20-Term Structure Page 615 Wednesday, February 4, 2004 1:33 PM
Term Structure Modeling and Valuation of Bonds and Bond Options 615All these responses would tend either to lower the net demand for,
or to increase the supply of, long-maturity bonds, and all three
responses would increase demand for short-term bonds. This would
require a rise in long-term yields in relation to short-term yields; that is,
these actions by investors, speculators, and borrowers would tilt the
term structure upward until it is consistent with expectations of higher
future interest rates. By analogous reasoning, an unexpected event lead-
ing to the expectation of lower future rates will result in the yield curve
sloping downward.
Unfortunately, the pure expectations theory suffers from one short-
coming, which, qualitatively, is quite serious. It neglects the risks inher-
ent in investing in bonds. If forward rates were perfect predictors of
future interest rates, the future prices of bonds would be known with
certainty. The return over any investment period would be certain and
independent of the maturity of the instrument initially acquired and of
the time at which the investor needed to liquidate the instrument. How-
ever, with uncertainty about future interest rates and hence about future
prices of bonds, these instruments become risky investments in the sense
that the return over some investment horizon is unknown.
There are two risks that cause uncertainty about the return over some
investment horizon: interest rate risk and reinvestment risk. Interest rate
risk is the uncertainty about the price of the bond at the end of the invest-
ment horizon. For example, an investor who plans to invest for five years
might consider the following three investment alternatives: (1) invest in a
5-year bond and hold it for five years; (2) invest in a 12-year bond and sell
it at the end of five years; and (3) invest in a 30-year bond and sell it at the
end of five years. The return that will be realized for the second and third
alternatives is not known because the price of each long-term bond at the
end of five years is not known. In the case of the 12-year bond, the price
will depend on the yield on 7-year debt securities five years from now; and
the price of the 30-year bond will depend on the yield on 25-year bonds
five years from now. Because forward rates implied in the current term
structure for a future 12-year bond and a future 25-year bond are not per-
fect predictors of the actual future rates, there is uncertainty about the
price for both bonds five years from now. Thus there is interest rate risk;
that is, the risk that the price of the bond will be lower than currently
expected at the end of the investment horizon. An important feature of
interest rate risk is that it is greater the longer the maturity of the bond.
The second risk has to do with the uncertainty about the rate at
which the proceeds from a bond can be reinvested until the expected
maturity date. This risk is referred to as reinvestment risk. For example,
an investor who plans to invest for five years might consider the follow-
ing three alternative investments: (1) invest in a 5-year bond and hold it