Financial Markets and Institutions (2-downloads)

Interpreting Yield Curves, 1980–2010

Figure 5.7 illustrates several yield curves that have appeared for U.S. government

bonds in recent years. What do these yield curves tell us about the public’s expec-

tations of future movements of short-term interest rates?

The steep inverted yield curve that occurred on January 15, 1981, indicated

that short-term interest rates were expected to decline sharply in the future. For

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

109

1

2

3

4

5

5

10

15

20

6

8

10

12

14

16

Terms to Maturity (Years)

Interest Rate (%)

May 16, 1980

March 28, 1985

January 15, 1981

May 13, 2010

March 3, 1997

0

4

2

F I G U R E   5 . 7

Yield Curves for U.S. Government Bonds

Sources: Federal Reserve Bank of St. Louis; U.S. Financial Data, various issues; Wall Street Journal,

various dates.

longer-term interest rates with their positive liquidity premium to be well below the

short-term interest rate, short-term interest rates must be expected to decline so

sharply that their average is far below the current short-term rate. Indeed, the pub-

lic’s expectations of sharply lower short-term interest rates evident in the yield curve

were realized soon after January 15; by March, three-month Treasury bill rates had

declined from the 16% level to 13%.

The steep upward-sloping yield curve on March 28, 1985, and May 13, 2010,

indicated that short-term interest rates would climb in the future. The long-

term interest rate is higher than the short-term interest rate when short-term

interest rates are expected to rise because their average plus the liquidity pre-

mium will be higher than the current short-term rate. The moderately upward-

sloping yield curves on May 16, 1980, and March 3, 1997, indicated that

short-term interest rates were expected neither to rise nor to fall in the near

future. In this case, their average remains the same as the current short-term rate,

and the positive liquidity premium for longer-term bonds explains the moderate

upward slope of the yield curve.

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In other words,

Through some tedious algebra we can solve for 

:

(4)

This measure of 

is called the forward rate because it is the one-period inter-

est rate that the pure expectations theory of the term structure indicates is expected

to prevail one period in the future. To differentiate forward rates derived from the

term structure from actual interest rates that are observed at time t, we call these

observed interest rates spot rates.

Going back to Example 3, which we used to discuss the pure expectations the-

ory earlier in this chapter, at time t the one-year interest rate is 5% and the two-

year rate is 5.5%. Plugging these numbers into Equation 4 yields the following

estimate of the forward rate one period in the future:

i

e

t

⫹1

⫽

11 ⫹ 0.0552

2

1

⫹ 0.05

⫺ 1 ⫽ 0.06 ⫽  6%

i

e

t

⫹1

i

e

t

⫹1

⫽

11 ⫹ i

2t

2

2

1

⫹ i

t

⫺ 1

i

e

t

⫹1

11 ⫹ i

t

2 11 ⫹ i

e

t

⫹1

2 ⫺ 1 ⫽ 11 ⫹ i

2t

2 11 ⫹ i

2t

2 ⫺ 1