THE ECONOMICS OF MONEY,BANKING, AND FINANCIAL MARKETS 168

136

PA R T I I

APP LI CAT IO N

Financial Markets

Forward Rate
A customer asks a bank if it would be willing to commit to making the customer
a one-year loan at an interest rate of 8% one year from now. To compensate for
the costs of making the loan, the bank needs to charge one percentage point more
than the expected interest rate on a Canada bond with the same maturity if it is to
make a profit. If the bank manager estimates the liquidity premium to be 0.4%, and
the one-year Canada bond rate is 6% and the two-year bond rate is 7%, should the
manager be willing to make the commitment?

Solution

The bank manager is unable to make the loan because at an interest rate of 8%,
the loan is likely to be unprofitable to the bank.
i
where
in 1t
*n 1t
int
*1t
n

e
t

n

=

two-year bond rate
liquidity premium
one-year bond rate
liquidity premium
number of years

11 + in + 1t - *n + 1t2n + 1
11 + int - *nt2n

- 1

0.07
0.004
0.06
0
1

Thus
i et

1

=

11 + 0.07 - 0.00422

1 + 0.06

- 1 = 0.072 = 7.2%

The market s forecast of the one-year Canada bond rate one year in the future is
therefore 7.2%. Adding the 1% necessary to make a profit on the one-year loan
means that the loan is expected to be profitable only if it has an interest rate of
8.2% or higher.

S U M M A RY
1. Bonds with the same maturity will have different
interest rates because of three factors: default risk, liquidity, and tax considerations. The greater a bond s
default risk, the higher its interest rate relative to other
bonds; the greater a bond s liquidity, the lower its
interest rate; and bonds with tax-exempt status will
have lower interest rates than they otherwise would.
The relationship among interest rates on bonds with
the same maturity that arises because of these three
factors is known as the risk structure of interest rates.
2. Four theories of the term structure provide explanations of how interest rates on bonds with different
terms to maturity are related. The expectations theory
views long-term interest rates as equalling the average

of future short-term interest rates expected to occur
over the life of the bond; by contrast, the segmented
markets theory treats the determination of interest
rates for each bond s maturity as the outcome of supply and demand in each market in isolation. Neither of
these theories by itself can explain the fact that interest rates on bonds of different maturities move
together over time and that yield curves usually slope
upward.

3. The liquidity premium and preferred habitat theories
combine the features of the other two theories and by
so doing are able to explain the facts just mentioned.
They view long-term interest rates as equalling the
average of future short-term interest rates expected to