Financial Markets and Institutions
Overview of the financial system
Paola Paiardini
University of Birmingham
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The five parts of the financial system
1
Money
2
Financial instruments
3
Financial markets
4
Financial institutions
5
Central banks
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The five core principles of the financial system
1
Time has value.
2
Risk requires compensation
3
Information is the basis for decisions
4
Markets determine prices and allocate resources
5
Stability improves welfare
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Flows of funds through the financial system
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Flows of funds through the financial system
Direct Finance: Borrowers sell securities directly to lenders in the financial
markets.
▶
Direct finance provides financing for governments and corporations.
Indirect Finance: An institution stands between lender and borrower.
▶
We get a loan from a bank or from a finance company to buy a car.
Asset: Something of value that you own.
Liability: Something you owe.
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Who are the users of the financial system?
1
Ultimate lenders: Agents whose excess of income over expenditure creates a
financial surplus which they are willing to lend.
2
Ultimate borrowers: Agents whose excess of expenditure over income creates
a financial deficit which they wish to meet by borrowing.
Borrowers and lenders have conflicting preferences:
▶
Borrowers
⋆
⋆
⋆
⋆
▶
low liquidity
minimum cost
minimum risk
minimum transaction costs
Lenders
⋆
⋆
⋆
⋆
high liquidity
maximum return
minimum risk
minimum transaction costs
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Money and how we use it
Money is an asset that is generally accepted as payment for goods and
services or repayment of debt.
Money has three functions:
1
It is a means of payment: used in exchange for goods and services.
2
It is an unit of account: used to quote prices.
3
It is a store of value: used to transfer purchasing power into the future.
Liquidity is a measure of the ease with which an asset can be turned into a
means of payment:
▶
Market liquidity is the ability to sell assets.
▶
Funding liquidity is the ability to borrow money.
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2007-2009 financial crisis and the liquidity spiral
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The importance of measuring money
Changes in the quantity of money are related to inflation:
▶
Inflation is the process of prices rising.
▶
Inflation rate is the measurement of the process.
With inflation, you need more money to buy the same basket of goods.
The primary cause of inflation is too much money.
▶
We therefore must be able to measure how much is circulating.
▶
Defining money means defining liquidity.
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Monetary aggregates
M1–Narrow Money
▶
is the sum of currency in circulation and overnight deposits.
M2–Intermediate Money
▶
is the sum of M1, short-term time deposits (i.e. with an agreed
maturity of up to 2-year) and deposits redeemable at notice of up to 3
months.
M3– Broad Money
▶
is the sum of M2 and long-term time deposits.
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Compositions of monetary aggregates in the eurozone, UK
and US
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Growth rates of the ECB M1 and M3, 1999–2010
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Consumer Price Index (CPI) to measure inflation
CPI measures “How much more would it cost for people to purchase today
the same basket of goods and services that they actually bought at some
fixed time in the past”
▶
Survey people to see what they bought.
▶
Figure out what it would cost to buy the same basket of goods and
services today.
▶
Compute the percentage change in the cost of the basket of goods:
CPI =
P.Paiardini (Week 1)
Cost of the basket in current year
∗ 100
Cost of the basket in base year
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Consumer Price Index (CPI) to measure inflation
Year
2014
2015
2016
Price of
Food
$100
110
120
Price of
Housing
$200
205
210
Price of
Transportation
$100
140
160
Inflation Rate 2015 =
P.Paiardini (Week 1)
Cost of
the Basket
$150
165
180
Consumer
Price Index
100
110
120
CPI2015 − CPI2014
∗ 100
CPI2014
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Spring Term 2023
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Financial instruments
The written legal obligation of one party to transfer something of value,
usually money, to another party at some future date, under certain
conditions.
▶
Tangible Assets
⋆
▶
Value is based on physical properties (e.g. buildings, land, machinery).
Intangible Assets
⋆
Claim to future income generated (ultimately) by tangible asset(s).
There are two fundamental classes of financial instruments:
1
Underlying instruments.
2
Derivative instruments.
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The role of financial instruments
Financial assets have three principal economic functions:
1
Act as a means of payment
▶
2
Act as a store of value
▶
3
Employees take stock options as payment for working.
Financial instruments generate increases in wealth that are larger than
from holding money.
Allow for the transfer or risk
▶
Futures and insurance contracts allow one person to transfer risk to
another.
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Classification of financial instruments by their use
Used primarily as store of value:
▶
▶
▶
▶
Bank loans
Bonds
Home mortgages
Stocks
Used primarily to transfer risk:
▶
▶
▶
Insurance contracts
Futures contracts
Options
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The role of financial markets
Financial markets are the places where financial instruments are bought and sold.
Financial markets provide three economic functions:
1
Market liquidity:
▶
2
Information:
▶
3
Ensure that owners of financial instruments can buy and sell them
cheaply and easily.
Pool and communicate information about the issuer of a financial
instrument.
Risk sharing:
▶
Provide individuals a place to buy and sell risk.
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Classification of financial markets
1
By nature of claims:
▶
▶
2
By maturity of claims:
▶
▶
3
▶
Primary Market
Secondary Market
By delivery time:
▶
▶
5
Money Market
Capital Market
By seasoning of claims:
▶
4
Debt Market
Equity Market
Spot Market
Derivative Market
By organisational structure
▶
▶
▶
Auction Market
Over-the-counter Market
Intermediate/Dealer Market
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Types of financial intermediaries
Deposit-takers
▶
Retail banks
▶
Commercial banks
Non-deposit takers
▶
Insurance companies
▶
Pension funds
▶
Securities firms (brokers, investment banks, mutual funds, private
equity and venture capital firms)
▶
Finance companies
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The role of financial intermediaries
In their role as financial intermediaries, financial institutions perform five
functions:
1
Pooling the resources of small savers.
2
Providing safekeeping and accounting services, as well as access to payments
system.
3
Supplying liquidity by converting savers’ balances directly into a means of
payment whenever needed.
4
Providing ways to diversify risk.
5
Collecting and processing information in ways that reduce information costs.
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1. Pooling savings
By accepting many small deposits, banks empower themselves to make large
loans.
In order to do this, the intermediary:
▶
Must attract substantial numbers of savers.
▶
Must convince potential depositors of the institution’s soundness.
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2. Safekeeping, payments system access, and accounting
Financial intermediaries, by providing us with a reliable and inexpensive
payments system, help our economy to function more efficiently.
Financial intermediaries also help us to manage our finances.
▶
They provide us with bookkeeping and accounting services.
▶
These force financial intermediaries to write legal contracts - but one
can be written and used over and over again - reducing the cost of
each.
▶
Much of what financial intermediaries do takes advantage of economies
of scale.
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3. Providing liquidity
Liquidity is a measure of the ease and cost with which an asset can be
turned into a means of payment.
Financial intermediaries offer us the ability to transform assets into money at
relatively low cost - ATMs, for example.
Banks can structure their assets accordingly, keeping enough funds in
short-term, liquid financial instruments to satisfy the few people who will
need them and lending out the rest.
By collecting funds from a large number of small investors, the bank can
reduce the cost of their combined investment, offering each individual
investor both liquidity and high rates of return.
Intermediaries offer both individuals and businesses lines of credit, which
provides customers with access to liquidity.
A financial intermediary must specialise in liquidity management, designing
its balance sheet to sustain sudden withdrawals.
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4. Diversifying risk
Financial institutions enable us to diversify our investments and reduce risk.
Banks take deposits from thousands of individuals and make thousands of
loans with them. Thus, each depositor has a very small stake in each one of
the loans.
All financial intermediaries provide a low-cost way for individuals to diversify
their investments.
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5. Collecting and processing information
The fact that the borrower knows whether he or she is trustworthy, while the
lender faces substantial costs to obtain that information, results in an
information asymmetry.
Borrowers have information that lenders do not have.
By collecting and processing standardized information, financial
intermediaries reduce the problems that information asymmetries create.
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Information asymmetries
Information plays a central role in the structure of financial markets and
financial institutions.
Markets require sophisticated information to work well.
▶
If the cost of information is too high, markets cease to function.
Issuers of financial instruments know more about their business prospects
and willingness to work than potential lenders/investors.
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Information asymmetries
Asymmetric information: One party lacks crucial information about
another party, impacting decision-making.
1
Adverse selection arises before the transaction occurs.
⋆
2
Lenders need to know how to distinguish good credit risks from bad.
Moral hazard occurs after the transaction.
⋆
Will borrowers use the money as they claim?
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1. Adverse selection
Used cars and the market for lemons:
Used car buyers can’t distinguish good cars from bad cars.
Buyers will at most pay the expected value of good and bad cars.
Sellers know if they have a good car, so they won’t accept less than the true
value.
If buyers are willing to pay only the average value of all the cars on the
market, sellers with good cars will withdraw their cars from the market.
Thus, only the worst cars (the lemons) will be left on the market.
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Adverse selection in financial markets
If you are not able to distinguish good from bad companies.
▶
Stocks of good companies are undervalued.
▶
Owners will not want to sell them.
If you are not able to distinguish good from bad bonds.
▶
Owners of good companies will have to sell bonds for a price that is
too low.
▶
Good bonds won’t be sold.
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2. Moral hazard
Moral hazard arises when we cannot observe people’s actions.
Moral hazard affects both equity and bond financing.
▶
Equity finance: If you buy a stock in a company, how do you know
your money will be used in the way that is best for you, the
stockholder?
⋆
▶
The separation of your ownership from managers’ control creates what
is called a principal-agent problem.
Debt finance: When the managers are the owners, moral hazard in
equity financing disappears. However, debt financing has its problems
too:
⋆
Because debt contracts allow owners to keep all the profits in excess of
the loan payments, they encourage risk taking.
⋆
People with risky projects are attracted to debt finance because they
get the full benefit of the upside, while the downside is limited to their
collateral.
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Possible solutions
Adverse selection:
▶
Government-required information disclosure.
▶
Private collection of information.
▶
Pledging of collateral to insure lenders against the borrower’s default.
▶
Requiring borrowers to invest substantial resources of their own.
Moral hazard:
▶
Requiring managers to report to owners.
▶
Requiring managers to invest substantial resources of their own.
▶
Covenants that restrict what borrowers can do with borrowed funds.
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Financial Markets and Institutions
The meaning of interest rates
Paola Paiardini
University of Birmingham
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Valuing monetary payments now and in the future
Credit is one of the critical mechanisms we have for allocating resources.
Interest rates
▶
Link the present to the future.
▶
Tell the future reward for lending today.
▶
Tell the cost of borrowing now and repaying later.
We must learn how to calculate and compare rates on different financial
instruments.
How and why is the promise to make a payment on one date more or less
valuable than the promise to make it on a different date?
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Future Value (FV)
Future value is the value on some future date of an investment made today.
What is the future value of £100 deposited in an interest-bearing account
today at 5% interest?
Future Value
FV = PV + PV × (i) = PV × (1 + i)
The higher the interest rate or the higher the amount invested, the higher
the future value.
What happens when time to repayment varies?
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Future Value (FV) and compound interest
When using one-year interest rates to compute the value repaid more than
one year from now, we must consider compound interest.
What if you leave your £100 in the bank for two years at 5% yearly interest
rate?
Future Value with compound interest
n
FV = PV × (1 + i)
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Future Value (FV) and compound interest
What if you leave your £100 in the bank for six months, or 21/2 years?
▶
In computing future value, both the interest rate and n must be
measured in the same time units.
If the annual interest rate is 5%, what is the monthly rate?
▶
0.41%
These fractions of percentage points are called basis points.
▶
A basis point is one one-hundredth of a percentage point, 0.01%.
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Present Value (PV)
Present value is the value today (in the present) of a payment that is
promised to be made in the future.
Present value of payment received n years in the future:
Present Value
PV =
FV
(1+i)n
The present value is higher:
▶
The higher future value of the payment, FV .
▶
The shorter time period until payment, n.
▶
The lower the interest rate, i.
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How present value changes
Doubling the future value of the payment, without changing the time of the
payment or the interest rate, doubles the present value.
▶
This is true for any percentage.
The sooner a payment is to be made, the more it is worth.
▶
See the figure in the next slide.
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Present value of £100 at 5% interest
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Present value of £100 payment
Interest rate
1%
2%
3%
4%
5%
1 Year
£99.01
£98.04
£97.09
£96.15
£95.24
Payment due in
5 Year
£95.15
£90.57
£86.26
£82.19
£78.35
10 Year
£90.53
£82.03
£74.41
£67.56
£61.39
20 Year
£81.95
£67.30
£55.37
£45.64
£37.69
Higher interest rates are associated with lower present values, no matter
what the size or timing of the payment.
At any fixed interest rate, an increase in the time reduces its present value.
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Bond basics
A bond is a promise to make a series of payments on specific future dates.
Bonds create obligations, and are therefore thought of as legal contracts
that:
▶
Require the borrower to make payments to the lender, and
▶
specify what happens if the borrower fails to do so.
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Bond prices
How much should you be willing to pay for a bond?
▶
The price of a bond depends on the bond characteristics.
1
Zero-coupon or discount bonds: single future payment.
2
Fixed-payment loans: sequence of fixed payments.
3
Coupon bonds: periodic interest payments + principal repayment at
maturity.
4
Consol or Perpetuity: like coupon bonds whose payments last forever
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1. Zero-coupon bonds
They represent a promise to pay a certain amount on a fixed future date.
There are no coupon payments, which is why they are known as zero-coupon
bonds.
They are also called discount bonds since the price is less than their face
value, they sell at a discount.
Because a zero-coupon bond makes a single payment on a future date, its
price is just the present value of that payment.
The relationship between the price and the interest rate is the same as we
saw on present value calculations. When the price moves, the interest rate
moves with it, in the opposite direction.
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1. Zero-coupon bonds
Price of a one-year zero-coupon bond:
Face Value
(1 + i)
Price of a six-month zero-coupon bond:
Face Value
1/2
(1 + i)
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2. Fixed-payment loans
Conventional home mortgages and car loans are fixed-payment loans.
Value of a fixed payment loan:
Fixed Payment Fixed Payment
Fixed Payment
+
+ ... +
n
2
(1 + i)
(1 + i)
(1 + i)
The sum of the present value of the payments.
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3. Coupon bonds
The issuer of a coupon bond promises to make a series of periodic interest
payments (coupon payments), plus a principal payment at maturity.
Price of a coupon bond:
Coupon Payment Coupon Payment
Coupon Payment Face Value
+
+ ... +
+
n
n
2
(1 + i)
(1 + i)
(1 + i)
(1 + i)
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4. Consol or Perpetuity
The issuer of a perpetuity promises to make a series of periodic interest
payments forever.
Price of a consol:
Yearly Coupon Payment
i
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Bond yields
Calculate the return to an investment, implicit in the bond’s price.
We combine information about the promised payments with the price to
obtain the yield:
▶
A measure of the cost of borrowing and the reward for lending.
▶
We will use the terms yield and interest rate interchangeably.
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Bond yields
Nominal yield is the stated rate of the bond.
Yield to maturity is the most useful measure of the return on holding a
bond.
▶
The yield bondholders receive if they hold the bond to its maturity
when the final principal payment is made.
Current yield is the interest rate of the bond given its current price.
Current Yield =
▶
Yearly Coupon Payment
Price Paid
It measures that part of the return from buying the bond that arises
solely from the coupon payments.
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Price-yield relationship
A fundamental property of a bond is that its price changes in the opposite
direction to the change in the required yield.
The reason is that the price of the bond is the present value of the cash
flows.
Bond Price ↑ ⇒ Yield to Maturity ↓
Maximum
Price
Yield
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Relationship among price, coupon rate, current yield, and
yield to maturity
Par Bond:
▶
Bond Price = Face value (par value): Coupon rate = Current yield =
Yield to maturity
Discount Bond:
▶
Bond price < Face value (par value): Coupon rate < Current yield<
Yield to maturity
Premium Bond:
▶
Bond price > Face value (par value): Coupon rate > Current yield >
Yield to maturity
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Holding Period Return
It is the return of holding a bond and selling it before maturity.
It can differ from the yield to maturity.
Whenever a price bond changes, there is a capital gain or loss.
The greater the price change, the more important the holding period return
becomes.
The longer the term of the bond, the greater those price movements and
associated risks can be.
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Real and nominal interest rates
Nominal Interest Rates (i)
▶
The interest rate expressed in current-pound terms.
Real Interest Rates (r )
▶
The inflation adjusted interest rate.
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Real and nominal interest rates
The nominal interest rate you agree on (i) must be based on expected
inflation (π e ) over the term of the loan plus the real interest rate you agree
on (r ).
Fisher Equation
i = r + πe
The higher expected inflation, the higher the nominal interest rate.
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Real and nominal interest rates (3-month Treasury bill),
1964–2010
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Real and nominal interest rates
Financial markets quote nominal interest rates.
When people use the term interest rate, they are referring to the nominal
rate.
We cannot directly observe the real interest rate; we have to estimate it:
Real interest rate
r = i − πe
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Financial Markets and Institutions
Measures of risk
Dr Paola Paiardini
University of Birmingham
P.Paiardini (Week 2)
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Spring Term 2023
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Defining Risk
According to the dictionary, risk is ”the possibility of loss or injury.”
For outcomes of financial and economic decisions, we need a different
definition.
Risk is a measure of uncertainty about the future payoff to an investment,
assessed over some time horizon and relative to a benchmark.
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Defining Risk
1
Risk is a measure that can be quantified.
▶
2
Risk arises from uncertainty about the future.
▶
3
Investment described very broadly.
Risk must be assessed over some time horizon.
▶
6
We must imagine all the possible payoffs and the likelihood of each.
Definition of risk refers to an investment or group of investments.
▶
5
We do not know which of many possible outcomes will follow in the
future.
Risk has to do with the future payoff of an investment.
▶
4
The riskier the investment, the less desirable and the lower the price.
In general, risk over shorter periods is lower.
Risk must be measured relative to some benchmark–not in isolation.
▶
A good benchmark is the performance of a group of experienced
investment advisors or money managers.
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Measuring Risk
We must become familiar with the mathematical concepts useful in thinking
about random events.
In determining expected inflation or expected return, we need to understand
expected value.
The investments return out of all possible values.
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Possibilities, Probabilities, and Expected Value
Probability theory states that considering uncertainty requires:
▶
Listing all the possible outcomes.
▶
Figuring out the chance of each one occurring.
Probability is a measure of the likelihood that an event will occur.
▶
It is always between zero and one.
▶
Can also be stated as frequencies.
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Possibilities, Probabilities, and Expected Value
We can construct a table of all outcomes and probabilities for an event, like
tossing a fair coin.
If constructed correctly, the values in the probabilities column will sum to
one.
Assume instead we have an investment that can rise or fall in value.
▶
£1,000 stock which can rise to £1,400 or fall to £700.
▶
The amount you could get back is the investment’s payoff.
▶
We can construct a similar table and determine the investment’s
expected value–the average or most likely outcome.
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Possibilities, Probabilities, and Expected Value
Expected value is the mean - the sum of their probabilities multiplied by
their payoffs.
Expected Value = 1/2(£700) + 1/2(£1,400) = £1,050
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Possibilities, Probabilities, and Expected Value
What if £1,000 investment could:
1
Rise in value to £2,000, with probability of 0.1
2
Rise in value to £1,400, with probability of 0.4
3
Fall in value to £700, with probability of 0.4
4
Fall in value to £100, with probability of 0.1
Expected Value:
▶
0.1x(£100) + 0.4x(£700) + 0.4x(£1,400) +0.1x(£2,000) = £1,050
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
8 / 26
Possibilities, Probabilities, and Expected Value
Using percentages allows comparison of returns regardless of the size of
initial investment.
▶
The expected return in both cases is £50 on a £1,000 investment, or
5%
Are the two investments the same?
▶
No - the second investment has a wider range of payoffs.
Variability equals risk
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
9 / 26
Measures of Risk
It seems intuitive that the wider the range of outcomes, the greater the risk.
A risk-free asset is an investment whose future value is known with certainty
and whose return is the risk free rate of return.
▶
The payoff you receive is guaranteed and cannot vary.
Measuring the spread allows us to measure the risk.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
10 / 26
Variance and Standard Deviation
The variance is the average of the squared deviations of the possible
outcomes from their expected value, weighted by their probabilities.
1
Compute expected value.
2
Subtract expected value from each of the possible payoffs and square
the result.
3
Multiply each result times the probability.
4
Add up the results.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
11 / 26
Variance and Standard Deviation
The standard deviation is more useful because it deals in normal units, not
squared units (like pounds-squared).
We can convert standard deviation into a percentage of the initial
investment, £1,000, or 35%.
We can compare other investments to this one.
Given a choice between two investments with equal expected payoffs, most
will choose the one with the lower standard deviation.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
12 / 26
Value at Risk
Sometimes we are less concerned with spread than with the worst possible
outcome.
▶
Example: We don’t want a bank to fail.
Value at Risk (VaR): The worst possible loss over a specific horizon at a
given probability.
For example, we can use this to assess whether a fixed or variable-rate
mortgage is better.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
13 / 26
Value at Risk
For a mortgage, the worst case scenario means you cannot afford your
mortgage and will lose your home.
▶
Expected value and standard deviation do not really tell you the risk
you face, in this case.
VaR answers the question: how much will I lose if the worst possible
scenario occurs?
▶
Sometimes this is the most important question.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
14 / 26
Risk Aversion, the Risk Premium, and the Risk-Return
Tradeoff
Most people do not like risk and will pay to avoid it because most of us are
risk averse.
▶
Insurance is a good example of this.
A risk averse investor will always prefer an investment with a certain return
to one with the same expected return but any amount of uncertainty.
Therefore, the riskier an investment, the higher the risk premium.
▶
The compensation investors required to hold the risky asset.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
15 / 26
Risk Aversion, the Risk Premium, and the Risk-Return
Tradeoff
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
16 / 26
Sources of risk: idiosyncratic and systematic risk
All risks can be classified into two groups:
1
Those affecting a small number of people but no one else:
⋆
2
idiosyncratic, diversifiable, or unique risks.
Those affecting everyone:
⋆
systematic, undiversifiable, or market risks.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
17 / 26
Sources of risk: idiosyncratic and systematic risk
Idiosyncratic risks can be classified into two types:
1
A risk is bad for one sector of the economy but good for another.
⋆
2
A rise in oil prices is bad for car industry but good for the energy
industry.
Unique risks specific to one person or company and no one else.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
18 / 26
Sources of risk: idiosyncratic and systematic risk
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
19 / 26
Riskiness of Portfolio
Sources of risk: idiosyncratic and systematic risk
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
20 / 26
Reducing risk through diversification
Risk can be reduced through diversification, the principle of holding more
than one risk at a time.
This reduces the idiosyncratic risk an investor bears.
One can hedge risks or spread them among many investments.
Hedging is the strategy of reducing idiosyncratic risk by making two
investments with opposing risks.
Spreading is the strategy of reducing idiosyncratic risk finding investments
unrelated.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
21 / 26
Hedging Risk
Hedging is the strategy of reducing idiosyncratic risk by making two
investments with opposing risks.
If one industry is volatile, the payoffs are stable.
Let’s compare three strategies for investing $100:
▶
Invest $100 in GE.
▶
Invest $100 in Texaco.
▶
Invest half in each company.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
22 / 26
Hedging Risk
Results of possible investment strategies (initial investment $100):
Investment Strategy
GE only
Texaco only
50% and 50%
Expected Payoff
$110
$110
$110
Standrd Deviation
$10
$10
$0
Investing $50 in each stock to ensure your payoff.
Hedging has eliminated your risk entirely.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
23 / 26
Spreading Risk
You can’t always hedge as investments don’t always move in a predictable
fashion.
The alternative is to spread risk around.
▶
Find investments whose payoffs are unrelated.
We need to look at the possibilities, probabilities and associated payoffs of
different investments.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
24 / 26
Spreading Risk
Let’s again compare three strategies for investing $100:
▶
Invest $100 in GE.
▶
Invest $100 in Microsoft.
▶
Invest half in each company.
Possibilities
1
2
3
4
P.Paiardini (Week 2)
GE
$60
$60
$50
$50
Microsoft
$60
$50
$60
$50
Total Payoff
$120
$110
$100
$100
Financial Markets and Institutions
Probabilities
1/4
1/4
1/4
1/4
Spring Term 2023
25 / 26
Spreading Risk
The more independent sources of risk you hold in your portfolio, the lower
your overall risk.
As we add more and more independent sources of risk, the standard
deviation becomes negligible.
Diversification through the spreading of risk is the basis for the insurance
business.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
26 / 26
Financial Markets and Institutions
The behaviour of interest rates
Paola Paiardini
University of Birmingham
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
1 / 32
Determinants of asset demand
Wealth: the total resources owned by the individual, including all assets.
Expected Return: the return expected over the next period on one asset
relative to alternative assets.
Risk: the degree of uncertainty associated with the return on one asset
relative to alternative assets.
Liquidity: the ease and speed with which an asset can be turned into cash
relative to alternative assets.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
2 / 32
Theory of asset demand
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
3 / 32
Equilibrium in the bond market
Supply and demand determine bond prices (and bond yields).
The bond supply curve is the relationship between the price and the
quantity of bonds people are willing to sell, all else equal.
▶
The bond supply curve slopes upward.
The bond demand curve is the relationship between the price and the
quantity of bonds that investors demand, all else equal.
▶
The bond demand curve slopes downward.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
4 / 32
Equilibrium in the bond market
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
5 / 32
Factors that shift bond supply
Changes in government borrowing
▶
Any increase in the government’s borrowing needs increases the
quantity of bonds outstanding, shifting the bond supply curve to the
right.
Change in general business conditions
▶
As business conditions improve, the bond supply curve shifts to the
right.
Changes in expected inflation
▶
When expected inflation rises, the cost of borrowing falls, shifting the
bond supply curve to the right.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
6 / 32
A shift in the supply of bonds
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
7 / 32
Factors that shift bond demand
Wealth
▶
Increases in wealth shift the demand for bonds to the right.
Expected inflation
▶
Declining inflation means promised payments have higher value - bond
demand shifts right.
Expected returns and expected interest rates
▶
If the return on bonds rises relative to the return on alternative
investments, bond demand shifts right.
▶
When interest rates are expected to fall, prices are expected to rise
shifting bond demand to the right.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
8 / 32
Factors that shift bond demand
Risk relative to alternatives
▶
If bonds become less risky relative to alternative investments, demand
for bonds shifts right.
Liquidity relative to alternatives
▶
The more liquid the bond, the higher the demand.
▶
If bonds become more liquid relative to alternative investments,
demand for bonds shifts right.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
9 / 32
A shift in the demand of bonds
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
10 / 32
The effect of an increase in expected inflation
Reduces the real cost of borrowing shifting bond supply to the right.
But, lowers real return on lending, shifting bond demand to the left.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
11 / 32
The effect of a business-cycle downturn
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
12 / 32
Why bonds are risky?
Bondholders face three major risks:
1
Default risk is the chance that the bond’s issuer may fail to make the
promised payment.
2
Inflation risk means investors cannot be sure of what the real value of
payments will be.
3
Interest-rate risk arises from a bond-holder’s investment horizon, which
may be shorter than the maturity date of the bond.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
13 / 32
Risk Premium
Risk Premium
The spread between the interest rates on bonds with default risk and the interest
rates on (same maturity) Treasury bonds
We can express the interest rate offered on a non-Treasury security as:
Base interest rate + spread
or equivalently as:
Base interest rate + risk premium
Base interest rate is the minimum interest rate or base interest rate that
investors will demand for investing in a non-Treasury security. It also
refereed to as the benchmark interest rate.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
14 / 32
Default Risk
Default Risk
The probability that the issuer of the bond is unable or unwilling to make interest
payments or pay off the face value when the bond matures
UK Treasury bonds have usually been considered default-free bonds.
When corporations or governments fail to meet their payments, what
happens to the price of their bonds?
In determining what happens to bond prices when we consider default risk,
we can look at an example of a corporate bond.
▶
▶
Assume the one-year risk-free interest rate is 5 percent.
A company has issued a 5 percent coupon bond with a face value of
£100.
What is the price of this bond?
▶
If this bond was risk-free.
▶
If there is a 10% probability of default.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
15 / 32
Inflation Risk
With few exceptions, bonds promise to make fixed-pound payments.
However, we care about the purchasing power of our money, not the number
of pounds.
▶
This means bondholders care about the real interest rate.
How does inflation risk affect the interest rate?
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
16 / 32
Inflation Risk
Think of the interest rate having three components:
1
The real interest rate.
2
Expected inflation.
3
Compensation for inflation risk.
Inflation rate
1 percent
2 percent
3 percent
Expected inflation
Standard deviation
P.Paiardini (Week 2)
Case I
0.50
0.50
2%
1.00%
Probabilities
Case II
0.25
0.50
0.25
2%
0.71%
Financial Markets and Institutions
Case III
0.10
0.80
0.10
2%
0.45%
Spring Term 2023
17 / 32
Interest–Rate Risk
Interest-rate risk arises from the fact that investors don’t know the holding
period return of a long-term bond.
▶
The longer the term of the bond, the larger the price change for a
given change in the interest rate.
For investors with holding periods shorter than the maturity of the bond, the
potential for a change in interest rates creates risk.
▶
The more likely the interest rates are to change during the
bondholder’s investment horizon, the larger the risk of holding a bond.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
18 / 32
Risk Structure of Interest Rates
Bonds with the same maturity have different interest rates due to:
1
Default risk
2
Liquidity
3
Tax considerations
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
19 / 32
Default risk
A corporation suffering big losses, such as the oil and gas exploration
company BP, might be more likely to suspend interest payments on its
bonds.
▶
Following the Gulf of Mexico oil disaster in 2010, BP bonds were
downgraded. The default risk on its bonds would therefore be quite
high.
Default is one of the most important risks a bondholder faces.
In fact, independent companies (rating agencies) have arisen to evaluate the
creditworthiness of potential borrowers.
These companies estimate the likelihood that the corporate or government
borrower will make a bond’s promised payments.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
20 / 32
Bond ratings
The best known bond rating services are:
▶
▶
▶
Moody’s
Standard&Poor’s
Fitch
They monitor the status of individual bond issuers and assess the likelihood
a lender will be repaid by the bond issuer.
A high rating suggests that a bond issuer will have little problem meeting a
bond’s payment obligations.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
21 / 32
Bond ratings
Firms or governments with an exceptionally strong financial position carry
the highest ratings and are able to issue the highest-rated bonds, AAA.
Investment-grade bonds are:
▶
▶
Bonds with a very low risk of default.
Reserved for most government issuers and corporations that are among
the most financially sound.
The distinction between investment-grade and speculative,
noninvestment-grade is important.
▶
A number of regulated institutional investors are not allowed to invest
in bonds rated below investment grade.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
22 / 32
Bond ratings
Speculative grade bonds are bonds
▶
▶
issued by companies and countries that may have difficulty meeting
their bond payments
but are not at risk of immediate default.
Highly speculative bonds consist of debts that are in serious risk of default.
All bonds with grades below investment grade are often referred to as junk
bonds or high-yield bonds.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
23 / 32
Bond Ratings by Moody’s, Standard and Poor’s, and Fitch
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
24 / 32
Bond ratings
Types of junk bonds:
▶
Fallen angels are bonds that were once investment-grade, but their
issuers fell on hard times.
▶
Bonds issued by issuers about which there is little known.
Material changes in a firm’s or government’s financial conditions precipitate
changes in its debt ratings.
▶
Ratings downgrade - lower an issuer’s bond rating.
▶
Ratings upgrade - upgrade an issuer’s bond rating.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
25 / 32
The impact of ratings on yields
Bond ratings are designed to reflect default risk.
The lower the rating
▶
The higher the risk of default.
▶
The lower its price and the higher its yield.
To understand quantitative ratings, it is easier to compare them to a
benchmark.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
26 / 32
The impact of ratings on yields
Treasury issues are viewed as having little default risk, so they are used as
benchmark bonds.
Yields on other bonds are measured in terms of the spread over Treasuries.
If bond ratings properly reflect risk, then the lower the rating if the issuer,
the higher the default-risk premium.
When Treasury yields move, all other yields move with them.
We can see this from Figure in the next slide showing a plot of the risk
structure of interest rates.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
27 / 32
Interest rate spreads between 10Y government bonds of
GIIPS countries and 10Y German government bonds (Jan
1999-May 2011)
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
28 / 32
Liquidity
Bonds trade with different degrees of liquidity.
The greater the expected liquidity at which an issue will trade, the lower is
the yield that investors require.
Treasury securities are the most liquid securities in the world.
Yield offered on Treasury securities relative to non-Treasury securities
reflects the difference in liquidity as well as perceived credit risk.
Even within the Treasury market, on-the-run issues have greater liquidity
than off-the-run issues.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
29 / 32
Income tax considerations
Taxes are also an important factor affecting the yield on a bond.
Bondholders must pay income tax on the interest income they receive from
owning privately issued bonds - taxable bonds.
The coupon payments on bonds issued by state and local governments,
municipal or tax-exempt bonds, are specifically exempt from taxation.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
30 / 32
Income tax considerations
What are the tax implications for bond yields?
▶
▶
▶
▶
▶
Consider a one-year £100 face value taxable bond with a coupon rate
of 6%.
Par is £100, and yield to maturity is 6%.
Government sees this 6% as taxable income.
If tax rate is 30%, the tax is £1.80.
Bond yields £104.20 after taxes, equivalent of 4.2%.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
31 / 32
Income tax considerations
The difference in yield between tax-exempt securities and Treasury securities
is typically measured in percentage terms.
The yield on a taxable bond issue after income taxes are paid is equal to:
Tax-Exempt Bond Yield = (Taxable Bond Yield) × (1 − Tax Rate)
Alternatively, we can determine the yield that must be offered on a taxable
bond issue to give the same after-tax yield as a tax-exempt issue.
This yield is called the equivalent taxable yield and is determined as follows:
Equivalent Taxable Yield =
tax-exempt yield
(1 − tax rate)
For an investor with a 30% tax rate, the tax-exempt yield on a 10% bond is
7%.
Overall, the higher the tax rate, the wider the gap between the yields on
taxable and tax-exempt bonds.
P.Paiardini (Week 2)
Financial Markets and Institutions
Spring Term 2023
32 / 32
Financial Markets and Institutions
Theories of the term structure of interest rates
Paola Paiardini
University of Birmingham
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
1 / 23
The Yield Curve
The Yield curve
The yield curve is the graphic representation of the relationship between the yield
of bonds of the same credit quality but different maturity.
In the past the yield curve was constructed from the observations of prices
and yields in the Treasury market
Two reasons account for this tendency:
1
2
Treasury securities are free of default risk and differences in
creditworthiness do not affect yield estimates.
Treasury market is very liquid.
The traditionally constructed Treasury yield curve is an unsatisfactory
measure of the relation between required yield and maturity.
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
2 / 23
Using the yield curve to price a bond
A price of a bond is the present value of its cash flows.
The appropriate interest rate is the yield on a Treasury security with the
same maturity as the bond plus an appropriate risk premium or spread.
However there is a problem with using the Treasury yield curve to determine
the appropriate yield at which to discount the cash flow of a bond.
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
3 / 23
Example
Consider two hypothetical five-year Treasury bonds, A and B.
The difference between these two Treasury bonds is the coupon rate which
is 12% for A and 3% for B.
The cash flow for these two bonds is per £100 of par value for the 10
six-month periods to maturity would be as follows:
Period
1-9
10
Cash Flow A
£6
106
Cash Flow B
£1.50
101.50
The value of a bond should equal the value of all the component
zero-coupon instruments.
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
4 / 23
Determinants of the shape of the term structure
If we plot the term structure the yield to maturity at successive maturities
against maturity what will it look like?
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
5 / 23
Term Structure of Interest Rates
The theory of the term structure of interest rates must explain the following
facts:
1
Interest rates on bonds of different maturities move together over time.
2
When short-term interest rates are low, yield curves are more likely to
have an upward slope; when short-term rates are high, yield curves are
more likely to slope downward and be inverted.
3
Yield curves almost always slope upward.
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
6 / 23
Determinants of the shape of the term structure
The expectations theory
The liquidity theory
The preferred-habitat theory
The market-segmentation theory
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
7 / 23
Forward rates
Consider an investor with a one year investment horizon and is faced with
the following two alternatives:
▶
Buy a one year Treasury bill
▶
Buy a six-month Treasury bill, and when it matures in six months,
buying another six-month Treasury bill
The investor will be indifferent between the two alternatives if they produce
the same return over the one-year investment horizon.
The investor knows the spot rate of the six-month Treasury bill
The investor does not know the forward rate, i.e. the yield on a six-month
Treasury bill that will be purchased six months from now
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
8 / 23
Example
The price of a one year Treasury bill will be:
100
(1 + z2 )2
Suppose that you purchased a six-month Treasury bill for £X.
At the end of six months, the value of this investment would be:
X (1 + z1 )
If the investor were to renew her investment by purchasing that bill at that
time, then the future pounds available at the end of one year from the £X
investment would be:
X (1 + z1 )(1 + f )
Which will give:
X =
P.Paiardini (Week 3)
100
(1 + z1 )(1 + f )
Financial Markets and Institutions
Spring Term 2023
9 / 23
Example
The investor will be indifferent if:
100
100
=
(1 + z2 )2
(1 + z1 )(1 + f )
Solving for f :
f =
(1 + z2 )2
−1
(1 + z1 )
Six-month bill spot rate:0.080; One-year bill spot rate:0.083; f =0.043
The price of a one-year Treasury bill with a £100 maturity value is:
100
= 92.19
(1.0415)2
If £92.19 is invested for six months at the six-month spot rate of 8%, the
amount at the end of six months would be: £95.8776
If £95.8776 is invested for six months at the six-month spot rate of 4.3%,
the amount at the end of one year would be: £100
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
10 / 23
The Pure Expectations Theory
For n-period bond we have:
int =
it + f1 + f2 + f3 + ... + ft+(n−1)
n
The interest rate on a long-term bond equals the average of short rates
expected to occur over life of the long-term bond.
Let’s consider a one-year interest rate over the next five years are expected
to be 5%, 6%, 7%, 8%, and 9%.
▶
▶
▶
Interest rate on two-year bond today:
(5% + 6%)/2 = 5.5%
Interest rate on five-year bond today:
(5% + 6%+7% +8%+9%)/5 = 7%
Interest rate one to five-year bonds:
5%, 5.5%, 6%, 6.5%, 7%
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
11 / 23
The Pure Expectations Theory
According to the pure expectations theory, the forward rates exclusively
represent expected future rates.
▶
▶
▶
A rising term structure, must indicate that the market expects
short-term rates to rise throughout the relevant future.
A flat term structure reflects an expectation that future short-term
rates will be mostly constant
A falling term structure must reflect an expectation that future
short-term rates will decline steadily.
How an expectation of a rising short-term future rate would affect the
behaviour of various market participants to result in a rising yield curve?
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
12 / 23
The Pure Expectations Theory
Assume an initially flat term structure.
Now suppose that economic news leads market participants to expect
interest rates to rise.
▶
▶
▶
Market participants interested in a long-term investment would not
want to buy long-term bonds because they expect a price decline.
Speculators expecting rising rates would anticipate a decline in the
price of long-term bonds and therefore would want to sell any
long-term bonds they own.
Borrowers wishing to acquire long-term funds be pulled toward
borrowing now.
These actions by investors, speculators, and borrowers would tilt the term
structure upward until it is consistent with expectations of higher future
interest rates
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
13 / 23
The Pure Expectations Theory
The Pure Expectations Theory does not account for the risks inherent in
investing in bonds
▶
If forward rates were perfect predictors of future interest rates, then the
future prices of bonds would be known with certainty.
▶
The return over any investment period would be certain and
independent of the maturity of the instrument initially acquired and of
the time at which the investor needed to liquidate the instrument.
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
14 / 23
The Pure Expectations Theory
There are two risks that cause uncertainty about the return over some
investment horizon:
1
2
The uncertainty about the price of the bond at the end of the
investment horizon.
The uncertainty about the rate at which the proceeds from a bond that
matures during the investment horizon can be reinvested and is known
as reinvestment risk.
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
15 / 23
The Pure Expectations Theory
Does this theory explain the three observations we started with?
1
Interest rates of different maturities will move together.
2
It explains different yield curves for short-term and long-term interest
rates.
⋆
⋆
⋆
3
We can see this holds from the equation.
When short rates are low, they are expected to rise to normal level, and
long rate = average of future short rates will be well above today’s
short rate; yield curve will have steep upward slope.
When short rates are high, they will be expected to fall in future, and
long rate will be below current short rate; yield curve will have
downward slope.
It does not explain why yield curves almost always slope upward.
⋆
⋆
It implies that the yield curve slopes upward only when interest rates
are expected to rise.
This hypothesis would suggest that interest rates are normally expected
to rise.
We need to extend the pure expectations theory to include risk.
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
16 / 23
Liquidity Premium Theory
Risk is the key to understanding the slope of the yield curve.
Bondholders face both inflation and interest-rate risk.
▶
The longer the term of the bond, the greater both types of risk.
Computing real return from nominal return requires a forecast of expected
future inflation.
▶
The further into the future we look, the greater the uncertainty.
▶
A bond’s inflation risk increases with its time to maturity.
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
17 / 23
Liquidity Premium Theory
Interest-rate risk arises from the mismatch between the investor’s investment
horizon and a bond’s time to maturity.
▶
If a bondholder plans to sell a bond prior to maturity, changes in the
interest rate generate capital gains or losses.
▶
The longer the term of the bond, the greater the price changes for a
given change in interest rates and the larger the potential for capital
losses.
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
18 / 23
Liquidity Premium Theory
Investors require compensation for the increase in risk they take for buying
longer term bonds.
We can think about bond yields as having two parts:
▶
One that is risk free - explained by the expectations theory.
▶
One that is a risk premium - explained by inflation and interest-rate
risk.
Together this forms the liquidity premium theory of the term structure of
interest rates.
We can add the risk premium (lnt ) to our previous equation to get:
int =
P.Paiardini (Week 3)
i1t + ft+1 + ft+2 + ... + ft+(n−1)
+ lnt
n
Financial Markets and Institutions
Spring Term 2023
19 / 23
Preferred Habitat Theory
Investors have a preference for bonds of one maturity over another.
They will be willing to buy bonds of different maturities only if they earn a
higher expected return.
Investors are likely to prefer short-term bonds over longer-term bonds.
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
20 / 23
The Relationship Between the Liquidity Premium
(Preferred Habitat) and Expectations Theory
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
21 / 23
Liquidity Premium & Preferred Habitat Theories
Interest rates on different maturity bonds move together over time;
explained by the first term in the equation.
Yield curves tend to slope upward when short-term rates are low and to be
inverted when short-term rates are high; explained by the liquidity premium
term in the first case and by a low expected average in the second case.
Yield curves typically slope upward; explained by a larger liquidity premium
as the term to maturity lengthens.
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
22 / 23
Segmented Markets Theory
Bonds of different maturities are not substitutes at all.
The interest rate for each bond with a different maturity is determined by
the demand for and supply of that bond.
Investors have preferences for bonds of one maturity over another.
If investors generally prefer bonds with shorter maturities that have less
interest-rate risk, then this explains why yield curves usually slope upward
(fact 3).
P.Paiardini (Week 3)
Financial Markets and Institutions
Spring Term 2023
23 / 23