THE ECONOMICS OF MONEY,BANKING, AND FINANCIAL MARKETS 156

124

PA R T I I

Financial Markets
We can conduct the same steps for bonds with a longer maturity so that we
can examine the whole term structure of interest rates. Doing so, we will find that
the interest rate of int on an n-period bond must equal
int *

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

(2)

Equation 2 states that the n-period interest rate equals the average of the oneperiod interest rates expected to occur over the n-period life of the bond. This is
a restatement of the expectations theory in more precise terms.1

APP LI CAT IO N

Expectations Theory and the Yield Curve
The one-year interest rate over the next five years is expected to be 5%, 6%, 7%,
8%, and 9%. Given this information, what are the interest rates on a two-year bond
and a five-year bond? Explain what is happening to the yield curve.

Solution

The interest rate on the two-year bond would be 5.5%.
i t + i et + 1 + i et + 2 + . . . + i te + (n - 1)
int *
n

where
it * year 1 interest rate * 5%
i te+ 1 * year 2 interest rate * 6%
n * number of years

*2

Thus
i 2t *

5% + 6%
* 5.5%
2

The interest rate on the five-year bond would be 7%.
it + ite+ 1 + ite+ 2 + . . . + ite+ (n - 1)
int *
n
where
it * year 1 interest rate * 5%
i te+ 1 * year 2 interest rate * 6%
i et + 2 * year 3 interest rate * 7%
i et + 3 * year 4 interest rate * 8%
i et + 4 * year 5 interest rate * 9%
n * number of years * 5

1

The analysis here has been conducted for discount bonds. Formulas for interest rates on coupon
bonds would differ slightly from those used here but would convey the same principle.