Selected Questions and Exercises
Chapter 11
2.
3.
8.
9.
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 longer-maturity loans?
How does a spot loan differ from a loan commitment? What are the advantages
and disadvantages of borrowing through a loan commitment?
What are compensating balances? What is the relationship between the amount
of compensating balance requirement and the return on the loan to the FI?
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+
σf + ( 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.
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.
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.
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.
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?
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
= p = (1 + I)/(1 + k)
For BB-rated bond
= (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)(α ) where α 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 AAArated bond? What is the probability of default?
p(1 + k) + γ (1 - p)(1 + k) = 1+I. Solve for the probability of repayment (p):
1+ i
− γ 1.055 − 0.5
1+ k
p=
= 1.085
= 0.9447 or 94.47 percent
1− γ
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+ i
− γ 1.055 − 0.9447
1+ k
p=
= 1.085
= 0.5000 or 50.00 percent
1 − 0.9447
1− γ
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.
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 ΔLN 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 credit quality (ΔR) 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, ΔLN represents the change in
loan value or the change in capital for the largest reasonable adverse changes in yield
spreads. The actual equation for ΔLN looks very similar to the duration equation.
RAROC =
Net Income
Risk ( or ΔLN )
where ΔLN = − D
ΔR
LN
x LN x
where R is the change in yield spread
1+ R
32. 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 ΔLN = -DLN*LN*(ΔR/(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/ΔLN = 0.10 ⇒ ΔLN = 125,000 / 0.10 = $1,250,000
⇒ -DLN * LN * (ΔR/(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
= $1,406,250 *0.10 = $140,625
Therefore, additional income = $140,625 - $125,000 = $15,625.
Chapter 12
1.
2.
How do loan portfolio risks differ from individual loan risks?
What does loan concentration risk mean?
6.
Explain how modern portfolio theory can be applied to lower the credit risk of
an FI’s portfolio.
Modern portfolio theory has demonstrated that a well-diversified portfolio can
provide opportunities for individuals to invest in 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, a banker 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 his or her risk-return trade-off.
Chapter 13
This chapter students should be able to identify Schedule L and non-schedule L OffBalance-Sheet.
1.
Classify the following items as either (1) on-balance-sheet assets, (2) onbalance-sheet liabilities, (3) off-balance-sheet assets, (4) off-balance-sheet
liabilities, or (5) capital account.
Classification
a. Loan commitments
3
b. Loan loss reserves
5
c. Letter of credit
2
d. Banker’s acceptance
2
e. Rediscounted banker’s acceptance
2
f. Loan sales without recourse
None of the
above.
g. Loan sales with recourse
3
h. Forward contracts to purchase
3
I. Forward contracts to sell
4
j. Swaps
4 (for liability
swaps)
k. Loan participations
1
l. Securities borrowed
3
m. Securities lent
4
n. Loss adjustment expense account (PC insurers)
2
o. Net policy reserves
2
2.
How does one distinguish between an off-balance-sheet asset and an offbalance-sheet liability?
Off-balance-sheet activities or items are contingent claim contracts. An item is
classified as an off-balance-sheet asset when the occurrence of the contingent event
results in the creation of an on-balance-sheet asset. An example is a loan commitment.
If the borrower decides to exercise the right to draw down on the loan, the bank will
incur a new asset on its portfolio. Similarly, an item is an off-balance-sheet liability
when the contingent event creates an on-balance-sheet liability. An example is a
standby letter of credit (LC). In the event that the original payer of the LC defaults,
then the bank is liable to pay the amount to the payee, incurring a liability on the
right-hand side of its balance sheet.
3. Contingent Bank has the following balance sheet in market value terms (in
millions of dollars):
Assets
Cash
Mortgages
Total Assets
$20
$220
$240
Liabilities
Deposits
Equity
Total Liabilities & Equity
$220
$20
$240
In addition, the bank has contingent assets with $100 million market value and
contingent liabilities with $80 million market value. What is the true
stockholder net worth? What does the term contingent mean?
Net worth = (240-220) + (100-80) = $40 million. The term contingent means an
event that may or may not happen. In financial economics, the term is used in
conjunction with the result given that some event does occur.
12. How is an FI exposed to interest rate risk when it makes loan commitments? In
what way can an FI control for this risk? How does basis risk affect the
implementation of the control for interest rate risk?
22. Distinguish between loan sales with and without recourse. Why would banks
want to sell loans with recourse? Explain how loan sales can leave banks
exposed to contingent interest rate risks.
Chapter 17
3. What are core deposits? What role do core deposits play in predicting the
probability distribution of net deposit drains?
6. What are two ways a DI can offset the liquidity effects of a net deposit drain of
funds? How do the two methods differ? What are the operational benefits and
costs of each method?
If the DI has a net deposit drain, it needs to either increase its liabilities (by borrowing
funds or issuing equity) or reduce its assets. An institution can reduce its assets by
drawing down on its cash reserves, selling securities, or calling back (or not
renewing) its loans. It can increase liabilities by issuing more Federal funds, longterm debt, or new issues of equity. If a DI offsets the drain by increasing liabilities,
the size of the firm remains the same. However, if it offsets the drain by reducing its
assets, the size of the firm is reduced. If it has a net negative deposit drain, then it
needs to follow the opposite strategy.
The operational benefit of addressing a net deposit drain is to restore the financial
stability and health of the DI. However, this process does not come without costs.
On the asset side, liquidating assets may occur only at fire-sale prices that will result
in realized losses of value, or asset-mix instability. Further, not renewing loans may
result in the loss of profitable relationships that could have negative affects on
profitability in the future. On the liability side, entering the borrowed funds market
normally requires paying market interest rates that are above those rates that it had
been paying on low interest deposits.
8.
A DI with the following balance sheet (in millions) expects a net deposit drain
of $15 million.
Assets
Liabilities and Equity
Cash
$10
Deposits
$68
Loans
$50
Equity
$7
Securities
$15
Total Liabilities & Equity $75
Total Assets
$75
Show the DI's balance sheet if the following conditions occur.
a. The DI purchases liabilities to offset this expected drain.
If the DI purchases liabilities, then the new balance sheet is:
Cash
$10
Deposits
$53
Loans
$50
Purchased liabilities
$15
Securities
$15
Equity
$7
b. The stored liquidity management method is used to meet the liquidity
shortfall.
If the DI uses reserve asset adjustment, a possible balance sheet may be:
Loans
$50
Deposits
$53
Securities
$10
Equity
$7
DIs will most likely use some combination of these two methods.
9.
AllStarBank has the following balance sheet (in millions):
Assets
Cash
Loans
Securities
Total Assets
$30
$90
$50
$170
Liabilities and Equity
Deposits
Borrowed funds
Equity
Total Liabilities & Equity
$110
$40
$20
$170
AllStarBank’s largest customer decides to exercise a $15 million loan
commitment. How will the new balance sheet appear if AllStar uses the
following liquidity risk strategies?
a. Asset management.
Assets
Cash
Loans
Securities
Total Assets
$30
$105
$35
$170
Liabilities and Equity
Deposits
Borrowed funds
Equity
Total Liabilities & Equity
$110
$40
$20
$170
Liabilities and Equity
Deposits
Borrowed funds
Equity
Total Liabilities & Equity
$110
$55
$20
$185
b. Liability management.
Assets
Cash
Loans
Securities
Total Assets
$30
$105
$50
$185
Chapter 18
1.
What are the benefits and costs to an FI of holding large amounts of liquid
assets? Why are Treasury securities considered good examples of liquid assets?
2.
How is an FI’s liability and liquidity risk management problem related to the
maturity of its assets relative to its liabilities?
3.
Consider the assets (in millions) of two banks, A and B. Each bank is funded by
$120 million in deposits and $20 million in equity. Which bank has the stronger
liquidity position? Which bank probably has a higher profit?
Bank A Asset
Bank B Assets
Cash
$10
Cash
Treasury securities $40
Consumer loans
Commercial loans
$90
Commercial loans
Total Assets $140
Total Assets
6.
$20
$30
$90
$140
Rank these financial assets according to their liquidity: cash, corporate bonds,
NYSE-traded stocks, and T-bills.
Chapter 19
2. How does federal deposit insurance help mitigate the problem of bank runs. What
other elements of the safety net are available to banks in the U.S.?
5. What is moral hazard? How did the fixed-rate deposit insurance program of the
FDIC contribute to the moral hazard problem of the savings and loan industry?
What other changes in the savings association environment during the 1980s
encouraged the developing instability of the industry?
6. How does a risk-based insurance program solve the moral hazard problem of
excessive risk taking by FIs?
10. What is capital forbearance? How does a policy of forbearance potentially
increase the costs of financial distress to the insurance fund as well as the
stockholders?
Capital forbearance refers to regulators’ permitting an FI with depleted capital to
continue operations. The primary advantage occurs in the short run through the
savings of liquidation costs. In the longer run, the likely cost is that the poorly
managed FI will become larger, more risky, but no more solvent. Eventually even
larger liquidation costs must be incurred.
13. Why did the fixed-rate deposit insurance system fail to induce insured and
uninsured depositors to impose discipline on risky banks in the United States in
the 1980s?
15. What failure resolution methods were available to regulators before the passage
of FDICIA in 1991? What was the “essentiality” provision?
Prior to FDICIA, the failure resolution methods included the payoff method, the
purchase and assumption method, and the open assistance method. The FDIC was
forced to use liquidation unless an alternative method cost less than liquidation to
implement. Further, the FDIC could choose to keep open a bank if the continued
operation was considered essential to providing financial services to the local
community.
Chapter 20
1. Identify and briefly discuss the importance of the five functions of an FI’s
capital?
a.
How does economic value accounting recognize the adverse effects of credit and
interest rate risk?
The loss in value caused by credit risk and interest rate risk is borne first by the
equity holders, and then by the liability holders. In market value accounting, the
adjustments to equity value are made simultaneously as the losses due to these
risk elements occur. Thus economic insolvency may be revealed before
accounting value insolvency occurs.
b. How does book value accounting recognize the adverse effects of credit and
interest rate risk?
Because book value accounting recognizes the value of assets and liabilities at
the time they were placed on the books or incurred by the firm, losses are not
recognized until the assets are sold or regulatory requirements force the firm to
make balance sheet accounting adjustments. In the case of credit risk, these
adjustments usually occur after all attempts to collect or restructure the loans
have occurred. In the case of interest rate risk, the change in interest rates will
not affect the recognized accounting value of the assets or the liabilities.
8. How is the leverage ratio for an FI defined?
10. Identify and discuss the weaknesses of the leverage ratio as a measure of capital
adequacy.
13. What is the total risk-based capital ratio?
14. Identify the five zones of capital adequacy and explain the mandatory regulatory
actions corresponding to each zone.
Zone 1: Well capitalized. The total risk-based capital ratio (RBC) ratio exceeds 10
percent. No regulatory action is required.
Zone 2: Adequately capitalized. The RBC ratio exceeds 8 percent, but is less than 10
percent. Institutions may not use brokered deposits except with the
permission of the FDIC.
Zone 3: Undercapitalized. The RBC ratio exceeds 6 percent, but is less than 8
percent. Requires a capital restoration plan, restricts asset growth, requires
approval for acquisitions, branching, and new activities, disallows the use of
brokered deposits, and suspends dividends and management fees.
Zone 4: Significantly undercapitalized. The RBC ratio exceeds 2 percent, but is less
than 6 percent. Same as zone 3 plus recapitalization is mandatory, places
restrictions on deposit interest rates, interaffiliate transactions, and the pay
level of officers.
Zone 5: Critically undercapitalized. The RBC ratio is less than 2 percent. Places the
bank in receivorship within 90 days, suspends payment on subordinated
debt, and restricts other activities at the discretion of the regulator.
The mandatory provisions for each of the zones described above include the penalties
for any of the zones prior to the specific zone.
15. What are the definitional differences between Tier I and Tier II capital?
17. Explain the process of calculating credit risk-adjusted on-balance-sheet assets.
Balance sheet assets are assigned to four categories of credit risk exposure. The
dollar amount of assets in each category is multiplied by an appropriate weight of 0
percent, 20 percent, 50 percent, and 100 percent respectively for the categories
representing no risk to full credit risk respectively. The weighted dollar amounts of
each category are added together to get the total risk-adjusted on-balance-sheet assets.
a. What assets are included in the four (five) categories of credit risk exposure
under Basel I (Basel II)?
Category 1 includes cash, United States Treasury bills, notes and bonds,
mortgage-backed securities, and Federal Reserve Bank balances.
Category 2 includes U.S. agency-backed securities, municipal issued general
obligation bonds, FHLMC and FNMA mortgage-backed securities, and
interbank deposits.
Category 3 includes other municipal revenue bonds and regular residential
mortgage loans. All other commercial, consumer, and credit card loans, real
assets and any other asset not included above are included in category 4.
Basel II attempts to align capital requirements more closely with the banking
risk of the FI. In addition to the above classifications, the Basel II categories
include the following:
Category 1:
Category 2:
Loans to sovereigns with an S&P rating of AA- or better.
Loans to sovereigns with an S&P rating between A- and A+
inclusive, and loans to banks and corporates with an S&P rating
of AA- or better.
Category 3:
Loans to sovereigns with an S&P rating between BBB- and
BBB+ inclusive, and loans to banks and corporates with an
S&P rating between AA- and A+ inclusive.
Category 4:
Loans to sovereigns with an S&P rating of B- to BB+. Loans
to banks with an S&P rating of B- to BBB+. Loans to
corporates with a credit rating of BB- to BBB+.
Category 5:
This is a new category introduced by Basel II. Loans to
sovereigns, banks, and securities firms with an S&P credit
rating below B-. Loans to corporates with a credit rating below
BB-.
b. What are the appropriate risk-weights for each category?
Category 1 has a risk weight of 0 percent, category 2 has a risk weight of 20
percent, category 3 has a risk weight of 50 percent, and category 4 has a risk
weight of 100 percent. In addition for Basel II, category 5 has a risk weight of
150 percent.
18. National Bank has the following balance sheet (in millions) and has no offbalance-sheet activities:
Assets
Liabilities and Equity
Cash
$20 Deposits
$980
Treasury bills
$40 Subordinated debentures
$40
Residential mortgages
$600 Common stock
$40
$30
Other loans
$430 Retained earnings
Total Liabilities and Equity $1,090
Total Assets
$1,090
a. What is the leverage ratio?
The leverage ratio is ($40 + $30)/$1,090 = 0.06422 or 6.422 percent.
b. What is the Tier I capital ratio?
Risk-adjusted assets = $20x0.0 + $40x0.0 + $600x0.5 + $430x1.0 = $730.
Tier I capital ratio = ($40 + $30)/$730 = 0.09589 or 9.59 percent.
c. What is the total risk-based capital ratio?
The total risk-based capital ratio = ($40 + $40 + $30)/$730 = 0.150685 or 15.07
percent.
d. In what capital category would the bank be placed?
The bank would be place in the well-capitalized category.
Chapter 28
1.
6.
What has been the effect of securitization on the asset portfolios of financial
institutions?
An FI is planning to issue $100 million in commercial loans. The FI will
finance the loans by issuing demand deposits.
a. What is the minimum capital required by the Basle accord?
The minimum capital required on commercial loans = $100 x 1.0 x 0.08 = $8
million.
b. What is the minimum amount of demand deposits needed to fund this loan
assuming there is a 10 percent average reserve requirement on demand
deposits?
Since there is an interaction between the demand deposits and cash reserves
held, the answer requires solving the following, assuming the $8 is funded by
equity and the reserve requirements are kept as cash:
$100 + (0.10 x DD) = DD + 8 ⇒ DD = 92/.9 = $102.22
c. Show a simple balance sheet with total assets, total liabilities, and equity if
this is the only project funded by the bank.
Assets
Cash
Loan
Total
$10.22
100.00
110.22
Liabilities
Demand deposits
Equity
$102.22
8.00
110.22
d. How does this balance sheet differ from Table 28-1? Why?
The example in Table 28-1 assumes that the capital ratio is only 4 percent, since
the loans are residential mortgages. Thus, because the loans in this problem are
commercial loans, the bank must keep a full 8 percent risk-based capital ratio
and the balance sheet is $0.44 less than the Table 28-1 example. In effect,
although the capital is higher, the reserve requirement tax is lower.
10. Consider the mortgage pass-through example presented in Table 28-3 and
Figure 28-2. The total monthly payment by the borrowers reflecting a 12
percent mortgage rate is $1,028,612.60. The payment passed through to the
ultimate investors reflecting an 11.5 percent return is $990,291.43. Who
receives the difference in these two payments? How are the shares determined?
The difference in the two payments (438,321.17) goes to the mortgage-serviceprovider and to GNMA for the insurance premium. If the total fee is 50 basis points,
and GNMA receives 6 basis points for the insurance premium, GNMA would receive
12 percent (6/50) of the difference ($4,598.54) in the two payments, and the mortgage
service provider would receive 88 percent (44/50) of the difference ($33,722.63) in
the two payments.
11. Consider a GNMA mortgage pool with principal of $20 million. The maturity
is 30 years with a monthly mortgage payment of 10 percent per annum. Assume
no prepayments.
a. What is the monthly mortgage payment (100 percent amortizing) on the pool
of mortgages?
The monthly mortgage payment, R, is (the monthly interest rate is .10/ 12 =
.00833):
$20m = PVAn=360, k=0.8333*(R) ⇒ R = $175,514.31
b. If the GNMA insurance fee is 6 basis points and the servicing fee is 44 basis
points, what is the yield on the GNMA pass-through?
The GNMA's annual interest rate is 0.10 - 0.0044 - 0.0006 = 9.5 percent. The
monthly interest rate is 0.095/12 = 0.0079167 or 0.79167 percent.
c. What is the monthly payment on the GNMA in part (b)?
The monthly GNMA payment, R, is: $20m = PVAn=360, k=0.79167%*R ⇒ R =
$168,170.84
d. Calculate the first monthly servicing fee paid to the originating FIs.
The first monthly servicing fee, R, is (the monthly fee rate is .44%/12 =
.0367%):
R = (.000367)$20m = $7,340
e. Calculate the first monthly insurance fee paid to GNMA.
The first monthly insurance payment, R, is (monthly insurance rate is .06%/12 =
.005%):
R = (.00005)$20m = $1,000