THE ECONOMICS OF MONEY,BANKING, AND FINANCIAL MARKETS 161

CHAPTER 6

The Risk and Term Structure of Interest Rates

129

The interest rate on the five-year bond would be 8%.
int

it + i te+ 1 + i et + 2 + . . . + i te+ (n - 1)
n

lnt

where
it

year 1 interest rate

5%

i et + 1
i et + 2
i et + 3
i et + 4

year 2 interest rate

6%

year 3 interest rate

7%

year 4 interest rate

8%

year 5 interest rate

9%

l5t

liquidity premium

1%

n

number of years

5

Thus
i5t =

5%

6%

7%
5

8%

9%

1%

8.0%

If you did similar calculations for the one-, three-, and four-year interest rates, the
one-year to five-year interest rates would be as follows: 5.0%, 5.75%, 6.5%, 7.25%, and
8.0%, respectively. Comparing these findings with those for the pure expectations
theory, we can see that the liquidity preference theory produces yield curves that
slope more steeply upward because of investors preferences for short-term bonds.

Let s see if the liquidity premium and preferred habitat theories are consistent
with all three empirical facts we have discussed. They explain fact 1, that interest
rates on different-maturity bonds move together over time: a rise in short-term
interest rates indicates that short-term interest rates will, on average, be higher in
the future, and the first term in Equation 3 then implies that long-term interest rates
will rise along with them.
They also explain why yield curves tend to have an especially steep upward
slope when short-term interest rates are low and to be inverted when short-term
rates are high (fact 2). Because investors generally expect short-term interest rates
to rise to some normal level when they are low, the average of future expected
short-term rates will be high relative to the current short-term rate. With the additional boost of a positive liquidity premium, long-term interest rates will be substantially above current short-term rates, and the yield curve would then have a
steep upward slope. Conversely, if short-term rates are high, people usually expect
them to come back down. Long-term rates would then drop below short-term rates

because the average of expected future short-term rates would be so far below
current short-term rates that despite positive liquidity premiums, the yield curve
would slope downward.
The liquidity premium and preferred habitat theories explain fact 3, that yield
curves typically slope upward, by recognizing that the liquidity premium rises with
a bond s maturity because of investors preferences for short-term bonds. Even if