The Mathematics of Financial Modelingand Investment Management

20-Term Structure Page 614 Wednesday, February 4, 2004 1:33 PM

614 The Mathematics of Financial Modeling and Investment Management

and also assume that the forward rates in current long-term bonds are

closely related to the market’s expectations about future short-term

rates. These three expectations theories differ, however, as to whether

other factors also affect forward rates, and how. The pure expectations

theory postulates that no systematic factors other than expected future

short-term rates affect forward rates; the liquidity theory and the pre-

ferred habitat theory assert that there are other factors. Accordingly, the

last two forms of the expectations theory are sometimes referred to as

biased expectations theories.

Pure Expectations Theory

According to the pure expectations theory, the forward rates exclusively

represent the expected future spot rates. Thus the entire term structure at a

given time reflects the market’s current expectations of the family of future

short-term rates. Under this view, a rising term structure must indicate

that the market expects short-term rates to rise throughout the relevant

future. Similarly, a flat term structure reflects an expectation that future

short-term rates will be mostly constant, and a falling term structure must

reflect an expectation that future short rates will decline steadily.

We can illustrate this theory by considering how the expectation of

a rising short-term future rate would affect the behavior of various mar-

ket participants so as to result in a rising yield curve. Assume an initially

flat term structure, and suppose that subsequent economic news leads

market participants to expect interest rates to rise.

1. Those market participants interested in long-term bonds would not
   want to buy long-term bonds because they would expect the yield
   structure to rise sooner or later, resulting in a price decline for the
   bonds and a capital loss on the long-term bonds purchased. Instead,
   they would want to invest in short-term debt obligations until the rise
   in yield had occurred, permitting them to reinvest their funds at the
   higher yield.


2. Speculators expecting rising rates would anticipate a decline in the
   price of long-term bonds and therefore would want to sell any long-
   term bonds they own and possibly to “short sell” some they do not
   own. (Should interest rates rise as expected, the price of longer-term
   bonds will fall. Because the speculator sold these bonds short and can
   then purchase them at a lower price to cover the short sale, a profit will
   be earned.) Speculators will reinvest in short-term bonds.


3. Borrowers wishing to acquire long-term funds would be pulled toward
   borrowing now in the long end of the market by the expectation that
   borrowing at a later time would be more expensive.