchange rate risk?
Specifically, what type of exchange rate movement concerns this insurance company?
In this case, the insurance company is worried about the value of the £ falling. If this happens,
the insurance company would be able to buy fewer dollars with the £s received. This would
happen if the exchange rate rose to say £1.68/$ since now it would take more £s to buy one
dollar, but the bond contract is paying a fixed amount of interest and principal.
26.
Assume that a bank has assets located in London worth £150 million on which it earns an
average of 8 percent per year. The bank has £100 million in liabilities on which it pays
an average of 6 percent per year. The current spot exchange rate is £1.50/$.
a. If the exchange rate at the end of the year is £2.00/$, will the dollar have appreciated or
devalued against the mark?
The dollar will have appreciated, or conversely, the £ will have depreciated.
b. Given the change in the exchange rate, what is the effect in dollars on the net interest
income from the foreign assets and liabilities? Note: The net interest income is interest
income minus interest expense.
Measurement in £
Interest received
Interest paid
Net interest income
=
=
=
£12 million
£6 million
£6 million
Measurement in $ before £ devaluation
Interest received in dollars
=
Interest paid in dollars
=
Net interest income
=
$8 million
$4 million
$4 million
Measurement in $ after £ devaluation
Interest received in dollars
=
Interest paid in dollars
=
Net interest income
=
$6 million
$3 million
$3 million
Thus, net interest income decreases by $1 million as a result of foreign exchange risk.
c. What is the effect of the exchange rate change on the value of assets and liabilities in
dollars?
1-24
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
The assets were worth $100 million (£150m/1.50) before depreciation, but after devaluation they
are worth only $75 million. The liabilities were worth $66.67 million before depreciation, but
they are worth only $50 million after devaluation. Since assets decline by $25 million and
liabilities by $16.67 million, net worth decreases by $8.33 million using spot rates at the end of
the year.
27.
Six months ago, Qualitybank, issued a $100 million, one-year maturity CD denominated in
euros. On the same date, $60 million was invested in a €-denominated loan and $40
million was invested in a U.S. Treasury bill. The exchange rate on this date was
€1.5675/$. Assume no repayment of principal and an exchange rate today of €1.2540/$.
a. What is the current value of the CD principal (in euros and dollars)?
The current principal value on the CD is €156.75m and $125m (€156.75m/1.2540).
b. What is the current value of the euro-denominated loan principal (in euros and
dollars)?
The current principal value on the loan is €94.050m and $75m (€94.050m/1.2540).
c. What is the current value of the U.S. Treasury bill (in euros and dollars)?
The current principal value on the U.S. Treasury bill is $40m and €50.16m ($40m x 1.2540). For
a U.S. bank this does not change in value.
d. What is Qualitybank’s profit/loss from this transaction (in euros and dollars)?
Qualitybank's loss is €12.540m (($40m x 1.5675) - €50.16m) or $10m (($125m - $100m) –
($75m - $60m)).
Solution matrix for problem 27:
At Issue Date:
Dollar Transaction Values (in millions)
Euro
Euro
Loan
$60
CD
$100
U.S T-bill $40
$100
$100
Euro Transaction Values (in millions)
Euro
Euro
Loan
€94.050 CD
U.S. T-bill
€62.700
€156.750
€156.75
€156.75
1-25
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Today:
Dollar Transaction Values (in millions)
Euro
Euro
Loan
$75
CD
$125
U.S. T-bill $40
$115
$125
Loss
-$ 10
28.
€Transaction Values (in millions)
Euro
Euro
Loan
€94.050 CD
U.S. T-bill
€50.160
€144.210
Loss
€156.75
€156.75
-€12.540
Suppose you purchase a 10-year, AAA-rated Swiss bond for par that is paying an annual
coupon of 6 percent. The bond has a face value of 1,000 Swiss francs (SF). The spot rate at
the time of purchase is SF1.15/$. At the end of the year, the bond is downgraded to AA and
the yield increases to 8 percent. In addition, the SF appreciates to SF1.05/$.
a. What is the loss or gain to a Swiss investor who holds this bond for a year? What portion
of this loss or gain is due to foreign exchange risk? What portion is due to interest rate risk?
Beginning of the Year
Price of Bond = SF 60 * PVAi = 6, n =10 + SF1,000 * PV i = 6, n =10 = SF1,000
End of the Year
Price of Bond = SF 60 * PVAi =8, n =9 + SF1,000 * PV i =8, n =9 = SF 875 .06
The loss to the Swiss investor (SF875.06 + SF60 - SF1,000)/SF1,000 = -6.49 percent. The entire
amount of the loss is due to interest rate risk.
b. What is the loss or gain to a U.S. investor who holds this bond for a year? What portion
of this loss or gain is due to foreign exchange risk? What portion is due to interest rate
risk?
Price at beginning of year
= SF1,000/SF1.15 = $869.565
Price at end of year
= SF875.06/SF1.05 = $833.393
Interest received at end of year = SF60/SF1.05
= $57.143
Gain to U.S. investor = ($833.393 + $57.143 - $869.565)/$869.565 = +2.41%.
The U.S. investor had an equivalent loss of 6.49 percent ([((SF875.06 + SF60)/SF1.15) $869.565]/$869.565) from interest rate risk, but had a gain of 8.90 percent (2.41% - (-6.49%)) from
foreign exchange risk.
1-26
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
29.
What is country or sovereign risk? What remedy does an FI realistically have in the event
of a collapsing country or currency?
Country risk is the risk that repayments to foreign lenders or investors may be interrupted
because of restrictions, intervention, or interference from foreign governments. A lender FI has
very little recourse in this situation unless the FI is able to restructure the debt or demonstrate
influence over the future supply of funds to the country in question. This influence likely would
involve significant working relationships with the IMF and the World Bank.
30.
What is market risk? How does this risk affect the operating performance of financial
institutions? What actions can be taken by an FI’s management to minimize the effects of
this risk?
Market risk is the risk incurred from assets and liabilities in an FI’s trading book due to changes
in interest rates, exchange rates, and other prices. Market risk affects any firm that trades assets
and liabilities. The risk can surface because of changes in interest rates, exchange rates, or any
other prices of financial assets that are traded rather than held on the balance sheet. Market risk
can be minimized by using appropriate hedging techniques such as futures, options, and swaps,
and by implementing controls that limit the amount of exposure taken by market makers.
31.
What is the nature of an off-balance-sheet activity? How does an FI benefit from such
activities? Identify the various risks that these activities generate for an FI, and explain
how these risks can create varying degrees of financial stress for the FI at a later time.
Off-balance-sheet activities are contingent commitments to undertake future on-balance-sheet
investments. The usual benefit of committing to a future activity is the generation of immediate
fee income without the normal recognition of the activity on the balance sheet. As such, these
contingent investments may be exposed to credit risk (if there is some default risk probability),
interest rate risk (if there is some price and/or interest rate sensitivity), and foreign exchange rate
risk (if there is a cross currency commitment).
32.
What is technology risk? What is the difference between economies of scale and economies
of scope? How can these economies create benefits for an FI? How can these economies
prove harmful to an FI?
Technology risk occurs when investment in new technologies does not generate the cost savings
expected in the production and expansion of financial services. Economies of scale occur when
the average cost of production decreases with the production of or an expansion in the amount of
financial services provided. Economies of scope occur when an FI is able to lower overall costs
by producing new products with inputs similar to those used for other products. In financial
service industries, the use of data from existing customer databases to assist in providing new
service products is an example of economies of scope. Failure to produce the perceived synergies
or costs savings can result in major losses in competitive efficiency of an FI and, ultimately, in
an FI’s long-term failure.
1-27
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
33.
What is the difference between technology risk and operational risk? How does
internationalizing the payments system among banks increase operational risk?
Technology risk is the risk incurred by an FI when its technological investments do not produce
anticipated cost savings. For example, if an FI spends millions on upgrading its computer
systems, but is not able to recapture its costs because its productivity has not increased
commensurately or because the technology has already become obsolete, it has invested in a
negative NPV investment in technology.
Operational risk refers to the risk that existing technology, auditing, monitoring, and other
support systems may malfunction or break down. This includes the failure of the back-room
support operations necessary to maintain the smooth functioning of the operation of FIs,
including settlement, clearing, and other transaction-related activities. For example,
computerized payment systems such as Fedwire, CHIPS, and SWIFT allow modern financial
intermediaries to transfer funds, securities, and messages across the world in seconds of real
time. This creates the opportunity to engage in global financial transactions over a short time in
an extremely cost-efficient manner. However, the interdependence of such transactions also
creates settlement risk. Typically, any given transaction leads to other transactions as funds and
securities trade across the globe. If there is either a transmittal failure or high-tech fraud affecting
any one of the intermediate transactions, this could cause an unraveling of all subsequent
transactions.
34.
Why can insolvency risk be classified as a consequence or outcome of any or all of the
other types of risks?
Insolvency risk is the risk that an FI may not have enough capital to offset a sudden decline in
the value of its assets. This risk involves the shortfall of capital in times when the operating
performance of the institution generates accounting losses. These losses may be the result of one
or more of interest rate, credit, liquidity, sovereign, foreign exchange, market, off-balance-sheet,
and technological risks.
1-28
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
35.
Discuss the interrelationships among the different sources of FI risk exposure. Why would
the construction of an FI risk management model to measure and manage only one type of
risk be incomplete?
Measuring each source of FI risk exposure individually creates the false impression that they are
independent of each other. For example, the interest rate risk exposure of an FI could be reduced
by requiring customers to take on more interest rate risk exposure through the use of floating-rate
products. However, this reduction in FI risk may be obtained only at the possible expense of
increased credit risk. That is, customers experiencing losses resulting from unanticipated interest
rate changes may be forced into insolvency, thereby increasing the FI’s default risk. Similarly,
off-balance-sheet risk encompasses several risks since off-balance-sheet contingent contracts
typically have credit risk and interest rate risk as well as currency risk. Moreover, the failure of
collection and payment systems may lead corporate customers into bankruptcy. Thus, technology
risk may influence the credit risk of FIs. As a result of these interdependencies, FIs have focused
on developing sophisticated models that attempt to measure all of the risks faced by the FI at any
point in time.
36.
Characterize the risk exposure(s) of the following FI transactions by choosing one or more
of the risk types listed below:
a. Interest rate risk
b. Credit risk
c. Off-balance-sheet risk
(1)
(2)
(3)
(4)
(5)
(6)
(7)
37.
d. Technology risk
e. Foreign exchange rate risk
f. Country or sovereign risk
A bank finances a $10 million, six-year fixed-rate commercial loan by selling oneyear certificates of deposit.
a, b
An insurance company invests its policy premiums in a long-term municipal bond
portfolio.
a, b
A French bank sells two-year fixed-rate notes to finance a two-year fixed-rate loan to
a British entrepreneur.
b, e, f
A Japanese bank acquires an Austrian bank to facilitate clearing operations.
a, b, c, d, e, f
A mutual fund completely hedges its interest rate risk exposure using forward
contingent contracts.
b, c
A bond dealer uses his own equity to buy Mexican debt on the less-developed country
(LDC) bond market.
a, b, e, f
A securities firm sells a package of mortgage loans as mortgage-backed securities.
a, b, c
Consider these four types of risks: credit, foreign exchange, market, and sovereign. These
risks can be separated into two pairs of risk types in which each pair consists of two
related risk types, with one being a subset of the other. How would you pair off the risk
types, and which risk type could be considered a subset of the other type in the pair?
1-29
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Credit risk and sovereign risk comprise one pair, while FX and market risk make up the other.
Sovereign risk is a type of credit risk in that one reason why a loan may default is because of
political upheaval in the country in which the borrower resides. FX risk is a type of market risk
in that one reason why the market value of an outstanding loan or security may change is due to
a change in exchange rates.
1-30
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Chapter Eight
Interest Rate Risk I
Chapter Outline
Introduction
The Level and Movement of Interest Rates
The Repricing Model
• Rate-Sensitive Assets
• Rate-Sensitive Liabilities
• Equal Changes in Rates on RSAs and RSLs
• Unequal Changes in Rates on RSAs and RSLs
Weaknesses of the Repricing Model
• Market Value Effects
• Overaggregation
• The Problem of Runoffs
• Cash Flows from Off-Balance Sheet Activities
Summary
Appendix 8A: The Maturity Model
• The Maturity Model with a Portfolio of Assets and Liabilities
Weaknesses of the Maturity Model
Appendix 8B: Term Structure of Interest Rates
• Unbiased Expectations Theory
• Liquidity Premium Theory
• Market Segmentation Theory
• Forecasting Interest Rates
1-31
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Solutions for End-of-Chapter Questions and Problems: Chapter Eight
1.
How do the supply of and demand for loanable funds, together, determine interest rates?
Changes in underlying factors that determine the demand and supply of loanable funds cause
continuous shifts in the supply and/or demand curves for loanable funds. Market forces will react
to the resulting disequilibrium with a change in the equilibrium interest rate and quantity of
funds traded in that market. Figure 8-2(a) shows the effects of an increase in the supply curve for
loanable funds, from SS to SS , (and the resulting decrease in the equilibrium interest rate, from
i* to i* ), while Figure 8-2(b) shows the effects of an increase in the demand curve for loanable
funds, from DD to DD , (and the resulting increase in the equilibrium interest rate, from i* to
i* ).
2.
How do monetary policy actions made by the Federal Reserve impact interest rates?
Through its daily open market operations, such as buying and selling Treasury bonds and
Treasury bills, the Fed seeks to influence the money supply, inflation, and the level of interest
rates. When the Fed finds it necessary to slow down the economy, it tightens monetary policy by
raising interest rates. The normal result is a decrease in business and household spending
(especially that financed by credit or borrowing). Conversely, if business and household
spending decline to the extent that the Fed finds it necessary to stimulate the economy it allows
interest rates to fall (an expansionary monetary policy). The drop in rates promotes borrowing
and spending.
3.
How has the increased level of financial market integration affected interest rates?
Increased financial market integration, or globalization, increases the speed with which interest
rate changes and volatility are transmitted among countries. The result of this quickening of
global economic adjustment is to increase the difficulty and uncertainty faced by the Federal
Reserve as it attempts to manage economic activity within the U.S. Further, because FIs have
become increasingly more global in their activities, any change in interest rate levels or volatility
caused by Federal Reserve actions more quickly creates additional interest rate risk issues for
these companies.
4.
What is the repricing gap? In using this model to evaluate interest rate risk, what is meant
by rate sensitivity? On what financial performance variable does the repricing model
focus? Explain.
The repricing gap is a measure of the difference between the dollar value of assets that will
reprice and the dollar value of liabilities that will reprice within a specific time period, where
repricing can be the result of a roll over of an asset or liability (e.g., a loan is paid off at or prior
to maturity and the funds are used to issue a new loan at current market rates) or because the
asset or liability is a variable rate instrument (e.g., a variable rate mortgage whose interest rate is
reset every quarter based on movements in a prime rate). Rate sensitivity represents the time
interval where repricing can occur. The model focuses on the potential changes in the net interest
1-32
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
income variable. In effect, if interest rates change, interest income and interest expense will
change as the various assets and liabilities are repriced, that is, receive new interest rates.
5.
What is a maturity bucket in the repricing model? Why is the length of time selected for
repricing assets and liabilities important when using the repricing model?
The maturity bucket is the time window over which the dollar amounts of assets and liabilities
are measured. The length of the repricing period determines which of the securities in a portfolio
are rate-sensitive. The longer the repricing period, the more securities either mature or need to be
repriced, and, therefore, the more the interest rate exposure. An excessively short repricing
period omits consideration of the interest rate risk exposure of assets and liabilities are that
repriced in the period immediately following the end of the repricing period. That is, it
understates the rate sensitivity of the balance sheet. An excessively long repricing period
includes many securities that are repriced at different times within the repricing period, thereby
overstating the rate sensitivity of the balance sheet.
6.
What is the CGAP effect? According to the CGAP effect, what is the relation between
changes in interest rates and changes in net interest income when CGAP is positive? When
CGAP is negative?
The CGAP effect describes the relations between changes in interest rates and changes in net
interest income. According to the CGAP effect, when CGAP is positive the change in NII is
positively related to the change in interest rates. Thus, an FI would want its CGAP to be positive
when interest rates are expected to rise. According to the CGAP effect, when CGAP is negative
the change in NII is negatively related to the change in interest rates. Thus, an FI would want its
CGAP to be negative when interest rates are expected to fall.
7.
If a bank manager was quite certain that interest rates were going to rise within the next six
months, how should the bank manager adjust the bank’s six-month repricing gap to take
advantage of this anticipated rise? What if the manger believed rates would fall in the next
six months.
When interest rates are expected to rise, a bank should set its repricing gap to a positive position.
In this case, as rates rise, interest income will rise by more than interest expense. The result is an
increase in net interest income. When interest rates are expected to fall, a bank should set its
repricing gap to a negative position. In this case, as rates fall, interest income will fall by less
than interest expense. The result is an increase in net interest income.
8.
Consider the following balance sheet positions for a depository institution:
•
Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million
•
Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million
•
Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million
1-33
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
a. Calculate the repricing gap and the impact on net interest income of a 1 percent
increase in interest rates for each position.
•
Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million.
Repricing gap = RSA - RSL = $200 - $100 million = +$100 million.
NII = ($100 million)(.01) = +$1.0 million, or $1,000,000.
•
Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million.
Repricing gap = RSA - RSL = $100 - $150 million = -$50 million.
NII = (-$50 million)(.01) = -$0.5 million, or -$500,000.
•
Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million.
Repricing gap = RSA - RSL = $150 - $140 million = +$10 million.
NII = ($10 million)(.01) = +$0.1 million, or $100,000.
b.
Calculate the impact on net interest income on each of the above situations assuming a 1
percent decrease in interest rates.
•
NII = ($100 million)(-.01) = -$1.0 million, or -$1,000,000.
•
NII = (-$50 million)(-.01) = +$0.5 million, or $500,000.
•
NII = ($10 million)(-.01) = -$0.1 million, or -$100,000.
c. What conclusion can you draw about the repricing model from these results?
The FIs in parts (1) and (3) are exposed to interest rate declines (positive repricing gap)
while the FI in part (2) is exposed to interest rate increases. The FI in part (3) has the
lowest interest rate risk exposure since the absolute value of the repricing gap is the lowest,
while the opposite is true for part (1).
9.
What are the reasons for not including demand deposits as rate-sensitive liabilities in the
repricing analysis for a commercial bank? What is the subtle, but potentially strong, reason
for including demand deposits in the total of rate-sensitive liabilities? Can the same
argument be made for passbook savings accounts?
The regulatory rate available on demand deposit accounts is zero. Although many banks are able
to offer NOW accounts on which interest can be paid, this interest rate seldom is changed and
thus the accounts are not really sensitive. However, demand deposit accounts do pay implicit
interest in the form of not charging fully for checking and other services. Further, when market
interest rates rise, customers draw down their DDAs, which may cause the bank to use higher
cost sources of funds. The same or similar arguments can be made for passbook savings
accounts.
1-34
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
10. What is the gap ratio? What is the value of this ratio to interest rate risk managers and regulators?
The gap ratio is the ratio of the cumulative gap position to the total assets of the bank. The
cumulative gap position is the sum of the individual gaps over several time buckets. The value of
this ratio is that it tells the direction of the interest rate exposure and the scale of that exposure
relative to the size of the bank.
11.
Which of the following assets or liabilities fit the one-year rate or repricing sensitivity test?
3-month U.S. Treasury bills
1-year U.S. Treasury notes
20-year U.S. Treasury bonds
20-year floating-rate corporate bonds with annual repricing
30-year floating-rate mortgages with repricing every two years
30-year floating-rate mortgages with repricing every six months
Overnight fed funds
9-month fixed rate CDs
1-year fixed-rate CDs
5-year floating-rate CDs with annual repricing
Common stock
12.
Yes
Yes
No
Yes
No
Yes
Yes
Yes
Yes
Yes
No
What is the spread effect?
The spread effect is the effect that a change in the spread between rates on RSAs and RSLs has
on net interest income as interest rates change. The spread effect is such that, regardless of the
direction of the change in interest rates, a positive relation occurs between changes in the spread
and changes in NII. Whenever the spread increases (decreases), NII increases (decreases).
13.
A bank manager is quite certain that interest rates are going to fall within the next six
months, but the fall will be different on RSAs versus RSLs. How should the bank manager
adjust the bank’s six-month repricing gap and spread to take advantage of this anticipated
rise? What if the manger believed rates would rise in the next six months.
When interest rates are expected to fall, a bank should set its repricing gap to a negative position.
Further, the manager would want to increase the spread between the return on RSAs and RSLs.
In this case, as rates fall, interest income will fall by less than interest expense. The result is an
increase in net interest income. When interest rates are expected to rise, a bank should set its
repricing gap to a positive position. Again, the manager would want to increase the spread
between the return on RSAs and RSLs. In this case, as rates rise, interest income will rise by
more than interest expense. The result is an increase in net interest income.
14.
Consider the following balance sheet for WatchoverU Savings, Inc. (in millions):
Assets
Floating-rate mortgages
(currently 10% annually)
Liabilities and Equity
1-year time deposits
(currently 6% annually)
$50
$70
1-35
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
30-year fixed-rate loans
(currently 7% annually)
Total Assets
3-year time deposits
(currently 7% annually)
Equity
Total Liabilities & Equity
$50
$100
$20
$10
$100
a. What is WatchoverU’s expected net interest income at year-end?
Current expected interest income: $50m(0.10) + $50m(0.07) = $8.5m.
Expected interest expense: $70m(0.06) - $20m(0.07) = $5.6m.
Expected net interest income:
$8.5m - $5.6m = $2.9m.
b. What will net interest income be at year-end if interest rates rise by 2 percent?
After the 200 basis point interest rate increase, net interest income declines to:
50(0.12) + 50(0.07) - 70(0.08) - 20(.07) = $9.5m - $7.0m = $2.5m, a decline of $0.4m.
c.
Using the cumulative repricing gap model, what is the expected net interest income for a 2
percent increase in interest rates?
Wachovia’s' repricing or funding gap is $50m - $70m = -$20m. The change in net interest income using the
funding gap model is (-$20m)(0.02) = -$.4m.
d. What will net interest income be at year-end if interest rates on RSAs increase by 2 percent but interest
rates on RSLs increase by 1 percent? Is it reasonable for changes in interest rates on RSAs and RSLs to
differ? Why?
After the unequal rate increases, net interest income will be 50(0.12) +
50(0.07) - 70(0.07) - 20(.07) = $9.5m - $6.3m = $3.2m, an increase of $0.3m. It is not
uncommon for interest rates to adjust in an unequal manner on RSAs versus RSLs. Interest
rates often do not adjust solely because of market pressures. In many cases the changes are
affected by decisions of management. Thus, you can see the difference between this answer
and the answer for part a.
15.
Use the following information about a hypothetical government security dealer named M.P.
Jorgan. Market yields are in parenthesis, and amounts are in millions.
Assets
Cash
1-month T-bills (7.05%)
3-month T-bills (7.25%)
2-year T-notes (7.50%)
8-year T-notes (8.96%)
5-year munis (floating rate)
(8.20% reset every 6 months)
Total assets
a.
$10
75
75
50
100
25
$335
Liabilities and Equity
Overnight repos
Subordinated debt
7-year fixed rate (8.55%)
Equity
Total liabilities & equity
$170
150
15
$335
What is the repricing gap if the planning period is 30 days? 3 months? 2 years? Recall that
cash is a noninterest-earning asset.
1-36
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Repricing gap using a 30-day planning period = $75 - $170 = -$95 million.
Repricing gap using a 3-month planning period = ($75 + $75) - $170 = -$20 million.
Reprising gap using a 2-year planning period = ($75 + $75 + $50 + $25) - $170 = +$55
million.
b.
What is the impact over the next 30 days on net interest income if interest rates increase 50
basis points? Decrease 75 basis points?
If interest rates increase 50 basis points, net interest income will decrease by $475,000.
NII = CGAP(R) = -$95m.(.005) = -$0.475m.
If interest rates decrease by 75 basis points, net interest income will increase by $712,500.
NII = CGAP(R) = -$95m.(-.0075) = $0.7125m.
c. The following one-year runoffs are expected: $10 million for two-year T-notes and $20
million for eight-year T-notes. What is the one-year repricing gap?
The repricing gap over the 1-year planning period = ($75m. + $75m. + $10m. + $20m. + $25m.) - $170m. =
+$35 million.
d.
If runoffs are considered, what is the effect on net interest income at year-end if interest
rates rise 50 basis points? Decrease 75 basis points?
If interest rates increase 50 basis points, net interest income will increase by $175,000.
NII = CGAP(R) = $35m.(0.005) = $0.175m.
If interest rates decrease 75 basis points, net interest income will decrease by $262,500.
NII = CGAP(R) = $35m.(-0.0075) = -$0.2625m.
16.
A bank has the following balance sheet:
Assets
Rate sensitive
Fixed rate
Nonearning
Total
$550,000
755,000
265,000
$1,570,000
Avg. Rate
7.75%
8.75
Liabilities/Equity
Rate sensitive $375,000
Fixed rate
805,000
Non paying
390,000
Total
$1,570,000
Avg. Rate
6.25%
7.50
Suppose interest rates rise such that the average yield on rate sensitive assets increases by
45 basis points and the average yield on rate sensitive liabilities increases by 35 basis
points.
a.
Calculate the bank’s repricing GAP and gap ratio.
Repricing GAP = $550,000 - $375,000 = $175,000
Gap ratio = $175,000/$1,570,000 = 11.15%
1-37
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
b.
Assuming the bank does not change the composition of its balance sheet, calculate the
resulting change in the bank’s interest income, interest expense, and net interest income.
II = $550,000(.0045) = $2,475
IE = $375,000(.0035) = $1,312.50
NII = $2,475 - $1,312.50 = $1,162.50
c.
Explain how the CGAP and spread effects influenced this increase in net interest income.
The CGAP affect worked to increase net interest income. That is, the CGAP was positive
while interest rates increased. Thus, interest income increased by more than interest
expense. The result is an increase in NII. The spread effect also worked to increase net
interest income. The spread increased by 10 basis points. According to the spread affect, as
spread increases, so does net interest income.
17.
A bank has the following balance sheet:
Assets
Rate sensitive
Fixed rate
Nonearning
Total
$550,000
755,000
265,000
$1,570,000
Avg. Rate
7.75%
8.75
Liabilities/Equity
Rate sensitive $575,000
Fixed rate
605,000
Nonpaying
390,000
Total
$1,570,000
Avg. Rate
6.25%
7.50
Suppose interest rates fall such that the average yield on rate sensitive assets decreases by
15 basis points and the average yield on rate sensitive liabilities decreases by 5 basis points.
a.
Calculate the bank’s CGAP and gap ratio.
CGAP = $550,000 - $575,000 = -$25,000
Gap ratio = -$25,000/$1,570,000 = -1.59%
b.
Assuming the bank does not change the composition of its balance sheet, calculate the
resulting change in the bank’s interest income, interest expense, and net interest income.
II = $550,000(-.0015) = -$825
IE = $575,000(-.0005) = -$287.50
NII = -$825 – (-$287.50) = -$537.50
c.
The bank’s CGAP is negative and interest rates decreased, yet net interest income
decreased. Explain how the CGAP and spread effects influenced this decrease in net
interest income.
The CGAP affect worked to increase net interest income. That is, the CGAP was negative while
interest rates decreased. Thus, interest income decreased by less than interest expense. The result
is an increase in NII. The spread effect, on the other hand, worked to decrease net interest
1-38
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
income. The spread decreased by 10 basis points. According to the spread affect, as spread
decreases, so does net interest income. In this case, the increase in NII due to the spread effect
was dominated by the decrease in NII due to the spread effect.
18.
The balance sheet of A. G. Fredwards, a government security dealer, is listed below.
Market yields are in parentheses, and amounts are in millions.
Assets
Cash
1-month T-bills (7.05%)
3-month T-bills (7.25%)
2-year T-notes (7.50%)
8-year T-notes (8.96%)
5-year munis (floating rate)
(8.20% reset every 6 months)
Total assets
a.
$20
150
150
100
200
50
$670
Liabilities and Equity
Overnight repos
Subordinated debt
7-year fixed rate (8.55%)
Equity
Total liabilities and equity
$340
300
30
$670
What is the repricing gap if the planning period is 30 days? 3 month days? 2 years?
Repricing gap using a 30-day planning period = $150 - $340 = -$190 million.
Repricing gap using a 3-month planning period = ($150 + $150) - $340 = -$40 million.
Reprising gap using a 2-year planning period = ($150 + $150 + $100 + $50) - $340 = $110
million.
b.
What is the impact over the next three months on net interest income if interest rates on
RSAs increase 50 basis points and on RSLs increase 60 basis points?
II = ($150m. + $150m.)(.005) = $1.5m.
IE = $340m.(.006) = $2.04m.
NII = $1.5m. – ($2.04m.) = -$.54m.
c. What is the impact over the next two years on net interest income if interest rates on
RSAs increase 50 basis points and on RSLs increase 75 basis points?
II = ($150m. + $150m. + $100 + $50)(.005) = $2.25m.
IE = $340m.(.0075) = $2.04m.
NII = $2.25m. – ($2.04m.) = $.21m.
d. Explain the difference in your answers to parts (b) and (c). Why is one answer a
negative change in NII, while the other is positive?
For the 3-month analysis, the CGAP affect worked to decrease net interest income. That is, the
CGAP was negative while interest rates increased. Thus, interest income increased by less than
interest expense. The result is a decrease in NII. For the 3-year analysis, the CGAP affect worked
to increase net interest income. That is, the CGAP was positive while interest rates increased.
Thus, interest income increased by more than interest expense. The result is an increase in NII.
1-39
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
19.
A bank has the following balance sheet:
Assets
Rate sensitive
Fixed rate
Nonearning
Total
$225,000
550,000
120,000
$895,000
Avg. Rate
6.35%
7.55
Liabilities/Equity
Rate sensitive $300,000
Fixed rate
505,000
Nonpaying
90,000
Total
$895,000
Avg. Rate
4.25%
6.15
Suppose interest rates rise such that the average yield on rate sensitive assets increases by
45 basis points and the average yield on rate sensitive liabilities increases by 35 basis
points.
a.
Calculate the bank’s repricing GAP.
Repricing GAP = $225,000 - $300,000 = $75,000
b.
Assuming the bank does not change the composition of its balance sheet, calculate the net
interest income for the bank before and after the interest rate changes. What is the resulting
change in net interest income?
NIb = ($225,000(.0635) +$550,000(.0755)) – ($300,000(.0425) + $505,000(.0615))
= $55,812.50 - $43,807.50 = $12,005
NIa = ($225,000(.0635 + .0045) +$550,000(.0755)) – ($300,000(.0425 + .0035) +
$505,000(.0615)) = $56,825 - $44,857.50 = $11,967.50
NII = $12,005 - $11,967.50 = $37.5
c.
Explain how the CGAP and spread effects influenced this increase in net interest income.
The CGAP affect worked to increase net interest income. That is, the CGAP was positive
while interest rates increased. Thus, interest income increased by more than interest
expense. The result is an increase in NII. The spread effect also worked to increase net
interest income. The spread increased by 10 basis points. According to the spread affect, as
spread increases, so does net interest income.
20.
What are some of the weakness of the repricing model? How have large banks solved the
problem of choosing the optimal time period for repricing? What is runoff cash flow, and
how does this amount affect the repricing model’s analysis?
The repricing model has four general weaknesses:
(1) It ignores market value effects.
1-40
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
(2)
It does not take into account the fact that the dollar value of rate sensitive assets and
liabilities within a bucket are not similar. Thus, if assets, on average, are repriced earlier in
the bucket than liabilities, and if interest rates fall, FIs are subject to reinvestment risks.
(3)
It ignores the problem of runoffs, that is, that some assets are prepaid and some liabilities
are withdrawn before the maturity date.
(4)
It ignores income generated from off-balance-sheet activities.
Large banks are able to reprice securities every day using their own internal models so
reinvestment and repricing risks can be estimated for each day of the year.
Runoff cash flow reflects the assets that are repaid before maturity and the liabilities that are
withdrawn unsuspectedly. To the extent that either of these amounts is significantly greater than
expected, the estimated interest rate sensitivity of the bank will be in error.
The following questions and problems are based on material in Appendix 8A.
21.
What is maturity gap? How can the maturity model be used to immunize an FI’s portfolio?
What is the critical requirement to allow maturity matching to have some success in
immunizing the balance sheet of an FI?
Maturity gap is the difference between the average maturity of assets and liabilities. If the
maturity gap is zero, it is possible to immunize the portfolio, so that changes in interest rates will
result in equal but offsetting changes in the value of assets and liabilities and net interest income.
Thus, if interest rates increase (decrease), the fall (rise) in the value of the assets will be offset by
a perfect fall (rise) in the value of the liabilities. The critical assumption is that the timing of the
cash flows on the assets and liabilities must be the same.
22.
Nearby Bank has the following balance sheet (in millions):
Assets
Cash
5-year treasury notes
30-year mortgages
Total Assets
$60
$60
$200
$320
Liabilities and Equity
Demand deposits
1-year Certificates of Deposit
Equity
Total Liabilities and Equity
$140
$160
$20
$320
What is the maturity gap for Nearby Bank? Is Nearby Bank more exposed to an increase or decrease in interest
rates? Explain why?
MA = [0*20 + 5*60 + 200*30]/320 = 19.69 years, and ML = [0*140 + 1*160]/300 = 0.533.
Therefore the maturity gap = MGAP = 19.69 – 0.533 = 19.16 years. Nearby bank is exposed to
an increase in interest rates. If rates rise, the value of assets will decrease much more than the
value of liabilities.
1-41
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
23.
County Bank has the following market value balance sheet (in millions, annual rates). All
securities are selling at par equal to book value.
Assets
Cash
$20
15-year commercial loan @ 10%
interest, balloon payment
$160
30-year Mortgages @ 8% interest,
balloon payment
$300
Total Assets
$480
Liabilities and Equity
Demand deposits
5-year CDs @ 6% interest,
balloon payment
20-year debentures @ 7% interest
Equity
Total Liabilities & Equity
$100
$210
$120
$50
$480
a. What is the maturity gap for County Bank?
MA = [0*20 + 15*160 + 30*300]/480 = 23.75 years.
ML = [0*100 + 5*210 + 20*120]/430 = 8.02 years.
MGAP = 23.75 – 8.02 = 15.73 years.
b.
What will be the maturity gap if the interest rates on all assets and liabilities increase by 1
percent?
If interest rates increase one percent, the value and average maturity of the assets will be:
Cash = $20
Commercial loans
Financial Calculator:
FV = 160, PMT = 0.1*160 = 16, N = 15, I=11%, Solve for PV = 148.49
Mortgages:
FV = 300, PMT = 24, I = 9%, N = 30, Solve for PV = 269.17
MA = [0*20 + 148.49*15 + 269.17*30]/(20 + 148.49 + 269.17) = 23.53 years
The value and average maturity of the liabilities will be:
Demand deposits = $100
CDs
FV = 210, PMT = 0.06*210 = 12.6, N = 5, I=7%, Solve for PV = 201.39
Debentures
FV = 120, PMT = 0.07*120 = 8.4, N = 20, I=8%, Solve for PV = 108.22
ML = [0*100 + 5*201.39 + 20*108.22]/(100 + 201.39 + 108.22) = 7.74 years
The maturity gap = MGAP = 23.53 – 7.74 = 15.79 years. The maturity gap increased because the average
maturity of the liabilities decreased more than the average maturity of the assets. This result occurred primarily
because of the differences in the cash flow streams for the mortgages and the debentures.
c. What will happen to the market value of the equity?
1-42
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
The market value of the assets has decreased from $480 to $437.66, or $42.34. The market
value of the liabilities has decreased from $430 to $409.61, or $20.69. Therefore, the
market value of the equity will decrease by $42.34 - $20.69 = 21.65.
24. If a bank manager is certain that interest rates were going to increase within the next six months, how should the
bank manager adjust the bank’s maturity gap to take advantage of this anticipated increase? What if the
manager believed rates would fall? Would your suggested adjustments be difficult or easy to achieve?
When rates rise, the value of the longer-lived assets will fall by more the shorter-lived liabilities.
If the maturity gap (or duration gap) is positive, the bank manager will want to shorten the
maturity gap. If the repricing gap is negative, the manager will want to move it towards zero or
positive. If rates are expected to decrease, the manager should reverse these strategies. Changing
the maturity, duration, or funding gaps on the balance sheet often involves changing the mix of
assets and liabilities. Attempts to make these changes may involve changes in financial strategy
for the bank which may not be easy to accomplish. Later in the text, methods of achieving the
same results using derivatives will be explored.
25. Consumer Bank has $20 million in cash and a $180 million loan portfolio. The assets are funded with demand
deposits of $18 million, a $162 million CD and $20 million in equity. The loan portfolio has a maturity of 2
years, earns interest at the annual rate of 7 percent, and is amortized monthly. The bank pays 7 percent annual
interest on the CD, but the interest will not be paid until the CD matures at the end of 2 years.
a.
What is the maturity gap for Consumer Bank?
MA = [0*$20 + 2*$180]/$200 = 1.80 years
ML = [0*$18 + 2*$162]/$180 = 1.80 years
MGAP = 1.80 – 1.80 = 0 years.
b.
Is Consumer Bank immunized or protected against changes in interest rates? Why or why
not?
It is tempting to conclude that the bank is immunized because the maturity gap is zero. However, the cash flow
stream for the loan and the cash flow stream for the CD are different because the loan amortizes monthly and
the CD pays annual interest on the CD. Thus any change in interest rates will affect the earning power of the
loan more than the interest cost of the CD.
c.
Does Consumer Bank face interest rate risk? That is, if market interest rates increase or
decrease 1 percent, what happens to the value of the equity?
The bank does face interest rate risk. If market rates increase 1 percent, the value of the cash and demand
deposits does not change. However, the value of the loan will decrease to $178.19, and the value of the CD will
fall to $159.01. Thus, the value of the equity will be ($178.19 + $20 - $18 - $159.01) = $21.18. In this case, the
increase in interest rates causes the market value of equity to increase because of the reinvestment opportunities
on the loan payments.
If market rates decrease 1 percent, the value of the loan increases to $181.84, and the value
of the CD increases to $165.07. Thus the value of the equity decreases to $18.77.
d. How can a decrease in interest rates create interest rate risk?
1-43
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
The amortized loan payments would be reinvested at lower rates. Thus, even though
interest rates have decreased, the different cash flow patterns of the loan and the CD have
caused interest rate risk.
26.
FI International holds seven-year Acme International bonds and two-year Beta Corporation
bonds. The Acme bonds are yielding 12 percent and the Beta bonds are yielding 14 percent
under current market conditions.
a.
What is the weighted-average maturity of FI’s bond portfolio if 40 percent is in Acme
bonds and 60 percent is in Beta bonds?
Average maturity = 0.40 x 7 years + 0.60 x 2 years = 4 years
b.
What proportion of Acme and Beta bonds should be held to have a weighted-average yield
of 13.5 percent?
Let X*(0.12) + (1 - X)*(0.14) = 0.135. Solving for X, we get 25 percent. In order to get an average yield of 13.5
percent, we need to hold 25 percent of Acme and 75 percent of Beta.
c.
What will be the weighted-average maturity of the bond portfolio if the weighted-average
yield is realized?
The average maturity of the portfolio will decrease to 0.25 x 7 + 0.75 x 2 = 3.25 years.
27. An insurance company has invested in the following fixed-income securities: (a) $10,000,000 of 5-year
Treasury notes paying 5 percent interest and selling at par value, (b) $5,800,000 of 10-year bonds paying 7
percent interest with a par value of $6,000,000, and (c) $6,200,000 of 20-year subordinated debentures paying 9
percent interest with a par value of $6,000,000.
a. What is the weighted-average maturity of this portfolio of assets?
MA = [5*$10 + 10*$5.8 + 20*$6.2]/$22 = 232/22 = 10.55 years
b.
If interest rates change so that the yields on all of the securities decrease 1 percent, how
does the weighted-average maturity of the portfolio change?
To determine the weighted-average maturity of the portfolio for a rate decrease of 1 percent, the new value of
each security must be determined. This calculation will require knowing the yield to maturity of each security
before the rate change.
T-notes are selling at par, so the yield to maturity = 5 percent. Therefore, the new value
FV = 10, PMT = 0.05*10 = 0.5, N = 5, I=4%, Solve for PV = 10.45 or 10,445,182.
10-year bonds: Par = $6,000,000, PV = $5,800,000, Cpn = 7 percent  YTM = 7.485%.
FV = 6, PMT = 0.42, I = 6.485%, N = 10, Solve for PV = 6.22 or 6,222,290
Debentures: Par = $6,000,000, PV = $6,200,000, Cpn = 9 percent  8.644 percent.
1-44
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
FV = 6, PMT = 0.54, I = 7.644%, N = 20, Solve for PV = 6.82 or 6,820,418
The total value of the assets after the change in rates will be $23,487,890, and the
weighted-average maturity will be [5*10,445,182 + 10*6,222,290 +
20*6,820,418]/23,487,890 = 250,857,170/23,487,890 = 10.68 years.
c. Explain the changes in the maturity values if the yields increase by 1 percent.
When interest rates increase 1 percent, the value of the T-note is $9,578,764, the value of
the 10-year bond is $5,414,993, and the value of the debenture is $5,662,882, and the new
value of the assets is $20,656,639. The weighted-average maturity is 10.42 years.
d.
Assume that the insurance company has no other assets. What will be the effect on the
market value of the company’s equity if the interest rate changes in (b) and (c) occur?
Assuming that the company is financed entirely with equity, the market value will increase $1,487,890 when
interest rates decrease 1 percent, and the market value will decrease $1,343,361 when rates increase 1 percent.
Notice that for the same absolute rate change, the increase in value is greater than the decrease in value.
28.
The following is a simplified FI balance sheet:
Assets
Loans
Total Assets
$1,000
0
$1,000
Liabilities and Equity
Deposits
Equity
Total Liabilities & Equity
$850
$150
$1,000
The average maturity of loans is four years, and the average maturity of deposits is two years. Assume loan and
deposit balances are reported as book value, zero-coupon items.
a.
Assume that interest rates on both loans and deposits are 9 percent. What is the market
value of equity?
The value of loans = $1,000/(1.09)4 = $708.43, and the value of deposits = $850/(1.09)2 =
$715.43. The net worth = $708.43 - $715.43 = -$7.0028. (That is, net worth is negative.)
b.
What must be the interest rate on deposits to force the market value of equity to be zero?
What economic market conditions must exist to make this situation possible?
In this case the deposit value should equal the loan value. Thus, $850/(1 + x)2 = $708.43.
Solving for x, we get 9.5374%. That is, deposit rates will have to increase more because
they have a shorter maturity. Note: for those using calculators, you need to compute
I/YEAR after entering 850 = FV, -708.43 = PV, 0 = PMT, 2 = N.
c.
Assume that interest rates on both loans and deposits are 9 percent. What must be the
average maturity of deposits for the market value of equity to be zero?
1-45
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
In this case, we need to solve the equation in part (b) for N. The result is 2.1141 years. If interest rates remain at
9 percent, then the average maturity of deposits has to be higher in order to match the value of a 4-year loan.
29. Gunnison Insurance has reported the following balance sheet (in thousands):
Assets
2-year Treasury note
15-year munis
$175
$165
Total Assets
$340
Liabilities and Equity
1-year commercial paper
5-year note
Equity
Total Liabilities & Equity
$135
$160
$45
$340
All securities are selling at par equal to book value. The two-year notes are yielding 5 percent, and the 15-year
munis are yielding 9 percent. The one-year commercial paper pays 4.5 percent, and the five-year notes pay 8
percent. All instruments pay interest annually.
a.
What is the weighted-average maturity of the assets for Gunnison?
MA = [2*$175 + 15*$165]/$340 = 8.31 years
b. What is the weighted-average maturity of the liabilities for Gunnison?
ML = [1*$135 + 5*$160]/$295 = 3.17 years
c. What is the maturity gap for Gunnison?
MGAP = 8.31- 3.17 = 5.14 years
d.
What does your answer to part (c) imply about the interest rate exposure of Gunnison
Insurance?
Gunnison Insurance is exposed to interest rate risk. If interest rates rise, net worth will decline because the
average maturity of the assets is higher than the average maturity of the liabilities. The opposite holds true if
interest rates fall (That is, net worth will increase.)
e.
Calculate the values of all four securities of Gunnison Insurance’s balance sheet assuming
that all interest rates increase 2 percent. What is the dollar change in the total asset and
total liability values? What is the percentage change in these values?
T-notes:
FV = 175, PMT = 8.75, I = 7%, N = 2, Solve for PV = 168.67
Munis:
FV = 165, PMT = 14.85, I = 11%, N = 15, Solve for PV = 141.27
Commercial Paper:
FV = 135, PMT = 6.075, I = 6.5%, N = 1, Solve for PV = 132.46
Note:
FV = 160, PMT = 12.8, I = 10%, N = 5, Solve for PV = 147.87
1-46
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Total assets = $168.67 + $141.27 = $309.94  A = -$30.06 or -8.84 percent change
Total liabilities = $132.46 + $147.87 = $280.33  L = -$14.67 or -4.97 percent change
f.
What is the dollar impact on the market value of equity for Gunnison? What is the
percentage change in the value of the equity?
E = A - L = -$30.06 – (-$14.67) = -$15.39  -34.2 percent
g. What would be the impact on Gunnison’s market value of equity if the liabilities paid
interest semiannually instead of annually?
The value of liabilities will be lower with semi-annual compounding, increasing the value of net worth. The
one-year CP will decline in value to $132.426. The five-year note will decline in value to $147.645. The value
of equity will increase to $29.869 = ($168.67 + $141.27) - ($132.426 + $147.645).
30.
Scandia Bank has issued a one-year, $1million CD paying 5.75 percent to fund a one-year
loan paying an interest rate of 6 percent. The principal of the loan will be paid in two
installments, $500,000 in 6 months and the balance at the end of the year.
a.
What is the maturity gap of Scandia Bank? According to the maturity model, what does
this maturity gap imply about the interest rate risk exposure faced by the bank?
The maturity gap is 1 year – 1 year = 0. The maturity gap model would state that the portfolio is immunized
against changes in interest rates because assets and liabilities are of equal maturity.
b.
What is the expected net interest income at the end of the year?
Principal received in six months
Interest received in six months (.03 x $1,000,000)
Total
$500,000
$30,000
$530,000
Principal received at the end of the year
Interest received at the end of the year (.03 x $500,000)
Future value of interest received in six months ($530,000 x 1.03*)
Total principal and interest received
$500,000
$15,000
$545,900
$1,060,900
Principal and interest paid on deposits ($1,000,000 x 0.0575)
Net interest income received
$1,057,500
$3,400
* It is assumed that the money will be reinvested at current loan rates. Note that the principal is also included in
the analysis because interest expense is based on $1,000,000.
c.
What would be the effect on annual net interest income of a 2 percent interest rate increase
that occurred immediately after the loan was made? What would be the effect of a 2
percent decrease in rates?
If interest rates increase 2 percent, then the reinvestment benefits of cash flows in six
months will be higher:
1-47
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Principal received in six months
Interest received in six months (.03 x $1,000,000)
Total
$500,000
$30,000
$530,000
Principal received at the end of the year
Interest received at the end of the year (.03 x $500,000)
Future value of interest received in six months ($530,000 x 1.04)
Total principal and interest received
$500,000
$15,000
$551,200
$1,066,200
Principal and interest paid on deposits ($1,000,000 x 0.0575)
Net interest income received
$1,057,500
$8,700
If interest rates decrease by 2 percent, then reinvestment income is reduced.
Principal received in six months
Interest received in six months (.03 x $1,000,000)
Total
$500,000
$30,000
$530,000
Principal received at the end of the year
Interest received at the end of the year (.03 x $500,000)
Future value of interest received in six months ($530,000 x 1.02)
Total principal and interest received
$500,000
$15,000
$540,600
$1,055,600
Principal and interest paid on deposits ($1,000,000 x 0.0575)
Net income received
$1,057,500
$-1,900
d. What do these results indicate about the maturity model’s ability to immunize
portfolios against interest rate exposure?
The results indicate that just matching assets and liabilities by maturity is not sufficient to immunize a portfolio.
If the timing of the cash flows within a period is different for assets and liabilities, the effects of interest rate
changes are different. For a truly effective immunization strategy, one also needs to account for the timing of
cash flows.
31. EDF Bank has a very simple balance sheet. Assets consist of a two-year, $1 million loan that pays an interest
rate of LIBOR plus 4 percent annually. The loan is funded with a two-year deposit on which the bank pays
LIBOR plus 3.5 percent interest annually. LIBOR currently is 4 percent, and both the loan and deposit principal
will be paid at maturity.
a. What is the maturity gap of this balance sheet?
Maturity gap = 2 - 2 = 0 years
b. What is the expected net interest income in year 1 and year 2?
Interest received in year 1
Interest paid in year 1
$80,000
$75,000
Interest received in year 2
Interest paid in year 2
$80,000
$75,000
1-48
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Net interest income in year 1
c.
$5,000
Net interest income in year 2
Immediately prior to the beginning of year 2, LIBOR rates increased to 6 percent. What is
the expected net interest income in year 2? What would be the effect on net interest
income of a 2 percent decrease in LIBOR?
Year 2: If interest rates increase 2 percent
Interest received in year 2
$100,000
Interest paid in year 2
$95,000
Net interest income in year 2 $5,000
32.
$5,000
Year 2: If interest rates decrease 2 percent
Interest received in year 2
$60,000
Interest paid in year 2
$55,000
Net interest income in year 2 $5,000
What are the weaknesses of the maturity model?
First, the maturity model does not consider the degree of leverage on the balance sheet. For
example, if assets are not financed entirely with deposits, a change in interest rates may
cause the assets to change in value by a different amount than the liabilities. Second, the
maturity model does not take into account the timing of the cash flows of either the assets
or the liabilities, and thus reinvestment and/or refinancing risk may become important
factors in profitability and valuation as interest rates change.
1-49
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Chapter Eight
Interest Rate Risk I
Chapter Outline
Introduction
The Level and Movement of Interest Rates
The Repricing Model
• Rate-Sensitive Assets
• Rate-Sensitive Liabilities
• Equal Changes in Rates on RSAs and RSLs
• Unequal Changes in Rates on RSAs and RSLs
Weaknesses of the Repricing Model
• Market Value Effects
• Overaggregation
• The Problem of Runoffs
• Cash Flows from Off-Balance Sheet Activities
Summary
Appendix 8A: The Maturity Model
• The Maturity Model with a Portfolio of Assets and Liabilities
Weaknesses of the Maturity Model
Appendix 8B: Term Structure of Interest Rates
• Unbiased Expectations Theory
• Liquidity Premium Theory
• Market Segmentation Theory
• Forecasting Interest Rates
1-50
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Solutions for End-of-Chapter Questions and Problems: Chapter Eight
1.
How do the supply of and demand for loanable funds, together, determine interest rates?
Changes in underlying factors that determine the demand and supply of loanable funds cause
continuous shifts in the supply and/or demand curves for loanable funds. Market forces will react
to the resulting disequilibrium with a change in the equilibrium interest rate and quantity of
funds traded in that market. Figure 8-2(a) shows the effects of an increase in the supply curve for
loanable funds, from SS to SS , (and the resulting decrease in the equilibrium interest rate, from
i* to i* ), while Figure 8-2(b) shows the effects of an increase in the demand curve for loanable
funds, from DD to DD , (and the resulting increase in the equilibrium interest rate, from i* to
i* ).
2.
How do monetary policy actions made by the Federal Reserve impact interest rates?
Through its daily open market operations, such as buying and selling Treasury bonds and
Treasury bills, the Fed seeks to influence the money supply, inflation, and the level of interest
rates. When the Fed finds it necessary to slow down the economy, it tightens monetary policy by
raising interest rates. The normal result is a decrease in business and household spending
(especially that financed by credit or borrowing). Conversely, if business and household
spending decline to the extent that the Fed finds it necessary to stimulate the economy it allows
interest rates to fall (an expansionary monetary policy). The drop in rates promotes borrowing
and spending.
3.
How has the increased level of financial market integration affected interest rates?
Increased financial market integration, or globalization, increases the speed with which interest
rate changes and volatility are transmitted among countries. The result of this quickening of
global economic adjustment is to increase the difficulty and uncertainty faced by the Federal
Reserve as it attempts to manage economic activity within the U.S. Further, because FIs have
become increasingly more global in their activities, any change in interest rate levels or volatility
caused by Federal Reserve actions more quickly creates additional interest rate risk issues for
these companies.
4.
What is the repricing gap? In using this model to evaluate interest rate risk, what is meant
by rate sensitivity? On what financial performance variable does the repricing model
focus? Explain.
The repricing gap is a measure of the difference between the dollar value of assets that will
reprice and the dollar value of liabilities that will reprice within a specific time period, where
repricing can be the result of a roll over of an asset or liability (e.g., a loan is paid off at or prior
to maturity and the funds are used to issue a new loan at current market rates) or because the
asset or liability is a variable rate instrument (e.g., a variable rate mortgage whose interest rate is
reset every quarter based on movements in a prime rate). Rate sensitivity represents the time
interval where repricing can occur. The model focuses on the potential changes in the net interest
1-51
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
income variable. In effect, if interest rates change, interest income and interest expense will
change as the various assets and liabilities are repriced, that is, receive new interest rates.
5.
What is a maturity bucket in the repricing model? Why is the length of time selected for
repricing assets and liabilities important when using the repricing model?
The maturity bucket is the time window over which the dollar amounts of assets and liabilities
are measured. The length of the repricing period determines which of the securities in a portfolio
are rate-sensitive. The longer the repricing period, the more securities either mature or need to be
repriced, and, therefore, the more the interest rate exposure. An excessively short repricing
period omits consideration of the interest rate risk exposure of assets and liabilities are that
repriced in the period immediately following the end of the repricing period. That is, it
understates the rate sensitivity of the balance sheet. An excessively long repricing period
includes many securities that are repriced at different times within the repricing period, thereby
overstating the rate sensitivity of the balance sheet.
6.
What is the CGAP effect? According to the CGAP effect, what is the relation between
changes in interest rates and changes in net interest income when CGAP is positive? When
CGAP is negative?
The CGAP effect describes the relations between changes in interest rates and changes in net
interest income. According to the CGAP effect, when CGAP is positive the change in NII is
positively related to the change in interest rates. Thus, an FI would want its CGAP to be positive
when interest rates are expected to rise. According to the CGAP effect, when CGAP is negative
the change in NII is negatively related to the change in interest rates. Thus, an FI would want its
CGAP to be negative when interest rates are expected to fall.
7.
If a bank manager was quite certain that interest rates were going to rise within the next six
months, how should the bank manager adjust the bank’s six-month repricing gap to take
advantage of this anticipated rise? What if the manger believed rates would fall in the next
six months.
When interest rates are expected to rise, a bank should set its repricing gap to a positive position.
In this case, as rates rise, interest income will rise by more than interest expense. The result is an
increase in net interest income. When interest rates are expected to fall, a bank should set its
repricing gap to a negative position. In this case, as rates fall, interest income will fall by less
than interest expense. The result is an increase in net interest income.
8.
Consider the following balance sheet positions for a depository institution:
•
Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million
•
Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million
•
Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million
1-52
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
a. Calculate the repricing gap and the impact on net interest income of a 1 percent
increase in interest rates for each position.
•
Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million.
Repricing gap = RSA - RSL = $200 - $100 million = +$100 million.
NII = ($100 million)(.01) = +$1.0 million, or $1,000,000.
•
Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million.
Repricing gap = RSA - RSL = $100 - $150 million = -$50 million.
NII = (-$50 million)(.01) = -$0.5 million, or -$500,000.
•
Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million.
Repricing gap = RSA - RSL = $150 - $140 million = +$10 million.
NII = ($10 million)(.01) = +$0.1 million, or $100,000.
b.
Calculate the impact on net interest income on each of the above situations assuming a 1
percent decrease in interest rates.
•
NII = ($100 million)(-.01) = -$1.0 million, or -$1,000,000.
•
NII = (-$50 million)(-.01) = +$0.5 million, or $500,000.
•
NII = ($10 million)(-.01) = -$0.1 million, or -$100,000.
c. What conclusion can you draw about the repricing model from these results?
The FIs in parts (1) and (3) are exposed to interest rate declines (positive repricing gap)
while the FI in part (2) is exposed to interest rate increases. The FI in part (3) has the
lowest interest rate risk exposure since the absolute value of the repricing gap is the lowest,
while the opposite is true for part (1).
9.
What are the reasons for not including demand deposits as rate-sensitive liabilities in the
repricing analysis for a commercial bank? What is the subtle, but potentially strong, reason
for including demand deposits in the total of rate-sensitive liabilities? Can the same
argument be made for passbook savings accounts?
The regulatory rate available on demand deposit accounts is zero. Although many banks are able
to offer NOW accounts on which interest can be paid, this interest rate seldom is changed and
thus the accounts are not really sensitive. However, demand deposit accounts do pay implicit
interest in the form of not charging fully for checking and other services. Further, when market
interest rates rise, customers draw down their DDAs, which may cause the bank to use higher
cost sources of funds. The same or similar arguments can be made for passbook savings
accounts.
1-53
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
10. What is the gap ratio? What is the value of this ratio to interest rate risk managers and regulators?
The gap ratio is the ratio of the cumulative gap position to the total assets of the bank. The
cumulative gap position is the sum of the individual gaps over several time buckets. The value of
this ratio is that it tells the direction of the interest rate exposure and the scale of that exposure
relative to the size of the bank.
11.
Which of the following assets or liabilities fit the one-year rate or repricing sensitivity test?
3-month U.S. Treasury bills
1-year U.S. Treasury notes
20-year U.S. Treasury bonds
20-year floating-rate corporate bonds with annual repricing
30-year floating-rate mortgages with repricing every two years
30-year floating-rate mortgages with repricing every six months
Overnight fed funds
9-month fixed rate CDs
1-year fixed-rate CDs
5-year floating-rate CDs with annual repricing
Common stock
12.
Yes
Yes
No
Yes
No
Yes
Yes
Yes
Yes
Yes
No
What is the spread effect?
The spread effect is the effect that a change in the spread between rates on RSAs and RSLs has
on net interest income as interest rates change. The spread effect is such that, regardless of the
direction of the change in interest rates, a positive relation occurs between changes in the spread
and changes in NII. Whenever the spread increases (decreases), NII increases (decreases).
13.
A bank manager is quite certain that interest rates are going to fall within the next six
months, but the fall will be different on RSAs versus RSLs. How should the bank manager
adjust the bank’s six-month repricing gap and spread to take advantage of this anticipated
rise? What if the manger believed rates would rise in the next six months.
When interest rates are expected to fall, a bank should set its repricing gap to a negative position.
Further, the manager would want to increase the spread between the return on RSAs and RSLs.
In this case, as rates fall, interest income will fall by less than interest expense. The result is an
increase in net interest income. When interest rates are expected to rise, a bank should set its
repricing gap to a positive position. Again, the manager would want to increase the spread
between the return on RSAs and RSLs. In this case, as rates rise, interest income will rise by
more than interest expense. The result is an increase in net interest income.
14.
Consider the following balance sheet for WatchoverU Savings, Inc. (in millions):
Assets
Floating-rate mortgages
(currently 10% annually)
Liabilities and Equity
1-year time deposits
(currently 6% annually)
$50
$70
1-54
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
30-year fixed-rate loans
(currently 7% annually)
Total Assets
3-year time deposits
(currently 7% annually)
Equity
Total Liabilities & Equity
$50
$100
$20
$10
$100
a. What is WatchoverU’s expected net interest income at year-end?
Current expected interest income: $50m(0.10) + $50m(0.07) = $8.5m.
Expected interest expense: $70m(0.06) - $20m(0.07) = $5.6m.
Expected net interest income:
$8.5m - $5.6m = $2.9m.
b. What will net interest income be at year-end if interest rates rise by 2 percent?
After the 200 basis point interest rate increase, net interest income declines to:
50(0.12) + 50(0.07) - 70(0.08) - 20(.07) = $9.5m - $7.0m = $2.5m, a decline of $0.4m.
c.
Using the cumulative repricing gap model, what is the expected net interest income for a 2
percent increase in interest rates?
Wachovia’s' repricing or funding gap is $50m - $70m = -$20m. The change in net interest income using the
funding gap model is (-$20m)(0.02) = -$.4m.
e. What will net interest income be at year-end if interest rates on RSAs increase by 2 percent but interest
rates on RSLs increase by 1 percent? Is it reasonable for changes in interest rates on RSAs and RSLs to
differ? Why?
After the unequal rate increases, net interest income will be 50(0.12) +
50(0.07) - 70(0.07) - 20(.07) = $9.5m - $6.3m = $3.2m, an increase of $0.3m. It is not
uncommon for interest rates to adjust in an unequal manner on RSAs versus RSLs. Interest
rates often do not adjust solely because of market pressures. In many cases the changes are
affected by decisions of management. Thus, you can see the difference between this answer
and the answer for part a.
15.
Use the following information about a hypothetical government security dealer named M.P.
Jorgan. Market yields are in parenthesis, and amounts are in millions.
Assets
Cash
1-month T-bills (7.05%)
3-month T-bills (7.25%)
2-year T-notes (7.50%)
8-year T-notes (8.96%)
5-year munis (floating rate)
(8.20% reset every 6 months)
Total assets
a.
$10
75
75
50
100
25
$335
Liabilities and Equity
Overnight repos
Subordinated debt
7-year fixed rate (8.55%)
Equity
Total liabilities & equity
$170
150
15
$335
What is the repricing gap if the planning period is 30 days? 3 months? 2 years? Recall that
cash is a noninterest-earning asset.
1-55
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Repricing gap using a 30-day planning period = $75 - $170 = -$95 million.
Repricing gap using a 3-month planning period = ($75 + $75) - $170 = -$20 million.
Reprising gap using a 2-year planning period = ($75 + $75 + $50 + $25) - $170 = +$55
million.
b.
What is the impact over the next 30 days on net interest income if interest rates increase 50
basis points? Decrease 75 basis points?
If interest rates increase 50 basis points, net interest income will decrease by $475,000.
NII = CGAP(R) = -$95m.(.005) = -$0.475m.
If interest rates decrease by 75 basis points, net interest income will increase by $712,500.
NII = CGAP(R) = -$95m.(-.0075) = $0.7125m.
d. The following one-year runoffs are expected: $10 million for two-year T-notes and $20
million for eight-year T-notes. What is the one-year repricing gap?
The repricing gap over the 1-year planning period = ($75m. + $75m. + $10m. + $20m. + $25m.) - $170m. =
+$35 million.
d.
If runoffs are considered, what is the effect on net interest income at year-end if interest
rates rise 50 basis points? Decrease 75 basis points?
If interest rates increase 50 basis points, net interest income will increase by $175,000.
NII = CGAP(R) = $35m.(0.005) = $0.175m.
If interest rates decrease 75 basis points, net interest income will decrease by $262,500.
NII = CGAP(R) = $35m.(-0.0075) = -$0.2625m.
16.
A bank has the following balance sheet:
Assets
Rate sensitive
Fixed rate
Nonearning
Total
$550,000
755,000
265,000
$1,570,000
Avg. Rate
7.75%
8.75
Liabilities/Equity
Rate sensitive $375,000
Fixed rate
805,000
Non paying
390,000
Total
$1,570,000
Avg. Rate
6.25%
7.50
Suppose interest rates rise such that the average yield on rate sensitive assets increases by
45 basis points and the average yield on rate sensitive liabilities increases by 35 basis
points.
a.
Calculate the bank’s repricing GAP and gap ratio.
Repricing GAP = $550,000 - $375,000 = $175,000
Gap ratio = $175,000/$1,570,000 = 11.15%
1-56
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
b.
Assuming the bank does not change the composition of its balance sheet, calculate the
resulting change in the bank’s interest income, interest expense, and net interest income.
II = $550,000(.0045) = $2,475
IE = $375,000(.0035) = $1,312.50
NII = $2,475 - $1,312.50 = $1,162.50
c.
Explain how the CGAP and spread effects influenced this increase in net interest income.
The CGAP affect worked to increase net interest income. That is, the CGAP was positive
while interest rates increased. Thus, interest income increased by more than interest
expense. The result is an increase in NII. The spread effect also worked to increase net
interest income. The spread increased by 10 basis points. According to the spread affect, as
spread increases, so does net interest income.
17.
A bank has the following balance sheet:
Assets
Rate sensitive
Fixed rate
Nonearning
Total
$550,000
755,000
265,000
$1,570,000
Avg. Rate
7.75%
8.75
Liabilities/Equity
Rate sensitive $575,000
Fixed rate
605,000
Nonpaying
390,000
Total
$1,570,000
Avg. Rate
6.25%
7.50
Suppose interest rates fall such that the average yield on rate sensitive assets decreases by
15 basis points and the average yield on rate sensitive liabilities decreases by 5 basis points.
a.
Calculate the bank’s CGAP and gap ratio.
CGAP = $550,000 - $575,000 = -$25,000
Gap ratio = -$25,000/$1,570,000 = -1.59%
b.
Assuming the bank does not change the composition of its balance sheet, calculate the
resulting change in the bank’s interest income, interest expense, and net interest income.
II = $550,000(-.0015) = -$825
IE = $575,000(-.0005) = -$287.50
NII = -$825 – (-$287.50) = -$537.50
c.
The bank’s CGAP is negative and interest rates decreased, yet net interest income
decreased. Explain how the CGAP and spread effects influenced this decrease in net
interest income.
The CGAP affect worked to increase net interest income. That is, the CGAP was negative while
interest rates decreased. Thus, interest income decreased by less than interest expense. The result
is an increase in NII. The spread effect, on the other hand, worked to decrease net interest
1-57
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
income. The spread decreased by 10 basis points. According to the spread affect, as spread
decreases, so does net interest income. In this case, the increase in NII due to the spread effect
was dominated by the decrease in NII due to the spread effect.
18.
The balance sheet of A. G. Fredwards, a government security dealer, is listed below.
Market yields are in parentheses, and amounts are in millions.
Assets
Cash
1-month T-bills (7.05%)
3-month T-bills (7.25%)
2-year T-notes (7.50%)
8-year T-notes (8.96%)
5-year munis (floating rate)
(8.20% reset every 6 months)
Total assets
a.
$20
150
150
100
200
50
$670
Liabilities and Equity
Overnight repos
Subordinated debt
7-year fixed rate (8.55%)
Equity
Total liabilities and equity
$340
300
30
$670
What is the repricing gap if the planning period is 30 days? 3 month days? 2 years?
Repricing gap using a 30-day planning period = $150 - $340 = -$190 million.
Repricing gap using a 3-month planning period = ($150 + $150) - $340 = -$40 million.
Reprising gap using a 2-year planning period = ($150 + $150 + $100 + $50) - $340 = $110
million.
b.
What is the impact over the next three months on net interest income if interest rates on
RSAs increase 50 basis points and on RSLs increase 60 basis points?
II = ($150m. + $150m.)(.005) = $1.5m.
IE = $340m.(.006) = $2.04m.
NII = $1.5m. – ($2.04m.) = -$.54m.
c. What is the impact over the next two years on net interest income if interest rates on
RSAs increase 50 basis points and on RSLs increase 75 basis points?
II = ($150m. + $150m. + $100 + $50)(.005) = $2.25m.
IE = $340m.(.0075) = $2.04m.
NII = $2.25m. – ($2.04m.) = $.21m.
d. Explain the difference in your answers to parts (b) and (c). Why is one answer a
negative change in NII, while the other is positive?
For the 3-month analysis, the CGAP affect worked to decrease net interest income. That is, the
CGAP was negative while interest rates increased. Thus, interest income increased by less than
interest expense. The result is a decrease in NII. For the 3-year analysis, the CGAP affect worked
to increase net interest income. That is, the CGAP was positive while interest rates increased.
Thus, interest income increased by more than interest expense. The result is an increase in NII.
1-58
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
19.
A bank has the following balance sheet:
Assets
Rate sensitive
Fixed rate
Nonearning
Total
$225,000
550,000
120,000
$895,000
Avg. Rate
6.35%
7.55
Liabilities/Equity
Rate sensitive $300,000
Fixed rate
505,000
Nonpaying
90,000
Total
$895,000
Avg. Rate
4.25%
6.15
Suppose interest rates rise such that the average yield on rate sensitive assets increases by
45 basis points and the average yield on rate sensitive liabilities increases by 35 basis
points.
a.
Calculate the bank’s repricing GAP.
Repricing GAP = $225,000 - $300,000 = $75,000
b.
Assuming the bank does not change the composition of its balance sheet, calculate the net
interest income for the bank before and after the interest rate changes. What is the resulting
change in net interest income?
NIb = ($225,000(.0635) +$550,000(.0755)) – ($300,000(.0425) + $505,000(.0615))
= $55,812.50 - $43,807.50 = $12,005
NIa = ($225,000(.0635 + .0045) +$550,000(.0755)) – ($300,000(.0425 + .0035) +
$505,000(.0615)) = $56,825 - $44,857.50 = $11,967.50
NII = $12,005 - $11,967.50 = $37.5
c.
Explain how the CGAP and spread effects influenced this increase in net interest income.
The CGAP affect worked to increase net interest income. That is, the CGAP was positive
while interest rates increased. Thus, interest income increased by more than interest
expense. The result is an increase in NII. The spread effect also worked to increase net
interest income. The spread increased by 10 basis points. According to the spread affect, as
spread increases, so does net interest income.
20.
What are some of the weakness of the repricing model? How have large banks solved the
problem of choosing the optimal time period for repricing? What is runoff cash flow, and
how does this amount affect the repricing model’s analysis?
The repricing model has four general weaknesses:
(1) It ignores market value effects.
1-59
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
(2)
It does not take into account the fact that the dollar value of rate sensitive assets and
liabilities within a bucket are not similar. Thus, if assets, on average, are repriced earlier in
the bucket than liabilities, and if interest rates fall, FIs are subject to reinvestment risks.
(3)
It ignores the problem of runoffs, that is, that some assets are prepaid and some liabilities
are withdrawn before the maturity date.
(4)
It ignores income generated from off-balance-sheet activities.
Large banks are able to reprice securities every day using their own internal models so
reinvestment and repricing risks can be estimated for each day of the year.
Runoff cash flow reflects the assets that are repaid before maturity and the liabilities that are
withdrawn unsuspectedly. To the extent that either of these amounts is significantly greater than
expected, the estimated interest rate sensitivity of the bank will be in error.
The following questions and problems are based on material in Appendix 8A.
21.
What is maturity gap? How can the maturity model be used to immunize an FI’s portfolio?
What is the critical requirement to allow maturity matching to have some success in
immunizing the balance sheet of an FI?
Maturity gap is the difference between the average maturity of assets and liabilities. If the
maturity gap is zero, it is possible to immunize the portfolio, so that changes in interest rates will
result in equal but offsetting changes in the value of assets and liabilities and net interest income.
Thus, if interest rates increase (decrease), the fall (rise) in the value of the assets will be offset by
a perfect fall (rise) in the value of the liabilities. The critical assumption is that the timing of the
cash flows on the assets and liabilities must be the same.
22.
Nearby Bank has the following balance sheet (in millions):
Assets
Cash
5-year treasury notes
30-year mortgages
Total Assets
$60
$60
$200
$320
Liabilities and Equity
Demand deposits
1-year Certificates of Deposit
Equity
Total Liabilities and Equity
$140
$160
$20
$320
What is the maturity gap for Nearby Bank? Is Nearby Bank more exposed to an increase or decrease in interest
rates? Explain why?
MA = [0*20 + 5*60 + 200*30]/320 = 19.69 years, and ML = [0*140 + 1*160]/300 = 0.533.
Therefore the maturity gap = MGAP = 19.69 – 0.533 = 19.16 years. Nearby bank is exposed to
an increase in interest rates. If rates rise, the value of assets will decrease much more than the
value of liabilities.
1-60
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
23.
County Bank has the following market value balance sheet (in millions, annual rates). All
securities are selling at par equal to book value.
Assets
Cash
$20
15-year commercial loan @ 10%
interest, balloon payment
$160
30-year Mortgages @ 8% interest,
balloon payment
$300
Total Assets
$480
Liabilities and Equity
Demand deposits
5-year CDs @ 6% interest,
balloon payment
20-year debentures @ 7% interest
Equity
Total Liabilities & Equity
$100
$210
$120
$50
$480
a. What is the maturity gap for County Bank?
MA = [0*20 + 15*160 + 30*300]/480 = 23.75 years.
ML = [0*100 + 5*210 + 20*120]/430 = 8.02 years.
MGAP = 23.75 – 8.02 = 15.73 years.
b.
What will be the maturity gap if the interest rates on all assets and liabilities increase by 1
percent?
If interest rates increase one percent, the value and average maturity of the assets will be:
Cash = $20
Commercial loans
Financial Calculator:
FV = 160, PMT = 0.1*160 = 16, N = 15, I=11%, Solve for PV = 148.49
Mortgages:
FV = 300, PMT = 24, I = 9%, N = 30, Solve for PV = 269.17
MA = [0*20 + 148.49*15 + 269.17*30]/(20 + 148.49 + 269.17) = 23.53 years
The value and average maturity of the liabilities will be:
Demand deposits = $100
CDs
FV = 210, PMT = 0.06*210 = 12.6, N = 5, I=7%, Solve for PV = 201.39
Debentures
FV = 120, PMT = 0.07*120 = 8.4, N = 20, I=8%, Solve for PV = 108.22
ML = [0*100 + 5*201.39 + 20*108.22]/(100 + 201.39 + 108.22) = 7.74 years
The maturity gap = MGAP = 23.53 – 7.74 = 15.79 years. The maturity gap increased because the average
maturity of the liabilities decreased more than the average maturity of the assets. This result occurred primarily
because of the differences in the cash flow streams for the mortgages and the debentures.
c. What will happen to the market value of the equity?
1-61
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
The market value of the assets has decreased from $480 to $437.66, or $42.34. The market
value of the liabilities has decreased from $430 to $409.61, or $20.69. Therefore, the
market value of the equity will decrease by $42.34 - $20.69 = 21.65.
24. If a bank manager is certain that interest rates were going to increase within the next six months, how should the
bank manager adjust the bank’s maturity gap to take advantage of this anticipated increase? What if the
manager believed rates would fall? Would your suggested adjustments be difficult or easy to achieve?
When rates rise, the value of the longer-lived assets will fall by more the shorter-lived liabilities.
If the maturity gap (or duration gap) is positive, the bank manager will want to shorten the
maturity gap. If the repricing gap is negative, the manager will want to move it towards zero or
positive. If rates are expected to decrease, the manager should reverse these strategies. Changing
the maturity, duration, or funding gaps on the balance sheet often involves changing the mix of
assets and liabilities. Attempts to make these changes may involve changes in financial strategy
for the bank which may not be easy to accomplish. Later in the text, methods of achieving the
same results using derivatives will be explored.
25. Consumer Bank has $20 million in cash and a $180 million loan portfolio. The assets are funded with demand
deposits of $18 million, a $162 million CD and $20 million in equity. The loan portfolio has a maturity of 2
years, earns interest at the annual rate of 7 percent, and is amortized monthly. The bank pays 7 percent annual
interest on the CD, but the interest will not be paid until the CD matures at the end of 2 years.
a.
What is the maturity gap for Consumer Bank?
MA = [0*$20 + 2*$180]/$200 = 1.80 years
ML = [0*$18 + 2*$162]/$180 = 1.80 years
MGAP = 1.80 – 1.80 = 0 years.
b.
Is Consumer Bank immunized or protected against changes in interest rates? Why or why
not?
It is tempting to conclude that the bank is immunized because the maturity gap is zero. However, the cash flow
stream for the loan and the cash flow stream for the CD are different because the loan amortizes monthly and
the CD pays annual interest on the CD. Thus any change in interest rates will affect the earning power of the
loan more than the interest cost of the CD.
c.
Does Consumer Bank face interest rate risk? That is, if market interest rates increase or
decrease 1 percent, what happens to the value of the equity?
The bank does face interest rate risk. If market rates increase 1 percent, the value of the cash and demand
deposits does not change. However, the value of the loan will decrease to $178.19, and the value of the CD will
fall to $159.01. Thus, the value of the equity will be ($178.19 + $20 - $18 - $159.01) = $21.18. In this case, the
increase in interest rates causes the market value of equity to increase because of the reinvestment opportunities
on the loan payments.
If market rates decrease 1 percent, the value of the loan increases to $181.84, and the value
of the CD increases to $165.07. Thus the value of the equity decreases to $18.77.
d. How can a decrease in interest rates create interest rate risk?
1-62
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
The amortized loan payments would be reinvested at lower rates. Thus, even though
interest rates have decreased, the different cash flow patterns of the loan and the CD have
caused interest rate risk.
26.
FI International holds seven-year Acme International bonds and two-year Beta Corporation
bonds. The Acme bonds are yielding 12 percent and the Beta bonds are yielding 14 percent
under current market conditions.
a.
What is the weighted-average maturity of FI’s bond portfolio if 40 percent is in Acme
bonds and 60 percent is in Beta bonds?
Average maturity = 0.40 x 7 years + 0.60 x 2 years = 4 years
b.
What proportion of Acme and Beta bonds should be held to have a weighted-average yield
of 13.5 percent?
Let X*(0.12) + (1 - X)*(0.14) = 0.135. Solving for X, we get 25 percent. In order to get an average yield of 13.5
percent, we need to hold 25 percent of Acme and 75 percent of Beta.
c.
What will be the weighted-average maturity of the bond portfolio if the weighted-average
yield is realized?
The average maturity of the portfolio will decrease to 0.25 x 7 + 0.75 x 2 = 3.25 years.
27. An insurance company has invested in the following fixed-income securities: (a) $10,000,000 of 5-year
Treasury notes paying 5 percent interest and selling at par value, (b) $5,800,000 of 10-year bonds paying 7
percent interest with a par value of $6,000,000, and (c) $6,200,000 of 20-year subordinated debentures paying 9
percent interest with a par value of $6,000,000.
a. What is the weighted-average maturity of this portfolio of assets?
MA = [5*$10 + 10*$5.8 + 20*$6.2]/$22 = 232/22 = 10.55 years
b.
If interest rates change so that the yields on all of the securities decrease 1 percent, how
does the weighted-average maturity of the portfolio change?
To determine the weighted-average maturity of the portfolio for a rate decrease of 1 percent, the new value of
each security must be determined. This calculation will require knowing the yield to maturity of each security
before the rate change.
T-notes are selling at par, so the yield to maturity = 5 percent. Therefore, the new value
FV = 10, PMT = 0.05*10 = 0.5, N = 5, I=4%, Solve for PV = 10.45 or 10,445,182.
10-year bonds: Par = $6,000,000, PV = $5,800,000, Cpn = 7 percent  YTM = 7.485%.
FV = 6, PMT = 0.42, I = 6.485%, N = 10, Solve for PV = 6.22 or 6,222,290
Debentures: Par = $6,000,000, PV = $6,200,000, Cpn = 9 percent  8.644 percent.
1-63
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
FV = 6, PMT = 0.54, I = 7.644%, N = 20, Solve for PV = 6.82 or 6,820,418
The total value of the assets after the change in rates will be $23,487,890, and the
weighted-average maturity will be [5*10,445,182 + 10*6,222,290 +
20*6,820,418]/23,487,890 = 250,857,170/23,487,890 = 10.68 years.
c. Explain the changes in the maturity values if the yields increase by 1 percent.
When interest rates increase 1 percent, the value of the T-note is $9,578,764, the value of
the 10-year bond is $5,414,993, and the value of the debenture is $5,662,882, and the new
value of the assets is $20,656,639. The weighted-average maturity is 10.42 years.
d.
Assume that the insurance company has no other assets. What will be the effect on the
market value of the company’s equity if the interest rate changes in (b) and (c) occur?
Assuming that the company is financed entirely with equity, the market value will increase $1,487,890 when
interest rates decrease 1 percent, and the market value will decrease $1,343,361 when rates increase 1 percent.
Notice that for the same absolute rate change, the increase in value is greater than the decrease in value.
28.
The following is a simplified FI balance sheet:
Assets
Loans
Total Assets
$1,000
0
$1,000
Liabilities and Equity
Deposits
Equity
Total Liabilities & Equity
$850
$150
$1,000
The average maturity of loans is four years, and the average maturity of deposits is two years. Assume loan and
deposit balances are reported as book value, zero-coupon items.
a.
Assume that interest rates on both loans and deposits are 9 percent. What is the market
value of equity?
The value of loans = $1,000/(1.09)4 = $708.43, and the value of deposits = $850/(1.09)2 =
$715.43. The net worth = $708.43 - $715.43 = -$7.0028. (That is, net worth is negative.)
b.
What must be the interest rate on deposits to force the market value of equity to be zero?
What economic market conditions must exist to make this situation possible?
In this case the deposit value should equal the loan value. Thus, $850/(1 + x)2 = $708.43.
Solving for x, we get 9.5374%. That is, deposit rates will have to increase more because
they have a shorter maturity. Note: for those using calculators, you need to compute
I/YEAR after entering 850 = FV, -708.43 = PV, 0 = PMT, 2 = N.
c.
Assume that interest rates on both loans and deposits are 9 percent. What must be the
average maturity of deposits for the market value of equity to be zero?
1-64
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
In this case, we need to solve the equation in part (b) for N. The result is 2.1141 years. If interest rates remain at
9 percent, then the average maturity of deposits has to be higher in order to match the value of a 4-year loan.
29. Gunnison Insurance has reported the following balance sheet (in thousands):
Assets
2-year Treasury note
15-year munis
$175
$165
Total Assets
$340
Liabilities and Equity
1-year commercial paper
5-year note
Equity
Total Liabilities & Equity
$135
$160
$45
$340
All securities are selling at par equal to book value. The two-year notes are yielding 5 percent, and the 15-year
munis are yielding 9 percent. The one-year commercial paper pays 4.5 percent, and the five-year notes pay 8
percent. All instruments pay interest annually.
a.
What is the weighted-average maturity of the assets for Gunnison?
MA = [2*$175 + 15*$165]/$340 = 8.31 years
b. What is the weighted-average maturity of the liabilities for Gunnison?
ML = [1*$135 + 5*$160]/$295 = 3.17 years
c. What is the maturity gap for Gunnison?
MGAP = 8.31- 3.17 = 5.14 years
d.
What does your answer to part (c) imply about the interest rate exposure of Gunnison
Insurance?
Gunnison Insurance is exposed to interest rate risk. If interest rates rise, net worth will decline because the
average maturity of the assets is higher than the average maturity of the liabilities. The opposite holds true if
interest rates fall (That is, net worth will increase.)
e.
Calculate the values of all four securities of Gunnison Insurance’s balance sheet assuming
that all interest rates increase 2 percent. What is the dollar change in the total asset and
total liability values? What is the percentage change in these values?
T-notes:
FV = 175, PMT = 8.75, I = 7%, N = 2, Solve for PV = 168.67
Munis:
FV = 165, PMT = 14.85, I = 11%, N = 15, Solve for PV = 141.27
Commercial Paper:
FV = 135, PMT = 6.075, I = 6.5%, N = 1, Solve for PV = 132.46
Note:
FV = 160, PMT = 12.8, I = 10%, N = 5, Solve for PV = 147.87
1-65
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Total assets = $168.67 + $141.27 = $309.94  A = -$30.06 or -8.84 percent change
Total liabilities = $132.46 + $147.87 = $280.33  L = -$14.67 or -4.97 percent change
f.
What is the dollar impact on the market value of equity for Gunnison? What is the
percentage change in the value of the equity?
E = A - L = -$30.06 – (-$14.67) = -$15.39  -34.2 percent
g. What would be the impact on Gunnison’s market value of equity if the liabilities paid
interest semiannually instead of annually?
The value of liabilities will be lower with semi-annual compounding, increasing the value of net worth. The
one-year CP will decline in value to $132.426. The five-year note will decline in value to $147.645. The value
of equity will increase to $29.869 = ($168.67 + $141.27) - ($132.426 + $147.645).
30.
Scandia Bank has issued a one-year, $1million CD paying 5.75 percent to fund a one-year
loan paying an interest rate of 6 percent. The principal of the loan will be paid in two
installments, $500,000 in 6 months and the balance at the end of the year.
a.
What is the maturity gap of Scandia Bank? According to the maturity model, what does
this maturity gap imply about the interest rate risk exposure faced by the bank?
The maturity gap is 1 year – 1 year = 0. The maturity gap model would state that the portfolio is immunized
against changes in interest rates because assets and liabilities are of equal maturity.
b.
What is the expected net interest income at the end of the year?
Principal received in six months
Interest received in six months (.03 x $1,000,000)
Total
$500,000
$30,000
$530,000
Principal received at the end of the year
Interest received at the end of the year (.03 x $500,000)
Future value of interest received in six months ($530,000 x 1.03*)
Total principal and interest received
$500,000
$15,000
$545,900
$1,060,900
Principal and interest paid on deposits ($1,000,000 x 0.0575)
Net interest income received
$1,057,500
$3,400
* It is assumed that the money will be reinvested at current loan rates. Note that the principal is also included in
the analysis because interest expense is based on $1,000,000.
c.
What would be the effect on annual net interest income of a 2 percent interest rate increase
that occurred immediately after the loan was made? What would be the effect of a 2
percent decrease in rates?
If interest rates increase 2 percent, then the reinvestment benefits of cash flows in six
months will be higher:
1-66
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Principal received in six months
Interest received in six months (.03 x $1,000,000)
Total
$500,000
$30,000
$530,000
Principal received at the end of the year
Interest received at the end of the year (.03 x $500,000)
Future value of interest received in six months ($530,000 x 1.04)
Total principal and interest received
$500,000
$15,000
$551,200
$1,066,200
Principal and interest paid on deposits ($1,000,000 x 0.0575)
Net interest income received
$1,057,500
$8,700
If interest rates decrease by 2 percent, then reinvestment income is reduced.
Principal received in six months
Interest received in six months (.03 x $1,000,000)
Total
$500,000
$30,000
$530,000
Principal received at the end of the year
Interest received at the end of the year (.03 x $500,000)
Future value of interest received in six months ($530,000 x 1.02)
Total principal and interest received
$500,000
$15,000
$540,600
$1,055,600
Principal and interest paid on deposits ($1,000,000 x 0.0575)
Net income received
$1,057,500
$-1,900
d. What do these results indicate about the maturity model’s ability to immunize
portfolios against interest rate exposure?
The results indicate that just matching assets and liabilities by maturity is not sufficient to immunize a portfolio.
If the timing of the cash flows within a period is different for assets and liabilities, the effects of interest rate
changes are different. For a truly effective immunization strategy, one also needs to account for the timing of
cash flows.
31. EDF Bank has a very simple balance sheet. Assets consist of a two-year, $1 million loan that pays an interest
rate of LIBOR plus 4 percent annually. The loan is funded with a two-year deposit on which the bank pays
LIBOR plus 3.5 percent interest annually. LIBOR currently is 4 percent, and both the loan and deposit principal
will be paid at maturity.
a. What is the maturity gap of this balance sheet?
Maturity gap = 2 - 2 = 0 years
b. What is the expected net interest income in year 1 and year 2?
Interest received in year 1
Interest paid in year 1
$80,000
$75,000
Interest received in year 2
Interest paid in year 2
$80,000
$75,000
1-67
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Net interest income in year 1
c.
$5,000
Net interest income in year 2
Immediately prior to the beginning of year 2, LIBOR rates increased to 6 percent. What is
the expected net interest income in year 2? What would be the effect on net interest
income of a 2 percent decrease in LIBOR?
Year 2: If interest rates increase 2 percent
Interest received in year 2
$100,000
Interest paid in year 2
$95,000
Net interest income in year 2 $5,000
32.
$5,000
Year 2: If interest rates decrease 2 percent
Interest received in year 2
$60,000
Interest paid in year 2
$55,000
Net interest income in year 2 $5,000
What are the weaknesses of the maturity model?
First, the maturity model does not consider the degree of leverage on the balance sheet. For
example, if assets are not financed entirely with deposits, a change in interest rates may
cause the assets to change in value by a different amount than the liabilities. Second, the
maturity model does not take into account the timing of the cash flows of either the assets
or the liabilities, and thus reinvestment and/or refinancing risk may become important
factors in profitability and valuation as interest rates change.
1-68
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Chapter 11
Credit Risk: Individual Loan Risk
Chapter Outline
Introduction
Credit Quality Problems
Types of Loans
• Commercial and Industrial Loans
• Real Estate Loans
• Individual (Consumer) Loans
• Other Loans
The Return on a Loan
• The Contractually Promised Return on a Loan
• The Expected Return on a Loan
Retail versus Wholesale Credit Decisions
• Retail
• Wholesale
Measurement of Credit Risk
Default Risk Models
• Qualitative Models
• Credit Scoring Models
Newer Models of Credit Risk Measurement and Pricing
• Term Structure Derivation of Credit Risk
• Mortality Rate Derivation of Credit Risk
• RAROC Models
• Option Models of Default Risk
Summary
Appendix 11A: CreditMetrics
• Rating Migration
• Valuation
• Calculation of VAR
• Capital Requirements
Appendix 11B: Credit Risk+
1-69
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Solutions for End-of-Chapter Questions and Problems: Chapter Eleven
1.
Why is credit risk analysis an important component of bank risk management? What recent
activities by FIs have made the task of credit risk assessment more difficult for both bank
managers and regulators?
Credit risk management is important for bank managers because it determines several features of
a loan: interest rate, maturity, collateral and other covenants. Riskier projects require more
analysis before loans are approved. If credit risk analysis is inadequate, default rates could be
higher and push a bank into insolvency, especially if the markets are competitive and the margins
are low.
Credit risk management has become more complicated over time because of the increase in offbalance-sheet activities that create implicit contracts and obligations between prospective lenders
and buyers. Credit risks of some off-balance-sheet products such as loan commitments, options,
and interest rate swaps, are difficult to assess because the contingent payoffs are not
deterministic, making the pricing of these products complicated.
2.
Differentiate between a secured and an unsecured loan. Who bears most of the risk in a
fixed-rate loan? Why would bankers prefer to charge floating rates, especially for longermaturity loans?
A secured loan is backed by some of the collateral that is pledged to the lender in the event of
default. A lender has rights to the collateral, which can be liquidated to pay all or part of the loan.
In a fixed-rate loan, the lender of the loan bears the risk of interest rate changes; if interest rates
rise, the opportunity cost of lending is higher. If interest rates fall, the lender benefits. Since it is
harder to predict longer-term rates, FIs prefer to charge floating rates for longer-term bonds and
pass the risks on to the borrower.
3.
How does a spot loan differ from a loan commitment? What are the advantages and
disadvantages of borrowing through a loan commitment?
A spot loan involves the immediate takedown of the loan amount by the borrower, while a loan
commitment allows a borrower the option to take down the loan any time during a fixed period
at a predetermined rate. This can be advantageous during periods of rising rates in that the
borrower can borrow as needed at a predetermined rate. If the rates decline, the borrower can
borrow from other sources. The disadvantage is the cost: an up-front fee is required in addition to
a back-end fee for the unused portion of the commitment.
4.
Why is commercial lending declining in importance in the U.S.? What effect does the
decline have on overall commercial lending activities?
Commercial bank lending has been declining in importance because of disintermediation, a
process in which customers are able to access financial markets directly such as in issuing
commercial paper. The total amount of commercial paper outstanding in the U.S. has grown
dramatically over the last decade. Historically, only the most creditworthy borrowers had access
1-70
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
the commercial paper market, but more middle-market firms and financial institutions now have
access to this market. As a consequence of this growth, the pool of borrowers available to
bankers has become smaller and riskier. This makes the credit assessment and monitoring of
loans more difficult.
5.
What are the primary characteristics of residential mortgage loans? Why does the ratio of
adjustable rate mortgages to fixed-rate mortgages in the economy vary over the interest rate
cycle? When would the ratio be highest?
Residential mortgages contracts differ in size, the ratio of the loan amount to the value of the
property, the maturity of the loan, the rate of interest of the loan, and whether the interest rate is
fixed or adjustable. In addition, mortgage agreements differ in the amount of fees, commissions,
discounts, and points that are paid by the borrower.
The ratio of adjustable rate mortgages to fixed-rate mortgages is lowest when interest rates are
low because borrowers prefer to lock in the low market rates for long periods of time. When
rates are high, the adjustable rate mortgages allow borrowers the potential to realize relief from
high interest rates in the future when rates decline.
6.
What are the two major classes of consumer loans at U.S. banks? How do revolving loans
differ from automobile and other consumer installment loans?
Consumer loans can be classified as either nonrevolving or revolving loans. Automobile loans
and fixed-term personal loans usually have a maturity date at which time the loan is expected to
have a zero balance, and thus they are considered to be nonrevolving loans. Revolving loans
usually involve credit card debt, or similar lines of credit, and as a result the balance will rise and
fall as borrowers make payments and utilize the accounts. These accounts typically have
maturities of 1 to 3 years, but the accounts normally are renewed if the payment history is
satisfactory. Many banks often recognize high rates of return on these loans, even though in
recent years, banks have faced chargeoff rates in the range of four to eight percent.
7.
How does the credit card transaction process assist in the credit monitoring function of
financial institutions? Which major parties receive a fee in the typical credit card
transaction? Do the services provided warrant the payment of these associated fees?
Credit card transactions typically must be authorized by the cardholder’s bank. Thus verification
of satisfactory credit quality occurs with each transaction. During the transaction process, fixed
fees are charged to the merchant, the merchant’s bank, and the card issuer. The fees cover the
data processing and technology services necessary to ensure that the revolving credit transaction
process is accomplished.
8.
What are compensating balances? What is the relationship between the amount of
compensating balance requirement and the return on the loan to the FI?
A compensating balance is the portion of a loan that a borrower must keep on deposit with the
credit-granting depository FI. Thus the funds are not available for use by the borrower. As the
1-71
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
amount of compensating balance for a given loan size increases, the effective return on the loan
increases for the lending institution.
9.
County Bank offers one-year loans with a stated rate of 9 percent but requires a
compensating balance of 10 percent. What is the true cost of this loan to the borrower?
How does the cost change if the compensating balance is 15 percent? If the compensating
balance is 20 percent?
The true cost is the loan rate ÷ (1 – compensating balance rate) = 9% ÷ (1.0 – 0.1) = 10 percent.
For compensating balance rates of 15 percent and 20 percent, the true cost of the loan would be
10.59 percent and 11.25 percent respectively. Note that as the compensating balance rate
increases by a constant amount, the true cost of the loan increases at an increasing rate.
10.
Metrobank offers one-year loans with a 9 percent stated or base rate, charges a 0.25 percent
loan origination fee, imposes a 10 percent compensating balance requirement, and must
pay a 6 percent reserve requirement to the Federal Reserve. The loans typically are repaid
at maturity.
a. If the risk premium for a given customer is 2.5 percent, what is the simple promised
interest return on the loan?
The simple promised interest return on the loan is BR + m = 0.09 + 0.025 = 0.115 or 11.5
percent.
b. What is the contractually promised gross return on the loan per dollar lent?
k =1+
f + ( BR + m )
1 − [ b (1 − RR )]
−1=1+
0.0025 + ( 0.09 + 0.025)
1 − [ 0.1(1 − 0.06 )]
−1=1+
0.1175
− 1 = 12.97 percent
0.906
c. Which of the fee items has the greatest impact on the gross return?
The compensating balance has the strongest effect on the gross return on the loan. Without
the compensating balance, the gross return would equal 11.75 percent, a reduction of 1.22
percent. Without the origination fee, the gross return would be 12.69 percent, a reduction
of only 0.28 percent. Eliminating the reserve requirement would cause the gross return to
increase to 13.06 percent, an increase of 0.09 percent.
11.
Why are most retail borrowers charged the same rate of interest, implying the same risk
premium or class? What is credit rationing? How is it used to control credit risks with
respect to retail and wholesale loans?
Most retail loans are small in size relative to the overall investment portfolio of an FI, and the
cost of collecting information on household borrowers is high. As a result, most retail borrowers
are charged the same rate of interest that implies the same level of risk.
1-72
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Credit rationing involves restricting the amount of loans that are available to individual
borrowers. On the retail side, the amount of loans provided to borrowers may be determined
solely by the proportion of loans desired in this category rather than price or interest rate
differences, thus the actual credit quality of the individual borrowers. On the wholesale side, the
FI may use both credit quantity and interest rates to control credit risk. Typically more risky
borrowers are charged a higher risk premium to control credit risk. However, the expected
returns from increasingly higher interest rates that reflect higher credit risk at some point will be
offset by higher default rates. Thus rationing credit through quantity limits will occur at some
interest rate level even though positive loan demand exists at even higher risk premiums.
12.
Why could a lender’s expected return be lower when the risk premium is increased on a
loan? In addition to the risk premium, how can a lender increase the expected return on a
wholesale loan? A retail loan?
An increase in risk premiums indicates a riskier pool of clients who are more likely to default by
taking on riskier projects. This reduces the repayment probability and lowers the expected return
to the lender. In both cases the lender often is able to charge fees that increase the return on the
loan. However, in both cases also, the fees may become sufficiently high as to increase the risk
of nonpayment of default on the loan.
13.
What are covenants in a loan agreement? What are the objectives of covenants? How can
these covenants be negative? Affirmative?
Covenants are restrictions that are written into loan or bond contracts that affect the actions of
the borrower. Negative covenants in effect restrict actions, that is, they are “thou shall not...”
conditions. Common examples include the nonincrease of dividend payments without
permission of the borrower, or the maintenance of net working capital above some minimum
level. Positive covenants encourage actions such as the submission of quarterly financial
statements. In effect both types of covenants are designed and implemented to assist the lending
firm in the monitoring and control of credit risk.
14.
Identify and define the borrower-specific and market-specific factors that enter into the
credit decision. What is the impact of each type of factor on the risk premium?
The borrower-specific factors are:
Reputation: Based on the lending history of the borrower; better reputation implies a lower
risk premium.
Leverage: A measure of the existing debt of the borrower; the larger the debt, the higher
the risk premium.
Volatility of earnings: The more stable the earnings, the lower the risk premium.
Collateral: If collateral is offered, the risk premium is lower.
Market-specific factors include:
Business cycle:
Lenders are less likely to lend if a recession is forecasted.
1-73
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Level of interest rates: A higher level of interest rates may lead to higher default rates, so
lenders are more reluctant to lend under such conditions.
a. Which of these factors is more likely to affect adversely small businesses rather than
large businesses in the credit assessment process by lenders?
Because reputation involves a history of performance over an extended time period, small
businesses that are fairly young in operating time may suffer.
b. How does the existence of a high debt ratio typically affect the risk of the borrower? Is
it possible that high leverage may reduce the risk of bankruptcy (or the risk of financial
distress)? Explain.
Increasing amounts of debt increase the interest charges that must be paid by the borrower,
and thus decrease the amount of cash flows available to repay the debt principal. Cases
have been made that high debt levels require the firm to be very efficient in its managerial
decision making, thus reducing the probability of bankruptcy.
c. Why is the volatility of the earnings stream of a borrower important to a lender?
A highly volatile earnings stream increases the probability that the borrower cannot meet
the fixed interest and principal payments for any given capital structure.
15.
Why is the degree of collateral as specified in the loan agreement of importance to the
lender? If the book value of the collateral is greater than or equal to the amount of the loan,
is the credit risk of the lender fully covered? Why, or why not?
Collateral provides the lender with some assets that can be used against the amount of the loan in
the case of default. However, collateral has value only to the extent of its market value, and thus
a loan fully collateralized at book value may not be fully collateralized at market value. Further,
errors in the recording of collateralized positions may limit or severely reduce the protected
positions of a lender.
16.
Why are FIs consistently interested in the expected level of economic activity in the
markets in which they operate? Why is monetary policy of the Federal Reserve System
important to FIs?
During recessions firms in certain industries are much more likely to suffer financial distress
because of the slowdown in economic activity. Specifically, the consumer durables industries
are particularly hard hit because of cutbacks in spending by consumers. Fed monetary actions
that increase interest rates cause FIs to sustain a higher cost of funds and cause borrowers to
increase the risk of investments. The higher cost of funds to the FI can be passed along to the
borrower, but the increased risk in the investment portfolio necessary to generate returns to cover
the higher funding cost to the borrower may lead to increased default risk realization. Thus
actions by the Fed often are signals of future economic activity.
1-74
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
17.
What are the purposes of credit scoring models? How could these models possibly assist
an FI manager to better administer credit?
Credit scoring models are used to calculate the probability of default or to sort borrowers into
different default risk classes. The primary benefit is to improve the accuracy of predicting
borrower’s performance without using additional resources. This benefit results in fewer
defaults and chargeoffs to the FI.
The models use data on observed economic and financial borrower characteristics to assist an FI
manager in (a) identifying factors of importance in explaining default risk, (b) evaluating the
relative degree of importance of these factors, (c) improving the pricing of default risk, (d)
screening bad loan applicants, and (e) more efficiently calculating the necessary reserves to
protect against future loan losses.
18.
Suppose the estimated linear probability model is PD = 0.3X1 + 0.2X2 - .05X3 + error,
where X1 = 0.75 is the borrower's debt/equity ratio; X2 = 0.10 is the volatility of borrower
earnings; and X3 = 0.10 is the borrower’s profit ratio.
a. What is the projected probability of default for the borrower?
PD = 0.3(.75) + 0.2(.25) - 0.05(.10) = 0.27
b. What is the projected probability of repayment if the debt/equity ratio is 2.5?
PD = 0.3(2.5) + 0.2(.25) - 0.05(.10) = 0.795
The expected probability of repayment is 1 - 0.795 = 0.205.
c. What is a major weakness of the linear probability model?
A major weakness of this model is that the estimated probabilities can be below 0 or above
1.0, an occurrence that does not make economic or statistical sense.
19.
Describe how a linear discriminant analysis model works. Identify and discuss the
criticisms that have been made regarding the use of this type of model to make credit risk
evaluations.
Linear discriminant models divide borrowers into high or low default classes contingent on their
observed characteristics. The overall measure of default risk classification (Z) depends on the
values of various financial ratios and the weighted importance of these ratios based on the past or
observed experience. These weights are derived from a discriminant analysis model.
Several criticisms have been levied against these types of models. First, the models identify only
two extreme categories of risk, default or no default. The real world considers several categories
of default severity. Second, The relative weights of the variables may change over time.
Further, the actual variables to be included in the model may change over time. Third, hard to
define, but potentially important, qualitative variables are omitted from the analysis. Fourth, the
1-75
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
real-world database of defaulted loans is very incomplete. Finally, the model is very sensitive to
changes in variables. A change in sales of 40 percent may cause the model to provide different
accept/reject decisions, but a decrease in sales in the real world normally is not seen as hard
evidence that credit should be denied or withdrawn from an otherwise successful company.
20.
MNO, Inc., a publicly traded manufacturing firm in the United States, has provided the
following financial information in its application for a loan.
Assets
Cash
Accounts Receivables
Inventory
$ 20
$ 90
$ 90
Plant and equipment
Total Assets
$500
$700
Liabilities and Equity
Accounts Payable
Notes Payable
Accruals
Long Term Debt
Equity
Total Liabilities & Equity
$ 30
$ 90
$ 30
$150
$400
$700
Also assume sales = $500, cost of goods sold = $360, taxes = $56, interest payments = $40,
net income = $44, the dividend payout ratio is 50 percent, and the market value of equity is
equal to the book value.
a. What is the Altman discriminant function value for MNO, Inc.? Recall that:
Net working capital = Current assets minus current liabilities.
Current assets = Cash + accounts receivable + inventories.
Current liabilities = Accounts payable + accruals + notes payable.
EBIT = Revenues - Cost of goods sold - depreciation.
Taxes = (EBIT - Interest)(tax rate).
Net income = EBIT - interest - taxes.
Retained earnings = Net income (1 - dividend payout ratio)
Altman’s discriminant function is given by: Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5
Assume prior retained earnings are zero.
X1 = (200 -30 -30 -90)/ 700 = .0714
X1 = Working capital/total assets (TA)
X2 = 22 / 700 = .0314
X2 = Retained earnings/TA
X3 = 140 / 700 = .20
X3 = EBIT/TA
X4 = 400 / 150 = 2.67
X4 = Market value of equity/long term debt
X5 = 500 / 700 = .7143
X5 = Sales/TA
Z = 1.2(0.07) + 1.4(0.03) + 3.3(0.20) + 0.6(2.67) + 1.0(0.71) = 3.104
= .0857 + .044 + .66
+ 1.6
+ .7143 = 3.104
b. Should you approve MNO, Inc.'s application to your bank for a $500 capital expansion
loan?
1-76
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Since the Z-score of 3.104 is greater than 1.81, ABC Inc.’s application for a capital
expansion loan should be approved.
c. If sales for MNO were $300, the market value of equity was only half of book value,
and the cost of goods sold and interest were unchanged, what would be the net income
for MNO? Assume the tax credit can be used to offset other tax liabilities incurred by
other divisions of the firm. Would your credit decision change?
ABC’s net income would be -$100 without taking into account text credits. Note, that
ABC's tax liability is -$56,000. If we assume that ABC uses this tax credit against other
tax liabilities, then:
X1 = (200 - 30 - 30 - 90) / 700 = .0714
X2 = -44 / 700 = -0.0629
X3 = -60 / 700 = -0.0857
X4 = 200 / 150 = 1.3333
X5 = 300 / 700 = 0.4286
Since ABC's Z-score falls to $.9434 < 1.81, credit should be denied.
d. Would the discriminant function change for firms in different industries? Would the
function be different for retail lending in different geographic sections of the country?
What are the implications for the use of these types of models by FIs?
The discriminant function models are very sensitive to the weights for the different
variables. Since different industries have different operating characteristics, a reasonable
answer would be affirmative with the condition that there is no reason that the functions
could not be similar for different industries. In the retail market, the demographics of the
market play a big role in the value of the weights. For example, credit card companies
often evaluate different models for different areas of the country. Because of the sensitivity
of the models, extreme care should be taken in the process of selecting the correct sample
to validate the model for use.
21.
Consider the coefficients of Altman’s Z-score. Can you tell by the size of the coefficients
which ratio appears most important in assessing the creditworthiness of a loan applicant?
Explain.
Although X3, or EBIT/total assets has the highest coefficient (3.3), it is not necessarily the most
important variable. Since the value of X3 is likely to be small, the product of 3.3 and X3 may be
quite small. For some firms, particularly those in the retail business, the asset turnover ratio, X5
may be quite large and the product of the X5 coefficient (1.0) and X5 may be substantially larger
than the corresponding number for X3. Generally, the factor that adds most to the Z score varies
from firm to firm and industry to industry.
1-77
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
22.
If the rate of one-year T-Bills currently is 6 percent, what is the repayment probability for
each of the following two securities? Assume that if the loan is defaulted, no payments are
expected. What is the market-determined risk premium for the corresponding probability
of default for each security?
a. One-year AA rated bond yielding 9.5 percent?
Probability of repayment
= p = (1 + I)/(1 + k)
For an AA-rated bond
= (1 + .06)/ (1 + .095) = 0.968, or 96.8 percent
The market determined risk premium is 0.095 – 0.060 = 0.035 or 3.5 percent
b. One-year BB rated bond yielding 13.5 percent?
Probability of repayment
For BB-rated bond
= p = (1 + I)/(1 + k)
= (1 + .06)/(1 + .135) = 93.39 percent
The market determined risk premium is 0.135 – 0.060 = 0.075 or 7.5 percent
23.
A bank has made a loan charging a base lending rate of 10 percent. It expects a probability
of default of 5 percent. If the loan is defaulted, it expects to recover 50 percent of its money
through the sale of its collateral. What is the expected return on this loan?
E(r) = p(1 + k) + (1 - p)(1 + k)( ) where  is the percentage generated when the loan is
defaulted. E(r) = .95(1 + .10) + .05(1 + .10)(.50) = 1.0450 + .0275 = 1.0725 - 1.0 = 7.25%
24.
Assume a one-year T-Bill is currently yielding 5.5 percent, and a AAA-rated discount bond
with similar maturity is yielding 8.5 percent.
a. If the expected recovery from collateral in the event of default is 50 percent of principal
and interest, what is the probability of repayment of the AAA-rated bond? What is the
probability of default?
p(1 + k) +  (1 - p)(1 + k) = 1+I. Solve for the probability of repayment (p):
1+ i
−  1.055 − 0.5
1+ k
p=
= 1.085
= 0.9447 or 94.47 percent
1− 
1 − 0.5
Therefore the probability of default is 1.0 - .9447 = 0.0553 or 5.53 percent.
b. What is the probability of repayment of the AAA-rated bond if the expected recovery
from collateral in the case of default is 94.47 percent of principal and interest? What is
the probability of default?
1-78
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
1+ i
−  1.055 − 0.9447
1+ k
p=
= 1.085
= 0.5000 or 50.00 percent
1− 
1 − 0.9447
Therefore the probability of default is 1.0 – 0.5000 = 0.5000 or 50.00 percent.
c. What is the relationship between the probability of default and the proportion of
principal and interest that may be recovered in the case of default on the loan?
The proportion of the loan’s principal and interest that is collectible on default is a perfect
substitute for the probability of repayment should such defaults occur.
25.
What is meant by the phrase marginal default probability? How does this term differ from
cumulative default probability? How are the two terms related?
Marginal default probability is the probability of default in the given time period, whereas
cumulative default probability is the probability of default across several time periods. For
example, the cumulative default probability across two time periods is given below, where (p) is
the probability of nondefault in a given time period.
CP2 = 1 – (p1) (p2)
26.
Calculate the term structure of default probabilities over three years using the following
spot rates from the Treasury and corporate bond (pure discount) yield curves. Be sure to
calculate both the annual marginal and the cumulative default probabilities.
Spot
1 year
5.0%
7.0%
Treasury Bonds
BBB rated Bonds
Spot
2 year
6.1%
8.2%
Spot
3 year
7.0%
9.3%
The notation used for implied forward rates is f12 = forward rate from period 1 to period 2.
Treasury Securities
(1.061)2 = (1.05)(1 + f12 )
f12 = 7.21%
BBB Graded Debt
(1.082)2 = (1.07)(1 + f12 )
f12 = 9.41%
(1.07)3 = (1.061)2(1 + f23 )
f23 = 8.82%
(1.093)3 = (1.082)2(1 + f23 )
f23 = 11.53%
Using the implied forward rates, estimate the annual marginal probability of repayment:
p01(1.07) = 1.05
=> p1 = 98.13 percent
1-79
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
p12(1.0941) = 1.0721
p23 (1.1153) = 1.0882
=> p2 = 97.99 percent
=> p3 = 97.57 percent
Using marginal probabilities, estimate the cumulative probability of default:
cp02
cp03
27.
= 1 - (p1 )(p2 )
= 1 - (.9813)(.9799) = 3.84 percent
= 1 - (p1 )(p2 )(p3 )
= 1 - (.9813)(.9799)(.9757) = 6.18 percent
The bond equivalent yields for U.S. Treasury and A-rated corporate bonds with maturities
of 93 and 175 days are given below:
Bond Maturities
U.S. Treasury
A-rated corporate
Spread
93 days
8.07%
8.42%
0.35%
175 days
8.11%
8.66%
0.55%
a. What are the implied forward rates for both an 82-day Treasury and an 82-day A-rated
bond beginning in 93 days? Use daily compounding on a 365-day year basis.
.
The forward rate, f, for the period 93 days to 175 days, or 82 days, for the Treasury is:
(1 + 0.0811)175/365 = (1 + 0.0807)93/365 (1 + f )82/365
 f = 8.16 percent
The forward rate, f, for the corporate bond for the 82-day period is:
(1 + 0.0866)175/365 = (1 + 0.0842)93/365 (1 + f )82/365
 f = 8.933%
b. What is the implied probability of default on A-rated bonds over the next 93 days?
Over 175 days?
The probability of repayment of the 93-day A-rated bond is:

p(1 + 0.0842)93/365 = (1 + 0.0807)93/365
p = 99.92 percent
Therefore, the probability of default is (1 - p) = (1 - .9992) = 0.0008 or 0.08 percent.
The probability of repayment of the 175-day A-rated bond is:

p(1 + 0.0866)175/365 = (1 +0.0811)175/365
p = 99.76 percent
Therefore, the probability of default is (1 - p) = (1 - .9976) = 0.0024 or 0.24 percent.
c. What is the implied default probability on an 82-day A-rated bond to be issued in 93
days?
The probability of repayment of the A-rated bond for the period 93 days to 175 days, p, is:
1-80
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
 p = .9984, or 99.84 percent
p (1.08933)82/365 = (1 + 0.0816)82/365
Therefore, the probability of default is (1 - p) or 0.0016 or 0.16 percent.
28.
What is the mortality rate of a bond or loan? What are some of the problems with using a
mortality rate approach to determine the probability of default of a given bond issue?
Mortality rates reflect the historic default risk experience of a bond or a loan. One major
problem is that the approach looks backward rather than forward in determining probabilities of
default. Further, the estimates are sensitive to the time period of the analysis, the number of
bond issues, and the sizes of the issues.
29.
The following is a schedule of historical defaults (yearly and cumulative) experienced by
an FI manager on a portfolio of commercial and mortgage loans.
Loan Type
Commercial:
Annual default
Cumulative default
Mortgage:
Annual default
Cumulative default
1 Year
Years after Issuance
2 Years
3 Years
4 Years
5 Years
0.00%
______
______
0.10%
0.50%
______
______
0.80%
0.30%
______
0.10%
______
0.25%
______
0.60%
______
______
1.64%
0.80%
______
a. Complete the blank spaces in the table.
Commercial: Annual default
Cumulative default:
Mortgage: Yearly default
Cumulative default
0.00%, 0.10%, 0.50%, 0.20%, and 0.30%
0.00%, 0.10%, 0.60%, 0.80%, and 1.10%
0.10%, 0.25%, 0.60%, 0.70%, and 0.80%
0.10%, 0.35%, 0.95%, 1.64%, and 2.43%
Note: The annual survival rate is pt = 1 – annual default rate, and the cumulative default
rate for n = 4 of mortgages is 1 – (p1* p2* p3* p4) = 1 – (0.999*0.9975*0.9940*0.9930).
b. What are the probabilities that each type of loan will not be in default after 5 years?
The cumulative survival rate is = (1-mmr1)*(1-mmr2)*(1-mmr3)*(1-mmr4)*(1-mmr5)
where mmr = marginal mortality rate
Commercial loan = (1-0.)*(1-0.001)*(1-0.005)*(1-0.002)*(1-0.003) = 0.989 or 98.9%.
Mortgage loan = (1-0.001)*(1-0.0025)*(1-0.006)*(1-0.007)*(1-0.008) = 0.9757 or 97.57%.
c. What is the measured difference between the cumulative default (mortality) rates for
commercial and mortgage loans after four years?
Looking at the table, the cumulative rates of default in year 4 are 0.80% and 1.64%,
respectively, for the commercial and mortgage loans. Another way of estimation is:
1-81
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Cumulative mortality rate (CMR) = 1- (1 - mmr1)(1 - mmr2)(1 - mmr3)(1 - mmr4)
For commercial loan
= 1- (1 - 0.0010)(1 - 0.0010)(1 - 0.0020)(1 - 0.0050)
= 1- .9920 = 0.0080 or 0.80 percent.
For mortgage loan
= 1- (1 - 0.0010)(1 - 0.0025)(1 - 0.0060)(1 - 0.0070)
= 1- .98359 = 0.01641 or 1.641 percent.
The difference in cumulative default rates is 1.641 - .80 = .8410 percent.
30.
The Table below shows the dollar amounts of outstanding bonds and corresponding default
amounts for every year over the past five years. Note that the default figures are in millions
while those outstanding are in billions. The outstanding figures reflect default amounts and
bond redemptions.
Years after Issuance
Loan Type
1 Year
2 Years 3 Years 4 Years 5 Years
A-rated: Annual default (millions)
0
0
0
$1
$2
Outstanding (billions)
$100
$95
$93
$91
$88
B-rated: Annual default (millions)
Outstanding (billions)
0
$100
$1
$94
$2
$92
$3
$89
$4
$85
C-rated: Annual default (millions)
Outstanding (billions)
$1
$100
$3
$97
$5
$90
$5
$85
$6
$79
a. What are the annual and cumulative default rates of the above bonds?
A-rated Bonds
Millions Millions
Annual Survival = Cumulative % Cumulative
Year Default Balance
Default 1 - An. Def. Default Rate
Default Rate
1
0
100,000
0.000000
1.000000
0.000000
0.0000%
2
0
95,000
0.000000
1.000000
0.000000
0.0000%
3
0
93,000
0.000000
1.000000
0.000000
0.0000%
4
1
91,000
0.000011
0.999989
0.000011
0.0011%
5
2
88,000
0.000023
0.999977
0.000034
0.0034%
Where cumulative default for nth year = 1 - product of survival rates to that year.
B-rated Bonds
Millions
Year Default
1
0
2
1
3
2
4
3
5
4
Millions
Balance
100,000
94,000
92,000
89,000
85,000
Annual Survival = Cumulative % Cumulative
Default 1 - An. Def. Default Rate
Default Rate
0.000000
1.000000
0.000000
0.0000%
0.000011
0.999989
0.000011
0.0011%
0.000022
0.999978
0.000032
0.0032%
0.000034
0.999966
0.000066
0.0066%
0.000047
0.999953
0.000113
0.0113%
1-82
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
C-rated Bonds
Millions
Year Default
1
1
2
3
3
5
4
5
5
6
Millions
Balance
100,000
97,000
90,000
85,000
79,000
Annual Survival = Cumulative % Cumulative
Default 1 - An. Def. Default Rate
Default Rate
0.000010
0.999990
0.000010
0.0010%
0.000031
0.999969
0.000041
0.0041%
0.000056
0.999944
0.000096
0.0096%
0.000059
0.999941
0.000155
0.0155%
0.000076
0.999924
0.000231
0.0231%
Years after Issuance
Bond Type
1 Year
2 Years 3 Years 4 Years 5 Years
A-rated: Yearly default
0%
0%
0% 0.0011% 0.0023%
Cumulative default
0%
0%
0% 0.0011% 0.0034%
B-rated: Yearly default
Cumulative default
0%
0%
0.0011% 0.0022% 0.0034% 0.0047%
0.0011% 0.0032% 0.0066% 0.0113%
C-rated: Yearly default
0.0010%
Cumulative default 0.0010%
0.0031% 0.0056% 0.0059% 0.0076%
0.0041% 0.0096% 0.0155% 0.0231%
Note: These percentage values seem very small. More reasonable values can be obtained
by increasing the default dollar values by a factor of ten, or by decreasing the outstanding
balance values by a factor of 0.10. Either case will give the same answers that are shown
below. While the percentage numbers seem somewhat more reasonable, the true values of
the problem are (a) that default rates are higher on lower rated assets, and (b) that the
cumulative default rate involves more than the sum of the annual default rates.
C-rated Bonds
Test with 10x default.
Millions Millions
Annual Survival = Cumulative % Cumulative
Year Default Balance
Default 1 - An. Def. Default Rate
Default Rate
1
10
100,000
0.000100
0.999900
0.000100
0.0100%
2
30
97,000
0.000309
0.999691
0.000409
0.0409%
3
50
90,000
0.000556
0.999444
0.000965
0.0965%
4
50
85,000
0.000588
0.999412
0.001552
0.1552%
5
60
79,000
0.000759
0.999241
0.002311
0.2311%
More meaningful to use 0.10x balance, will get same result.
31.
What is RAROC? How does this model use the concept of duration to measure the risk
exposure of a loan? How is the expected change in the credit premium measured? What
precisely is LN in the RAROC equation?
RAROC is a measure of expected loan income in the form of interest and fees relative to some
measure of asset risk. The RAROC model uses the duration model formulation to measure the
change in the value of the loan for given changes or shocks in credit quality. The change in
1-83
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
credit quality (R) is measured by finding the change in the spread in yields between Treasury
bonds and bonds of the same risk class of the loan. The actual value chosen is the highest
change in yield spread for the same maturity or duration value assets. In this case, LN
represents the change in loan value or the change in capital for the largest reasonable adverse
changes in yield spreads. The actual equation for LN looks very similar to the duration
equation.
RAROC =
Net Income
Risk ( or LN )
32.
where LN = − D
R
LN
x LN x
.
where R is the change in yield spread
1+ R
A bank is planning to make a loan of $5,000,000 to a firm in the steel industry. It expects
to charge a servicing fee of 50 basis points. The loan has a maturity of 8 years and a
duration of 7.5 years. The cost of funds (the RAROC benchmark) for the bank is 10
percent. Assume the bank has estimated the maximum change in the risk premium on the
steel manufacturing sector to be approximately 4.2 percent, based on two years of historical
data. The current market interest rate for loans in this sector is 12 percent.
a. Using the RAROC model, determine whether the bank should make the loan?
RAROC = Fees and interest earned on loan/ Loan or capital risk
Loan risk, or LN = -DLN*LN*(R/(1 + R) = = -7.5 * $5m * (.042/1.12) = -$1,406,250
Expected interest
= 0.12 x $5,000,000
= $600,000
Servicing fees
= 0.0050 x $5,000,000 = $25,000
Less cost of funds
= 0.10 x $5,000,000
= -$500,000
Net interest and fee income
= $125,000
RAROC = $125,000/1,406,250 = 8.89 percent. Since RAROC is lower than the cost of
funds to the bank, the bank should not make the loan.
b. What should be the duration in order for this loan to be approved?
For RAROC to be 10 percent, loan risk should be:
$125,000/LN = 0.10  LN = 125,000 / 0.10 = $1,250,000
 -DLN * LN * (R/(1 + R)) = 1,250,000
DLN = 1,250,000/(5,000,000 * (0.042/1.12)) = 6.67 years.
Thus, this loan can be made if the duration is reduced to 6.67 years from 7.5 years. The
duration can be reduced.
c. Assuming that duration cannot be changed, how much additional interest and fee
income would be necessary to make the loan acceptable?
Necessary RAROC = Income/Risk  Income = RAROC * Risk
1-84
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
= $1,406,250 *0.10 = $140,625
Therefore, additional income = $140,625 - $125,000 = $15,625.
d. Given the proposed income stream and the negotiated duration, what adjustment in the
risk premium would be necessary to make the loan acceptable?
$125,000/0.10 = $1,250,000  -$1,250,000 = -7.5*$5,000,000*(R/1.12)
Thus R = 1.12(-$1,250,000)/(-7.5*$5,000,000) = 0.0373
33.
A firm is issuing a two-year debt in the amount of $200,000. The current market value of
the assets is $300,000. The risk-free rate is 6 percent, and the standard deviation of the rate
of change in the underlying assets of the borrower is 10 percent. Using an options
framework, determine the following:
a. The current market value of the loan.
b. The risk premium to be charged on the loan.
The following need to be estimated first: d, h1 and h2 .
d = Be-rt /A = $200,000e-.06(2) /300,000 = .5913 or 59.13 percent.
h1 = -[0.5*(.10)2 *2 - ln(.5913)]/(.10)21/2 = -3.7863
h2 = -[0.5*(.10)2 *2 + ln(.5913)]/(.10)21/2 = 3.6449
Current market value of loan
= l(t) = Be-rt [N(h1)1/d + N(h2)]
= $177,384.09[1.6912 * N(-3.7863) + N(3.6449)]
= $177,384.09[1.6912 * 0.0001 + 0.9999] = $177,396.35
The risk premium k – I = (-1/t) ln[N(h2) + (1/d)N(h1)]
= (-½)ln[0.9999 + 1.6912*0.0001] = 0.00035
34.
A firm has assets of $200,000 and total debts of $175,000. Using an option pricing model,
the implied volatility of the firm’s assets is estimated at $10,730. Under the KMV method,
what is the expected default frequency (assuming a normal distribution for assets)?
The firm will be in technical bankruptcy if the value of the assets fall’s below $175,000. If  =
$10,730, then it takes 25,000/10,730 = 2.33 standard deviations for the assets to fall below this
value. Under the assumption that the market value of the assets are normally distributed, then
2.33 represents a 1 percent probability that the firm will become bankrupt.
35.
Carman County Bank (CCB) has outstanding a $5,000,000 face value, adjustable rate loan
to a company that has a leverage ratio of 80 percent. The current risk free rate is 6 percent,
and the time to maturity on the loan is exactly ½ year. The asset risk of the borrower, as
measured by the standard deviation of the rate of change in the value of the underlying
assets, is 12 percent. The normal density function values are given below:
1-85
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
h
-2.55
-2.60
-2.65
-2.70
-2.75
N(h)
0.0054
0.0047
0.0040
0.0035
0.0030
h
2.50
2.55
2.60
2.65
2.70
N(h)
0.9938
0.9946
0.9953
0.9960
0.9965
a. Use the Merton option valuation model to determine the market value of the loan.
The following need to be estimated first: d, h1 and h2 .
h1 = -[0.5*(0.12)2*0.5 - ln(0.8)]/(0.12)0.5 = -0.226744/0.084853 = -2.672198
h2 = -[0.5*(0.12)2*0.5 + ln(0.8)]/(0.12)0.5 = 0.219544/0.084853 = 2.587346
Current market value of loan
= l(t) = Be-rt [N(h1)1/d + N(h2)]
= $4,852,227.67[1.25*N(-2.672198) + N(2.587346)]
= $4,852,227.67 [1.25*0.003778 + 0.995123]
= $4,851,478.00
b. What should be the interest rate for the last six months of the loan?
The risk premium k – I = (-1/t) ln[N(h2) + (1/d)N(h1)]
= (-1/0.5)ln[0.995123 + 1.25*0.003778] = 0.000308
The loan rate = risk-free rate plus risk premium = 0.06 + 0.000308 = 0.060308 or 6.0308%.
The questions and problems that follow refer to Appendixes 11A and 11B. Refer to the example
information in Appendix 11A.
36.
From Table 11A-1, what is the probability of a loan upgrade? A loan downgrade?
The probability of an upgrade is 5.95% + 0.33% + 0.02% = 6.30%. The probability of a
downgrade is 5.30% + 1.17% + 0.12% = 5.59%.
a. What is the impact of a rating upgrade or downgrade?
The effect of a rating upgrade or downgrade will be reflected on the credit-risk spreads or
premiums on loans, and thus on the implied market value of the loan. A downgrade should
cause this credit spread premium to rise.
b. How is the discount rate determined after a credit event has occurred?
The discount rate for each year in the future in which cash flows are expected to be
received includes the forward rates from the current Treasury yield curve plus the annual
1-86
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
credit spreads for loans of a particular rating class for each year. These credit spreads are
determined by observing the spreads of the corporate bond market over Treasury securities.
c. Why does the probability distribution of possible loan values have a negative skew?
The negative skew occurs because the probability distribution is non-normal. The potential
downside change in a loan’s value is greater than the possible upside change in value.
d. How do the capital requirements of the CreditMetrics approach differ from those of the
BIS and Federal Reserve System?
The Fed and the BIS require the capital reserve to be 8 percent of the book value of the
loan. Under CreditMetrics each loan is likely to have a different VAR and thus a different
implied capital requirement. Further, this required capital is likely to be greater than 8
percent of book value because of the non-normality of the probability distributions.
37.
A five-year fixed-rate loan of $100 million carries a 7 percent annual interest rate. The
borrower is rated BB. Based on hypothetical historical data, the probability distribution
given below has been determined for various ratings upgrades, downgrades, status quo, and
default possibilities over the next year. Information also is presented reflecting the forward
rates of the current Treasury yield curve and the annual credit spreads of the various
maturities of BBB bonds over Treasuries.
New Loan
Probability
Value plus
Forward Rate Spreads at time t
Rating
Distribution Coupon $
t
rt%
st %
AAA
0.01%
$114.82
1
3.00%
0.72%
AA
0.31%
$114.60
2
3.40%
0.96%
A
1.45%
$114.03
3
3.75%
1.16%
BBB
6.05%
4
4.00%
1.30%
BB
85.48%
$108.55
B
5.60%
$98.43
CCC
0.90%
$86.82
Default
0.20%
$54.12
a. What is the present value of the loan at the end of the one-year risk horizon for the case
where the borrower has been upgraded from BB to BBB?
PV = $7 +
$7
$7
$7
$107
+
+
+
= $113.27 million
2
3
1.0372 (1.0436) (1.0491) (1.0530) 4
b. What is the mean (expected) value of the loan at the end of year one?
The solution table on the following page reveals a value of $108.06.
c. What is the volatility of the loan value at the end of the year?
1-87
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
The volatility or standard deviation of the loan value is $4.19.
d. Calculate the 5 percent and 1 percent VARs for this loan assuming a normal
distribution of values.
The 5 percent VAR is 1.65 x $4.19 = $6.91.
The 1 percent VAR is 2.33 x $4.19 = $9.76.
Year-end
Rating
Probability
AAA
0.0001
AA
0.0031
A
0.0145
BBB
0.0605
BB
0.8548
B
0.056
CCC
0.009
Default
0.002
1.000
Value
$114.82
$114.60
$114.03
$113.27
$108.55
$98.43
$86.82
$54.12
Mean =
Probability
Probability
* Deviation
* Value Deviation Squared
$0.01
6.76
0.0046
$0.36
6.54
0.1325
$1.65
5.97
0.5162
$6.85
5.21
1.6402
$92.79
0.49
0.2025
$5.51
-9.63
5.1968
$0.78
-21.24
4.0615
$0.11
-53.94
5.8197
$108.06 Variance =
17.5740
Standard Deviation =
$4.19
e. Estimate the “approximate” 5 percent and 1 percent VARs using the actual distribution
of loan values and probabilities.
5% VAR = 95% of actual distribution = $108.06 - $102.02 = $6.04
1% VAR = 99% of actual distribution = $108.06 - $86.82 = $21.24
where:
5% VAR is approximated by 0.056 + 0.009 + 0.002 = 0.067 or 6.7 percent, and
1% VAR is approximated by 0.009 + 0.002 = 0.011 or 1.1 percent.
Using linear interpolation, the 5% VAR = $10.65 million and the 1% VAR = $19.31
million. For the 1% VAR, $19.31 = (1 – 0.1/1.1)*$21.24.
f. How do the capital requirements of the 1 percent VARs calculated in parts (d) and (e)
above compare with the capital requirements of the BIS and Federal Reserve System?
The Fed and BIS systems would require 8 percent of the loan value, or $8 million. The 1
percent VAR would require $19.31 million under the approximate method, and $9.76
million in capital under the normal distribution assumption. In each case, the amounts
exceed the Fed/BIS amount.
g. Go to the J.P. Morgan Chase website
(www.jpmorgan.com/RiskManagement/CreditMetrics). What data set information is
provided for use with CreditMetrics?
1-88
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
38.
How does the Credit Risk+ model of Credit Suisse Financial Products differ from the
CreditMetrics model of J.P. Morgan?
Credit Risk attempts to estimate the expected loss of loans and the distribution of these losses
with the focus on calculating the required capital reserves necessary to meet these losses. The
method assumes that the probability of any individual loan defaulting is random, and that the
correlation between the defaults on any pair of loan defaults is zero. CreditMetrics is focussed
on estimating a complete VAR framework.
39.
An FI has a loan portfolio of 10,000 loans of $10,000 each. The loans have an historical
default rate of 4 percent, and the severity of loss is 40 cents per $1. Note: This question
refers to material in Appendix 11B.
a. Over the next year, what are the probabilities of having default rates of 2, 3, 4, 5, and 8
percent?
Pr obability of 2 defaults =
n
Probability
2
0.1465
e − m m n (2.71828) −4 x 4 2 0.018316x16
=
=
= 0.1465
n!
1x 2
2
3
0.1954
4
0.1954
5
0.1563
8
0.0298
b. What would be the dollar loss on the portfolios with default rates of 4 and 8 percent?
Dollar loss of 4 loans defaulting = 4 x 0.40 x $10,000 = $16,000
Dollar loss of 8 loans defaulting = 8 x 0.40 x $10,000 = $32,000
c. How much capital would need to be reserved to meet the 1 percent worst-case loss
scenario? What proportion of the portfolio’s value would this capital reserve be?
The probability of 8 defaults is ~3 percent. The probability of 10 defaults is 0.0106 or
close to 1 percent. The dollar loss of 10 loans defaulting is $40,000. Thus a 1 percent
chance of losing $40,000 exists.
A capital reserve should be held to meet the difference between the unexpected 1 percent
loss rate and the expected loss rate of 4 defaults. This difference is $40,000 minus $16,000
or $24,000. This amount is 0.024 percent of the total portfolio.
1-89
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Solution for End-of-Chapter Questions and Problems: Chapter Eleven
1.
How do loan portfolio risks differ from individual loan risks?
Loan portfolio risks refer to the risks of a portfolio of loans as opposed to the risks of a single
loan. Inherent in the distinction is the elimination of some of the borrower-specific risks of
individual loans because of benefits from diversification.
2.
What is migration analysis? How do FIs use it to measure credit risk concentration? What
are its shortcomings?
Migration analysis uses information from the market to determine the credit risk of an individual
loan or sectoral loans. With this method, FI managers track credit ratings, such as S&P and
Moody’s ratings, of firms in particular sectors or ratings classes for unusual declines to
determine whether firms in a particular sector are experiencing repayment problems. This
information can be used to either curtail lending in that sector or to reduce maturity and/or
increase interest rates. A problem with migration analysis is that the information may be too late,
because ratings agencies usually downgrade issues only after the firm or industry has
experienced a downturn.
3.
What does loan concentration risk mean?
Loan concentration risk refers to the extra risk borne by having too many loans concentrated
with one firm, industry, or economic sector. To the extent that a portfolio of loans represents
loans made to a diverse cross section of the economy, concentration risk is minimized.
4.
A manager decides not to lend to any firm in sectors that generate losses in excess of 5
percent of capital.
a.
If the average historical losses in the automobile sector total 8 percent, what is the
maximum loan a manager can lend to firms in this sector as a percentage of total
capital?
Concentration limit = (Maximum loss as a percent of capital) x (1/Loss rate) = 0.05 x 1/0.08 =
62.5 percent of capital is the maximum amount that can be lent to firms in the automobile sector.
b. If the average historical losses in the mining sector total 15 percent, what is the
maximum loan a manager can lend to firms in this sector as a percentage of total
capital?
Concentration limit = (Maximum loss as a percent of capital) x (1/Loss rate) = 0.05 x 1/0.15 =
33.3 percent of capital is the maximum amount that can be lent to firms in the mining sector.
1-90
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
5.
An FI has set a maximum loss of 2 percent of total capital as a basis for setting
concentration limits on loans to individual firms. If it has set a concentration limit of 25
percent to a firm, what is the expected loss rate for that firm?
Concentration limit = (Maximum loss as a percent of capital) x (1/Loss rate)
25 percent = 2 percent x 1/Loss rate => Loss rate = 0.02/0.25 = 8 percent
6.
Explain how modern portfolio theory can be applied to lower the credit risk of an FI’s
portfolio.
The fundamental lesson of modern portfolio theory is that, to the extent that an FI manager holds
widely traded loans and bonds as assets, or can calculate loan or bond returns, portfolio
diversification models can be used to measure and control the FI’s aggregate credit risk
exposure. By taking advantage of its size, an FI can diversify considerable amounts of credit risk
as long as the returns on different assets are imperfectly correlated with respect to their default
risk adjusted returns. By fully exploiting diversification potential with bonds or loans whose
returns are negatively correlated or that have a low positive correlations with those in the
existing portfolio, the FI manager can produce a set of efficient frontier portfolios, defined as
those portfolios that provide the maximum returns for a given level of risk or the lowest risk for a
given level of returns. By choosing portfolios on the efficient frontier, an FI manager may be
able to reduce credit risk to the fullest extent. As shown in Figure 11-1, a manager’s selection of
a particular portfolio on the efficient frontier is determined by the risk-return trade-off.
7.
Suppose that an FI holds two loans with the following characteristics:
Loan i
1
2
Xi
0.55
0.45
Ri
8%
10
σi
8.55%
9.15
σi 2 .
73.1025%
83.7225
ρ12 = 0.24
σ12 = 18.7758
Calculate the return and risk of the portfolio.
The return on the loan portfolio is:
Rp = 0.55 (8%) + 0.45 (10%) = 8.90%
The risk of the portfolio is:
1-91
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
σp2 = (0.55)2 (73.1025%) + (0.45)2 (83722.5%) + 2 (0.55) (0.45) (18.7758%) = 48.36133%
or
σp2 = (0.55)2 (73.1025%) + (0.45)2 (83722.5%) + 2 (0.55) (0.45) (0.24)(8.55%)(9.15%) =
48.36133%
and σp = √ 48.36133% = 6.95%
Notice that the risk (or standard deviation of returns) of the portfolio, σp (6.95 percent), is less
than the risk of either individual asset (8.55 percent and 9.15 percent, respectively). The low
correlation of the returns of the two loans (0.24) results in an overall reduction of risk when they
are put together in an FI's portfolio.
8.
The Bank of Tinytown has two $20,000 loans that have the following characteristics. Loan
A has an expected return of 10 percent and a standard deviation of returns of 10 percent.
The expected return and standard deviation of returns for loan B are 12 percent and 20
percent, respectively.
a.
If the correlation coefficient between loans A and B is 0.15, what are the expected return
and standard deviation of this portfolio?
XA = XB = $20,000/$40,000 = 0.5
Expected return = 0.5(10%) + 0.5(12%) = 11 percent
Standard deviation = [0.52(0.10)2 + 0.52(0.20)2 + 2(0.5)(0.5)(0.10)(0.20)(.15)]½ = 11.83%
b. What is the standard deviation of the portfolio if the correlation is -0.15?
Standard deviation = [0.52(0.10)2 + 0.52(0.20)2 + 2(0.5)(0.5)(0.10)(0.20)(-0.15)]½ = 10.49%
c.
What role does the covariance, or correlation, play in the risk reduction attributes of
modern portfolio theory?
The risk of the portfolio as measured by the standard deviation is reduced when the covariance is
reduced. If the correlation is less than +1.0, the standard deviation of the portfolio will always be
less than the weighted average of the standard deviations of the individual assets.
1-92
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
9.
Why is it difficult for small banks and thrifts to measure credit risk using modern portfolio
theory?
The basic premise behind modern portfolio theory is the ability to diversify and reduce risk by
eliminating diversifiable risk. Small banks and thrifts may not have the ability to diversify their
asset base, especially if the local markets which they serve have a limited number of industries.
The ability to diversify is even more acute if these loans cannot be traded easily.
10.
What is the minimum risk portfolio? Why is this portfolio usually not the portfolio chosen
by FIs to optimize the return-risk tradeoff?
The minimum risk portfolio is the combination of assets that reduces portfolio risk as measured
by the standard deviation of returns to the lowest possible level. This portfolio usually is not the
optimal portfolio choice because the returns on this portfolio are low relative to other alternative
portfolio selections. By accepting some additional risk, portfolio managers are able to realize a
higher level of return relative to the risk of the portfolio.
11.
The obvious benefit to holding a diversified portfolio of loans is to spread risk exposures so
that a single event does not result in a great loss to an FI. Are there any benefits to not
being diversified?
One benefit to not being diversified is that an FI that lends to a certain industrial or geographic
sector is likely to gain expertise about that sector. Being diversified requires that the FI becomes
familiar with many more areas of business. This may not always be possible, particularly for
small FIs.
12.
A bank vice president is attempting to rank, in terms of the risk-reward trade-off, the loan
portfolios of three loan officers. Information on the portfolios is noted below. How would
you rank the three portfolios?
Expected
Portfolio
A
B 12%
C
Standard
Return
10%
9%
11%
Deviation
8%
10%
Portfolio B dominates portfolio C because B has a higher expected return and a lower standard
deviation. Thus, C is clearly inferior. A comparison of portfolios A and B represents a risk-return
trade-off in that B has a higher expected return, but B also has higher risk. A crude comparison
may use the coefficient of variation or the Sharpe measure, but a judgment regarding which
portfolio is “better” would be based on the risk preference of the vice president.
1-93
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
13. Suppose that an FI holds two loans with the following characteristics.
Loan
1
2
Xi
0.45
0.55
Annual
Spread between
Loan Rate and FI’s
Cost of Funds
5.5%
3.5
Annual
Fees
2.25%
1.75
Loss to FI
Given
Default
30%
20
Expected
Default
Frequency
3.5%
1.0
ρ12 = -0.15
Calculate of the return and risk on the two-asset portfolio using Moody’s Analytics
Portfolio Manager.
The return and risk on loan 1 are:
R1 = (0.055 + 0.0225) - [0.035 x 0.30] = 0.0670 or 6.70%
σ1 = [0.035 x (1 - 0.035)]1/2 x 0.30 = 0.05513 or 5.513%
The return and risk on loan 2 are:
R2 = (0.035 + 0.0175) - [0.01 x 0.20] = 0.0505 or 5.05%
σ2 = [0.01 x (1 - 0.01)]1/2 x 0.20 = 0.01990 or 1.990%
The return and risk of the portfolio is then:
Rp = 0.45 (6.70%) + 0.55 (5.05%) = 5.7925%
σp2 = (0.45)2 (5.513%)2 + (0.55)2 (1.990%)2 + 2 (0.45) (0.55)(-0.15)(5.513%)(1.990%) = 6.53876%
and, σp = (6.53876%)1/2 = 2.56%
14.
CountrySide Bank uses the Moody’s Analytics Portfolio Manager model to evaluate the
risk-return characteristics of the loans in its portfolio. A specific $10 million loan earns 2
percent per year in fees and the loan is priced at a 4 percent spread over the cost of funds
for the bank. Because of collateral considerations, the loss to the bank if the borrower
defaults will be 20 percent of the loan’s face value. The expected probability of default is 3
percent. What is the anticipated return on this loan? What is the risk of the loan?
Expected return = AISi – E(Li) = (0.02 + 0.04) – (0.03 x 0.20) = 0.054 or 5.4 percent
Risk of the loan = Di x LGDi = [0.03(0.97)]½ x 0.20 = 0.0341 or 3.41 percent
1-94
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
15.
Suppose that an FI holds two loans with the following characteristics.
Loan
1
2
Xi
?
?
Annual
Spread between
Loan Rate and FI’s
Cost of Funds
4.0%
2.5
Annual
Fees
1.50%
1.15
Loss to FI
Given
Default
?%
?
Expected
Default
Frequency
4.0%
1.5
ρ12 = -0.10
The return on loan 1 is R1 = 6.25%, the risk on loan 2 is σ2 = 1.8233%, and the return of the
portfolio is Rp = 4.555%. Calculate of the loss given default on loans 1 and 2, the
proportions of loans 1 and 2 in the portfolio, and the risk of the portfolio, σp, using
Moody’s Analytics Portfolio Manager.
R1 = 0.0625 = (0.04 + 0.015) - [0.040 x LGD1] => LGD1 = (0.0625 – (0.04 + 0.015))/(-0.04) = 0.1875
=> σ1 = [0.04(1 - 0.04)]1/2 x 0.1875 = 0.03674 or 3.674%
σ2 = 0.018233 = [(0.015(1 - 0.015)]1/2 x LGD2 => LGD2 = 0.018233/[(0.015(1 - 0.015)]1/2 = 0.15
=> R2 = (0.025 + 0.0115) - [0.015 x 0.15] = 0.03425 or 3.425%
=> Rp = X1 (0.0625) + (1 – X1) (0.03425) = 0.04555
=> X1 = (0.04555 - 0.03425)/(0.0625 - 0.03425) = 0.40 and X2 = 1 - 0.40 = 0.60
σp2 = (0.40)2 (0.03674)2 + (0.60)2 (0.018233)2 + 2 (0.40)(0.60)(-0.10)(0.03674)(0.018233) = 0.000303523
Thus, σp = (0.000303523)1/2 = 0.0174 = 1.74%.
16.
What databases are available that contain loan information at national and regional levels?
How can they be used to analyze credit concentration risk?
Two publicly available databases are (a) the commercial bank Call Reports of the Federal
Reserve Board which contain various information supplied by banks quarterly and (b) the Shared
National Credit database, which provides information on loan volumes of FIs separated by twodigit SIC (Standard Industrial Classification) codes. Such data can be used as a benchmark to
determine whether an FI’s asset allocation is significantly different from the national or regional
average.
1-95
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
17.
Information concerning the allocation of loan portfolios to different market sectors is given
below:
Allocation of Loan Portfolios in Different Sectors (%)
Sectors
National
Bank A
Bank B
Commercial
30%
50%
10%
Consumer
40
30
40
Real Estate
30
20
50
Bank A and Bank B would like to estimate how much their portfolios deviate from the
national average.
a. Which bank is further away from the national average?
Using Xs to represent portfolio holdings:
Bank A
(0.50 - 0.30)2 = 0.0400
(X1j - X1 )2
(X2j - X2 )2
(X3j - X3 )2
n

i −1
( X ij −X i ) 2
n
=
(0.30 - 0.40)2 = 0.0100
(0.20 - 0.30)2 = 0.0100
 (X
i =1
ij
n =3
 = 0.0600
i =1
− X i )2
A = 14.14 percent
n
Bank B deviates from the national average more than Bank A.
Bank B
(0.10 - 0.30)2 = 0.0400
(0.40 - 0.40)2 = 0.0000
(0.50 - 0.30)2 = 0.0400
n =3
 = 0.0800
i =1
B = 16.33 percent
b. Is a large standard deviation necessarily bad for an FI using this model?
No, a higher standard deviation is not necessarily bad for an FI because the FI could have
comparative advantages that are not required or available to a national well-diversified bank. For
example, an FI could generate high returns by serving specialized markets or product niches that
are not well diversified. Further, an FI could specialize in only one product, such as mortgages,
but be well-diversified within this product line by investing in several different types of
mortgages that are distributed both nationally and internationally. This would still enable it to
obtain portfolio diversification benefits that are similar to the national average.
1-96
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
18.
Assume that, on average, national banks engaged primarily in mortgage lending have their
assets diversified in the following proportions: 60 percent residential, 15 percent
commercial, 5 percent international, and 20 percent mortgage-backed securities. A local
bank has the following distribution of mortgage loans: 50 percent residential, 30 percent
commercial, and 20 percent international. How does the local bank differ from national
banks?
Using Xs to represent portfolio holdings:
(X1j - X1 )2
(0.50 - 0.60)2
(X2j - X2 )2
(0.30 - 0.15)2
(X3j - X3 )2
(0.20 - 0.05)2
(X4j - X4 )2
(0.00 - 0.20)2
n

i =1
=
 (X
i =1
ij
= 0.0225
= 0.0225
= 0.0400
n =4
 = 0.0950
( X ij −X i ) 2
n
= 0.0100
i =1
− X i )2
n
 = 15.41 percent
The bank’s standard deviation in its loan portfolio allocation is 15.41 percent. This suggests that
the bank is different from the national average. Whether it is significantly different cannot be
stated without comparing it to other banks.
19.
Over the past 10 years, a bank has experienced the following loan losses on its C&I loans,
consumer loans, and total loan portfolio.
Year
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
C&I Loans
0.0080
0.0088
0.0100
0.0120
0.0104
0.0084
0.0072
0.0080
0.0096
0.0144
Consumer Loans
0.0165
0.0183
0.0210
0.0255
0.0219
0.0174
0.0147
0.0165
0.0201
0.0309
Total Loans
0.0075
0.0085
0.0100
0.0125
0.0105
0.0080
0.0065
0.0075
0.0095
0.0155
1-97
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Using regression analysis on these historical loan losses, the bank has estimated the
following:
XC = 0.002 + 0.8XL and Xh = 0.003 + 1.8XL
where XC = loss rate in the commercial sector, Xh = loss rate in the consumer (household)
sector, XL = loss rate for its total loan portfolio.
a.
If the bank’s total loan loss rates increase by 10 percent, what are the expected loss rate
increases in the commercial and consumer sectors?
Commercial loan loss rates will increase by 0.002 + 0.8(0.10) = 8.20 percent.
Consumer loan loss rates will increase by 0.003 + 1.8(0.10) = 18.30 percent.
b.
In which sector should the bank limit its loans and why?
The bank should limit its loans to the consumer sector because the loss rates are systematically
higher than the loss rates for the total loan portfolio. Loss rates are lower for the commercial
sector. For a 10 percent increase in the total loan portfolio, the consumer loss rate is expected to
increase by 18.30 percent, as opposed to only 8.2 percent for the commercial sector.
20.
What reasons did the Federal Reserve Board offer for recommending the use of subjective
evaluations of credit concentration risk instead of quantitative models? How did this
change in 2006?
The Federal Reserve Board recommended a subjective evaluation of credit concentration risk
instead of quantitative models because (a) current methods to identify credit concentrations were
not reliable and (b) there was insufficient data to develop reliable quantitative models. This
change in June 2006 as the Bank for International Settlements released guidance on sound credit
risk assessment and valuation for loans. The guidance addresses how common data and
processes related to loans may be used for assessing credit risk, accounting for loan impairment
and determining regulatory capital requirements and is structured around ten principles that fall
within two broad categories: i) supervisory expectations concerning sound credit risk assessment
and valuation for loans and ii) supervisory evaluation of credit risk assessment for loans, controls
and capital adequacy.
1-98
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
21.
What rules on credit concentrations has the National Association of Insurance
Commissioners enacted? How are they related to modern portfolio theory?
The NAIC set a maximum limit of 3% that life insurers can hold in securities belonging to a
single issuer. Similarly, the limit is 5% for property-casualty (PC) insurers. This forces life
insurers to hold a minimum of 33 different securities and PC insurers to hold a minimum of 20
different securities. Modern portfolio theory shows that by holding well-diversified portfolios,
investors can eliminate undiversifiable risk and be subject only to market risk. This enables
investors to hold portfolios that provide either high returns for a given level of risk or low risks
for a given level of returns.
22.
An FI is limited to holding no more than 8 percent of its assets in securities of a single
issuer. What is the minimum number of securities it should hold to meet this requirement?
What if the requirements are 2 percent, 4 percent, and 7 percent?
If an FI is limited to holding a maximum of 8 percent of securities of a single issuer, it will be
forced to hold 100/8 = 12.5, or 13 different securities.
For 2%, it will be 100/2, or 50 different securities.
For 4%, it will be 100/4, or 25 different securities.
For 7%, it will be 100/7, or 15 different securities.
The questions and problems that follow refer to Appendixes 11A and 11B. Refer to the information
in Appendix 11A for problems 23 through 25. Refer to Appendix 11B for problem 26.
23.
From Table 11A-1, what is the probability of a loan upgrade? A loan downgrade?
The probability of an upgrade is 5.95% + 0.33% + 0.02% = 6.30%. The probability of a
downgrade is 5.30% + 1.17% + 0.12% = 6.59%.
a. What is the impact of a rating upgrade or downgrade?
The effect of a rating upgrade or downgrade will be reflected on the credit-risk spreads or
premiums on loans and thus on the implied market value of the loan. A downgrade should cause
this credit-risk spread to rise.
b. How is the discount rate determined after a credit event has occurred?
The discount rate for each year in the future in which cash flows are expected to be received
includes the forward rates from the current Treasury yield curve plus the annual credit spreads
for loans of a particular rating class for each year. These credit spreads are determined by
observing the spreads of the corporate bond market over Treasury securities.
1-99
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
c. Why does the probability distribution of possible loan values have a negative skew?
The negative skew occurs because the probability distribution is non-normal. The potential
downside change in a loan’s value is greater than the possible upside change in value.
d. How do the capital requirements of the CreditMetrics approach differ from those of the
BIS and Federal Reserve System?
The Fed and the BIS require the capital reserve to be a fixed percentage of the risk-weighted
book value of the loan (e.g., 8 percent). Under CreditMetrics each loan is likely to have a
different VAR and thus a different implied capital requirement. Further, this required capital is
likely to be greater than 8 percent of the risk-weighted book value because of the non-normality
of the probability distributions.
24
A five-year fixed-rate loan of $100 million carries a 7 percent annual interest rate. The
borrower is rated BB. Based on hypothetical historical data, the probability distribution
given below has been determined for various ratings upgrades, downgrades, status quo, and
default possibilities over the next year. Information also is presented reflecting the forward
rates of the current Treasury yield curve and the annual credit spreads of the various
maturities of BBB bonds over Treasuries.
Rating
AAA
AA
A
BBB
BB
B
CCC
Default
Probability
Distribution
0.01%
0.31
1.45
6.05
85.48
5.60
0.90
0.20
New Loan
Value plus
Coupon $
$114.82m
114.60m
114.03m
Forward Rate Spreads at Time t
t
rt%
ϕt% .
1
3.00%
0.72%
2
3.40
0.96
3
3.75
1.16
4
4.00
1.30
108.55m
98.43m
86.82m
54.12m
a. What is the present value of the loan at the end of the one-year risk horizon for the case
where the borrower has been upgraded from BB to BBB?
PV = $7m +
$7m
$7m
$7m
$107m
+
+
+
= $113.27 million
2
3
1.0372 (1.0436) (1.0491) (1.0530) 4
b. What is the mean (expected) value of the loan at the end of year 1?
The solution table on the following page reveals a value of $108.06 million.
c. What is the volatility of the loan value at the end of year 1?
1-100
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
The volatility or standard deviation of the loan value is $4.19 million.
d. Calculate the 5 percent and 1 percent VARs for this loan assuming a normal
distribution of values.
The 5 percent VAR is 1.65 x $4.19m = $6.91m.
The 1 percent VAR is 2.33 x $4.19m = $9.76m.
Year-end
Rating
AAA
AA
A
BBB
BB
B
CCC
Default
Probability
0.0001
0.0031
0.0145
0.0605
0.8548
0.056
0.009
0.002
1.000
Value
(m of $)
$114.82
114.60
114.03
113.27
108.55
98.43
86.82
54.12
Mean =
Probability
x Value
Deviation
$0.01
6.76
0.36
6.54
1.65
5.97
6.85
5.21
92.79
0.49
5.51
-9.63
0.78
-21.24
0.11
-53.94
$108.06m Variance =
Standard Deviation =
Probability
x Deviation
Squared
0.0046
0.1325
0.5162
1.6402
0.2025
5.1968
4.0615
5.8197
17.5740
$4.19m
e. Estimate the approximate 5 percent and 1 percent VARs using the actual distribution of
loan values and probabilities.
5% VAR = 95% of actual distribution = $108.06m - $98.43m = $9.63m
1% VAR = 99% of actual distribution = $108.06m - $86.82m = $21.24m
where:
5% VAR is approximated by 0.056 + 0.009 + 0.002 = 0.067 or 6.7 percent, and
1% VAR is approximated by 0.009 + 0.002 = 0.011 or 1.1 percent.
Using linear interpolation, the 5% VAR = $10.65 million and the 1% VAR = $19.31 million.
For the 1% VAR, $19.31m = (1 – 0.1/1.1) x $21.24m.
f. How do the capital requirements of the 1 percent VARs calculated in parts (d) and (e)
above compare with the capital requirements of the BIS and Federal Reserve System?
The Fed and BIS systems would require 8 percent of the loan value, or $8 million. The 1 percent
VAR would require $19.31 million under the approximate method, and $9.76 million (2.33 x
$4.19m) in capital under the normal distribution assumption. In each case, the amounts exceed
the Fed/BIS amount.
1-101
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
25.
How does the Credit Risk+ model of Credit Suisse Financial Products differ from the
CreditMetrics model of J.P. Morgan Chase?
CreditRisk+ attempts to estimate the expected loss of loans and the distribution of these losses
with the focus on calculating the required capital reserves necessary to meet these losses. The
method assumes that the probability of any individual loan defaulting is random and that the
correlation between the defaults on any pair of loan defaults is zero. CreditMetrics focuses on
estimating a complete VAR framework.
26.
An FI has a loan portfolio of 10,000 loans of $10,000 each. The loans have a historical
average default rate of 4 percent and the severity of loss is 40 cents per dollar.
a. Over the next year, what are the probabilities of having default rates of 2, 3, 4, 5, and 8
percent?
e − m m n (2.71828) −4 x 4 2 0.018316x16
Pr obability of 2 defaults =
=
=
= 0.1465 = 14.65%
n!
1x 2
2
n
Probability
2
14.65%
3
19.54%
4
19.54%
5
15.63%
8
2.98%
.
b. What would be the dollar loss on the portfolios with default rates of 4 and 8 percent?
Dollar loss of 4 loans defaulting = 4 x 0.40 x $10,000 = $16,000
Dollar loss of 8 loans defaulting = 8 x 0.40 x $10,000 = $32,000
c. How much capital would need to be reserved to meet the 1 percent worst-case loss
scenario? What proportion of the portfolio’s value would this capital reserve be?
The probability of 8 defaults is ~3 percent. The probability of 10 defaults is 0.00529 or close to 1
percent. The dollar loss of 10 loans defaulting is $40,000. Thus, a 1 percent chance of losing
$40,000 exists.
A capital reserve should be held to meet the difference between the unexpected 1 percent loss
rate and the expected loss rate of 4 defaults. This difference is $40,000 minus $16,000 or
$24,000. This amount is 0.024 percent of the total portfolio.
1-102
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Integrated Mini Case: Loan Portfolio Analysis
As a senior loan officer at MC Financial Corp, you have a loan application from a firm in the
biotech industry. While the loan has been approved on the basis of an individual loan, you must
evaluate the loan based on its impact on the risk of the overall loan portfolio. The FI uses the
following three methods to assess its loan portfolio risk.
1. Concentration Limits - The FI currently has lent an amount equal to 40 percent of its capital
to the biotech industry and does not lend to a firm in any sector that generates losses in excess
of 2 percent of capital. The average historical losses in the biotech industry total 5 percent.
Concentration limit = (Maximum loss as a percent of capital) x (1/Loss rate) = .02 x
1/0.05 = 40 percent of capital is the maximum amount that can be lent to firms in the
biotech sector.
MC Financial already has 40 percent of its capital lent out to the biotech industry. To give out
this new loan would put the FI over its concentration limit. Thus, MC Financial should not grant
this loan.
2. Loan Volume-based Model - National and MC Financial’s loan portfolio allocations are as
follows.
Allocation of Loan Portfolios in Different Sectors (%)
Sectors
National
MC Financial
Commercial
30%
40%
Real Estate
50%
45%
Consumer
20%
15%
MC Financial does not want to deviate from the national average by more than 12.25 percent.
Using Xs to represent portfolio holdings:
(X1j - X1 )2
(0.40 - 0.30)2 = 0.0100
(X2j - X2 )2
(0.45 - 0.50)2 = 0.0025
(X3j - X3 )2
(0.15 - 0.20)2 = 0.0025
n

i =1
( X ij −X i ) 2
n
=
 (X
i =1
ij
− X i )2
n
n =3
 = 0.0150
i =1
 = 12.25 percent
1-103
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
The FI’s standard deviation in its loan portfolio allocation is 12.25 percent. To issue
another C&I loan would push MC Financial even further from the national average. Thus,
the FI would not want to give out the loan
3. Loan Loss Ratio-based Model - Based on regression analysis on historical loan losses, the FI
estimates the following loan loss ratio models:
XC&I = 0.001 + 0.85XL and Xcon = 0.003 + 0.65XL
where XC&I = loss rate in the commercial sector, Xcon = loss rate in the consumer
(household) sector, XL = loss rate for its total loan portfolio.
MC Financial’s total increase in the loan loss ratio is expected to be 12 percent next year.
Commercial loan loss rates will increase by 0.001 + 0.85(0.12) = 10.30 percent.
Consumer loan loss rates will increase by 0.003 + .65(0.12) = 8.10 percent.
MC Financial should limit its loans to the commercial sector because the loss rates are
systematically higher than the loss rates for the total loan portfolio. Loss rates are lower for the
consumer sector. For a 12 percent increase in the total losses in the loan portfolio, the
commercial loss rate is expected to increase by 10.30 percent, as opposed to only 8.1 percent for
the consumer sector. Thus, MC Financial should not issue this loan.
Should MC Financial Corp. grant this loan?
Based on all three models, from an overall loan portfolio perspective, MC Financial would not
want to issue this loan to a firm in the biotech sector.
1-104
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 01 - Why Are Financial Institutions Special?
Additional Example for Chapter 12
Allocation of Loan Portfolios in Different Sectors (%)
National
Bank A
Bank B
Sectors
Commercial
Consumer
Real Estate
20%
40%
40%
50%
20%
30%
30%
40%
30%
How different are Banks A and B from the national benchmark? When using this example, note
that there is an implied assumption that Bank A and B belong to a certain size class or have some
common denominator linking them to the national benchmark. If that is the case, then the
solution is to estimate the standard deviation.
We use Xs to represent the portfolio concentrations. X1, X2 and X3 are the national benchmark
percentages
Bank A
Bank B
(X1j - X1 )2
(50 - 20)2 = 900
(30 - 20)2 = 100
(X2j - X2 )2
(20 - 40)2 = 400
(40 - 40)2 = 0
(X3j - X3 )2
(30 - 40)2 = 100
(30 - 40)2 = 100
n

i =1
( X ij −X i ) 2
n
=
 (X
i =1
ij
− X i )2
n
n =3
n =3
 =1,400
 = 200
 = 37.42 percent
 = 14.14 percent
i =1
i =1
Thus we can see here that Bank A is significantly different from the national benchmark
1-105
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.