Financial Markets and Institutions (2-downloads)

110

Part 2 Fundamentals of Financial Markets

T H E   P R A C T I C I N G   M A N A G E R

Using the Term Structure to Forecast

Interest Rates

As was discussed in Chapter 4, interest-rate forecasts are extremely important to

managers of financial institutions because future changes in interest rates have a sig-

nificant impact on the profitability of their institutions. Furthermore, interest-rate

forecasts are needed when managers of financial institutions have to set interest rates

on loans that are promised to customers in the future. Our discussion of the term

structure of interest rates has indicated that the slope of the yield curve provides gen-

eral information about the market’s prediction of the future path of interest rates. For

example, a steeply upward-sloping yield curve indicates that short-term interest rates

are predicted to rise in the future, and a downward-sloping yield curve indicates that

short-term interest rates are predicted to fall. However, a financial institution man-

ager needs much more specific information on interest-rate forecasts than this. Here

we show how the manager of a financial institution can generate specific forecasts

of interest rates using the term structure.

To see how this is done, let’s start the analysis using the approach we took in

developing the pure expectations theory. Recall that because bonds of different matu-

rities are perfect substitutes, we assumed that the expected return over two peri-

ods from investing $1 in a two-period bond, which is (1 + i

2t

)(1 + i

2t

) – 1, must

equal the expected return from investing $1 in one-period bonds, which is (1 + i

t

)

. This is shown graphically as follows:

11 ⫹ i

e

t

⫹1

2 ⫺ 1

Today

0

1

 i

t

Year

1

Year

2

1

 i

e

t

 1

(1

 i

2t

) (1

 i

2t

)

---

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

111

Not surprisingly, this 6% forward rate is identical to the expected one-year interest rate

one year in the future that we used in Example 3. This is exactly what we should find,

as our calculation here is just another way of looking at the pure expectations theory.

We can also compare holding the three-year bond against holding a sequence

of one-year bonds, which reveals the following relationship:

and plugging in the estimate for 

derived in Equation 4, we can solve for 

:

Continuing with these calculations, we obtain the general solution for the forward

rate n periods into the future:

(5)

Our discussion indicated that the pure expectations theory is not entirely sat-

isfactory because investors must be compensated with liquidity premiums to induce

them to hold longer-term bonds. Hence we need to modify our analysis, as we did

when discussing the liquidity premium theory, by allowing for these liquidity pre-

miums in estimating predictions of future interest rates.

Recall from the discussion of those theories that because investors prefer to hold

short-term rather than long-term bonds, the n-period interest rate differs from

that indicated by the pure expectations theory by a liquidity premium of l