Financial Markets and Institutions (2-downloads)

nt

. So to

allow for liquidity premiums, we need merely subtract l

nt

from i

nt

in our formula

to derive 

:

(6)

This measure of 

is referred to, naturally enough, as the adjusted forward-

rate forecast.

In the case of 

, Equation 6 produces the following estimate

Using Example 4 in our discussion of the liquidity premium theory, at time t

the l

2t

liquidity premium is 0.25%, l

1t

= 0, the one-year interest rate is 5%, and the

two-year interest rate is 5.75%. Plugging these numbers into our equation yields

the following adjusted forward-rate forecast for one period in the future:

which is the same as the expected interest rate used in Example 3, as it should be.

Our analysis of the term structure thus provides managers of financial institu-

tions with a fairly straightforward procedure for producing interest-rate forecasts.

First they need to estimate l

nt

, the values of the liquidity premiums for various n.

Then they need merely apply the formula in Equation 6 to derive the market’s fore-

casts of future interest rates.

i

e

t

⫹1

⫽

11 ⫹ 0.0575 ⫺ 0.00252

2

1

⫹ 0.05

⫺ 1 ⫽ 0.06 ⫽ 6%

i

e

t

⫹1

⫽

11 ⫹ i

2t

⫺ l

2t

2

2

1

⫹ i

t

⫺ 1

i

e

t

⫹1

i

e

t

⫹n

i

e

t

⫹n

⫽

11 ⫹ i

n

⫹1t

⫺ l

n

⫹1t

2

n

⫹1

11 ⫹ i

nt

⫺ l

nt

2

n

⫺ 1

i

e

t

⫹n

i

e

t

⫹n

⫽

11 ⫹ i

n

⫹1t

2

n

⫹1

11 ⫹ i

nt

2

n

⫺ 1

i

e

t

⫹2

⫽

11 ⫹ i

3t

2

3

11 ⫹ i

2t

2

2

⫺ 1

i

e

t

⫹2

i

e

t

⫹1

11 ⫹ i

t

2 11 ⫹ i

e

t

⫹1

2 11 ⫹ i

e

t

⫹2

2 ⫺ 1 ⫽ 11 ⫹ i

3t

2 11 ⫹ i

3t

2 11 ⫹ i

3t

2 ⫺ 1

---

As we will see in Chapter 6, the bond market’s forecasts of interest rates may

be the most accurate ones possible. If this is the case, the estimates of the market’s

forecasts of future interest rates using the simple procedure outlined here may be

the best interest-rate forecasts that a financial institution manager can obtain.

112

Part 2 Fundamentals of Financial Markets

A customer asks a bank if it would be willing to commit to making the customer a one-

year loan at an interest rate of 8% one year from now. To compensate for the costs of mak-

ing the loan, the bank needs to charge one percentage point more than the expected

interest rate on a Treasury bond with the same maturity if it is to make a profit. If the

bank manager estimates the liquidity premium to be 0.4%, and the one-year Treasury bond

rate is 6% and the two-year bond rate is 7%, should the manager be willing to make

the commitment?

Solution

The bank manager is unwilling to make the loan because at an interest rate of 8%, the loan

is likely to be unprofitable to the bank.

where

i

n + 1t

=

two-year bond rate 

= 0.07

l

n + 1t

=

liquidity premium 

= 0.004

i

nt

=

one-year bond rate 

= 0.06

l

1t

=

liquidity premium 

= 0

n

=

number of years 

= 1

Thus,

The market’s forecast of the one-year Treasury bond rate one year in the future is there-

fore 7.2%. Adding the 1% necessary to make a profit on the one-year loan means that

the loan is expected to be profitable only if it has an interest rate of 8.2% or higher.

i

e

t

⫹1

⫽

11 ⫹ 0.07 ⫺ 0.0042

2

1

⫹ 0.06

⫺ 1 ⫽ 0.072 ⫽ 7.2%

i

e

t

⫹n

⫽

11 ⫹ i

n

⫹1t

⫺ l

n

⫹1t

2

n

⫹1

11 ⫹ i

nt

⫺ l

nt

2

n

⫺ 1

E X A M P L E   5 . 5

Forward Rate

S U M M A R Y

1. Bonds with the same maturity will have different

interest rates because of three factors: default risk,

liquidity, and tax considerations. The greater a bond’s

default risk, the higher its interest rate relative to

other bonds; the greater a bond’s liquidity, the lower

its interest rate; and bonds with tax-exempt status

will have lower interest rates than they otherwise

would. The relationship among interest rates on

bonds with the same maturity that arise because of

these three factors is known as the risk structure of

interest rates.

2. Several theories of the term structure provide expla-

nations of how interest rates on bonds with different

terms to maturity are related. The expectations the-

ory views long-term interest rates as equaling the

average of future short-term interest rates expected

---

7. If a yield curve looks like the one below, what is the

market predicting about the movement of future

short-term interest rates? What might the yield curve

indicate about the market’s predictions about the

inflation rate in the future?

Chapter 5 How Do Risk and Term Structure Affect Interest Rates?

113

to occur over the life of the bond. By contrast, the

market segmentation theory treats the determination

of interest rates for each bond’s maturity as the out-

come of supply and demand in that market only.

Neither of these theories by itself can explain the fact

that interest rates on bonds of different maturities

move together over time and that yield curves usually

slope upward.

3. The liquidity premium theory combines the features

of the other two theories, and by so doing is able to

explain the facts just mentioned. It views long-term

interest rates as equaling the average of future

short-term interest rates expected to occur over the

life of the bond plus a liquidity premium. This the-

ory allows us to infer the market’s expectations

about the movement of future short-term interest

rates from the yield curve. A steeply upward-sloping

curve indicates that future short-term rates are

expected to rise, a mildly upward-sloping curve indi-

cates that short-term rates are expected to stay the

same, a flat curve indicates that short-term rates are

expected to decline slightly, and an inverted yield

curve indicates that a substantial decline in short-

term rates is expected in the future.

Yield to

Maturity

Term to Maturity

K E Y   T E R M S

credit-rating agencies, p. 92

default, p. 90

default-free bonds, p. 90

expectations theory, p. 98

forward rate, p. 110

inverted yield curve, p. 96

junk bonds, p. 92

liquidity premium theory, p. 103

market segmentation theory, p. 102

risk premium, p. 90

risk structure of interest rates, p. 89

spot rate, p. 110

term structure of interest rates, 

p. 89

yield curve, p. 96

Q U E S T I O N S

1. Which should have the higher risk premium on its

interest rates, a corporate bond with a Moody’s Baa

rating or a corporate bond with a C rating? Why?

2. Why do U.S. Treasury bills have lower interest rates

than large-denomination negotiable bank CDs?

3. Risk premiums on corporate bonds are usually anti-

cyclical; that is, they decrease during business cycle

expansions and increase during recessions. Why is

this so?

4. “If bonds of different maturities are close substitutes,

their interest rates are more likely to move together.”

Is this statement true, false, or uncertain? Explain

your answer.

5. If yield curves, on average, were flat, what would this

say about the liquidity premiums in the term struc-

ture? Would you be more or less willing to accept the

pure expectations theory?

6. If a yield curve looks like the one shown here, what

is the market predicting about the movement of

future short-term interest rates? What might the yield

curve indicate about the market’s predictions about

the inflation rate in the future?

Yield to

Maturity

Term to Maturity

---

114

Part 2 Fundamentals of Financial Markets