Dynamic Macroeconomics

20.4.2 The Term Structure of Interest Rates
The federal funds rate is the central interest rate in the US financial market. It
influences other interest rates, such as the 
prime rate
, which is the rate banks
charge their customers with higher credit ratings. Additionally, the federal
funds rate indirectly influences longer-term interest rates, such as the yield of
government bonds, corporate bonds, mortgages, loans, and savings, all of

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which are very important to the cost of borrowing, consumer wealth, and
confidence.
Interest rates on short- and long-term securities are related through the
term structure of interest rates
. Assume that there are two types of discount
bonds, which are perfect substitutes: a short-term bond, which pays an
interest rate 
i
1
at the end of one period, and a long-term bond, which lasts for
n
periods and pays a rate of return 
ni
n
at the end of 
n
periods. Here 
i
n
is the
per period interest rate of the 
n
-period bond.
Assuming that investors are risk neutral, they will be indifferent between
investing in a sequence of one-period bonds for 
n
periods and an 
n
-period
bond, if the two types of portfolio investment have the same expected rate of
return. Hence, at time 
t
, arbitrage would ensure that
From 
(20.28)
, it follows that the per period rate of return of the 
n
-period
bond would be equal to the average expected rate of return of one-period
bonds between period 
t
and period 
t
+ 
n
:
Thus, open market operations that affect short-term rates would cause long-
term rates to move in the same direction. If the change in short-term rates is
temporary, then a rise in the short-term rate by one percentage point would
raise long-term rates by 1
/n
of a percentage point. If the change is permanent,
it will raise long-term rates by one full percentage point as well. If it is
expected to persist for 
m
periods, where 
m < n
, then the effect on long-term
rates will be 
m/n
of a percentage point as well.
This theory of the term structure of interest rates, which results in long-
term rates being the average of the expected future short-term rates, is called
the 
expectations theory of the term structure
.
The theory can be extended to allow for risk-averse investors. In that
case, 
(20.29)
 is modified to

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where is a positive 
term premium
to holding an 
n
-period bond, reflecting
the higher uncertainty about the rate of return of the long-term bond.
Hence, on the basis of the expectations theory of the term structure, open
market operations that affect short-term rates (such as the federal funds rate)
also affect the whole spectrum of interest rates in the same direction.