Because the liquidity premium is always positive and grows as the term to maturity
increases, the yield curve implied by the liquidity premium theory is always above
the yield curve implied by the expectations theory and has a steeper slope. For simplic-
ity, the yield curve implied by the expectations theory is drawn under the scenario of
Chapter 5 How Do Risk and Term Structure Affect Interest Rates?
105
As in Example 3, let’s suppose that the one-year interest rates over the next five years
are expected to be 5%, 6%, 7%, 8%, and 9%. Investors’ preferences for holding short-term
bonds have the liquidity premiums for one-year to five-year bonds as 0%, 0.25%, 0.5%,
0.75%, and 1.0%, respectively. What is the interest rate on a two-year bond and a five-
year bond? Compare these findings with the answer from Example 3 dealing with the pure
expectations theory.
Solution
The interest rate on the two-year bond would be 5.75%.
where
i
t
=
year 1 interest rate
= 5%
=
year 2 interest rate
= 6%
l
nt
=
liquidity premium
= 0.25%
n
=
number of years
= 2
Thus,
The interest rate on the five-year bond would be 8%.
where
i
t
=
year 1 interest rate
= 5%
=
year 2 interest rate
= 6%
=
year 3 interest rate
= 7%
=
year 4 interest rate
= 8%
=
year 5 interest rate
= 9%
l
2t
=
liquidity premium
= 1%
n
=
number of years
= 5
Thus,
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.
i
5t
⫽
5%
⫹ 6% ⫹ 7% ⫹ 8% ⫹ 9%
5
⫹ 1% ⫽ 8.0%
i
e
t
⫹4
i
e
t
⫹3
i
e
t
⫹2
i
e
t
⫹1
i
nt
⫽
i
t
⫹ i
e
t
⫹1
⫹ i
e
t
⫹2
⫹ p ⫹ i
e
t
⫹1n⫺12
n
⫹ l
nt
i
2t
⫽
5%
⫹ 6%
2
⫹ 0.25% ⫽ 5.75%
i
e
t
⫹1
i
nt
⫽
i
t
⫹ i
e
t
⫹1
⫹ i
e
t
⫹2
⫹ p ⫹ i
e
t
⫹1n⫺12
n
⫹ l
nt
E X A M P L E 5 . 4 Liquidity Premium Theory
106
Part 2 Fundamentals of Financial Markets
Let’s see if the liquidity premium theory is consistent with all three empirical facts
we have discussed. They explain fact 1, which states 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 higher
than current short-term rates, and the yield curve will then have a steep upward
slope. Conversely, if short-term rates are high, people usually expect them to come
back down. Long-term rates will then drop below short-term rates because the aver-
age of expected future short-term rates will be so far below current short-term rates
that despite positive liquidity premiums, the yield curve will slope downward.
The liquidity premium theory explains fact 3, which states that yield curves typ-
ically slope upward, by recognizing that the liquidity premium rises with a bond’s matu-
rity because of investors’ preferences for short-term bonds. Even if short-term interest
rates are expected to stay the same on average in the future, long-term interest rates
will be above short-term interest rates, and yield curves will typically slope upward.
How can the liquidity premium theory explain the occasional appearance of
inverted yield curves if the liquidity premium is positive? It must be that at times
short-term interest rates are expected to fall so much in the future that the aver-
age of the expected short-term rates is well below the current short-term rate. Even
when the positive liquidity premium is added to this average, the resulting long-
term rate will still be lower than the current short-term interest rate.
As our discussion indicates, a particularly attractive feature of the liquidity pre-
mium theory is that it tells you what the market is predicting about future short-term
interest rates just from the slope of the yield curve. A steeply rising yield curve, as
in panel (a) of Figure 5.6, indicates that short-term interest rates are expected to rise
in the future. A moderately steep yield curve, as in panel (b), indicates that short-
term interest rates are not expected to rise or fall much in the future. A flat yield
curve, as in panel (c), indicates that short-term rates are expected to fall moderately
in the future. Finally, an inverted yield curve, as in panel (d), indicates that short-
term interest rates are expected to fall sharply in the future.
Evidence on the Term Structure
In the 1980s, researchers examining the term structure of interest rates questioned
whether the slope of the yield curve provides information about movements of future
short-term interest rates.
5
They found that the spread between long- and short-
term interest rates does not always help predict future short-term interest rates, a
finding that may stem from substantial fluctuations in the liquidity (term) premium
for long-term bonds. More recent research using more discriminating tests now favors
5
Robert J. Shiller, John Y. Campbell, and Kermit L. Schoenholtz, “Forward Rates and Future Policy:
Interpreting the Term Structure of Interest Rates,”
Brookings Papers on Economic Activity 1 (1983):
173–217; N. Gregory Mankiw and Lawrence H. Summers, “Do Long-Term Interest Rates Overreact to
Short-Term Interest Rates?” Brookings Papers on Economic Activity 1 (1984): 223–242.
