178 Part 3 Financial Assets
weaker economic conditions generally lead to declining in" ation, which, in turn,
results in lower long-term rates.^11
Now let’s consider the yield curve for corporate bonds. Recall that corporate
bonds include a default risk premium (DRP) and a liquidity premium (LP). Therefore,
the yield on a corporate bond that matures in t years can be expressed as follows:Corporate bond yield! r*t " IPt " MRPt " DRPt " LPtCorporate bonds’ default and liquidity risks are affected by their maturities. For
example, the default risk on Coca-Cola’s short-term debt is very small since there is(^11) Note that yield curves tend to rise or fall relatively sharply over the # rst 5 to 10 years and then! atten out. One
reason this occurs is that when forecasting future interest rates, people often predict relatively high or low in! ation
for the next few years, after which they assume an average long-run in! ation rate. Consequently, the short end of
the yield curve tends to have more curvature and the long end of the yield curve tends to be more stable.
Throughout the text, we use the following equation to
describe the link between expected in" ation and the nomi-
nal risk-free rate of interest, rRF:
rRF! r " IP
Recall that r is the real risk-free interest rate and IP is the cor-
responding in" ation premium. This equation suggests that
there is a simple link between expected in" ation and nomi-
nal interest rates.
It turns out, however, that this link is a bit more complex.
To fully understand this relationship, $ rst recognize that indi-
viduals get utility through the consumption of real goods and
services such as bread, water, haircuts, pizza, and textbooks.
When we save money, we are giving up the opportunity to
consume these goods today in return for being able to con-
sume more of them in the future. Our gain from waiting is
measured by the real rate of interest, r.
To illustrate this point, consider the following example.
Assume that a loaf of bread costs $1 today. Also assume that
the real rate of interest is 3% and that in" ation is expected to
be 5% over the next year. The 3% real rate indicates that the
average consumer is willing to trade 100 loaves of bread
today for 103 loaves next year. If a “bread bank” were avail-
able, consumers who wanted to defer consumption until
next year could deposit 100 loaves today and withdraw 103
loaves next year. In practice, most of us do not directly trade
real goods such as bread—instead, we purchase these goods
with money because in a well-functioning economy, it is
more e# cient to exchange money than goods. However,
when we lend money over time, we worry that borrowers
might pay us back with dollars that aren’t worth as much due
to in" ation. To compensate for this risk, lenders build in a
premium for expected in" ation.
With these concerns in mind, let’s compare the dollar
cost of 100 loaves of bread today to the cost of 103 loaves
next year. Given the current price, 100 loaves of bread today
would cost $100. Since expected in" ation is 5%, this means
that a loaf of bread is expected to cost $1.05 next year. Conse-
quently, 103 loaves of bread are expected to cost $108.15
next year (103 $ $1.05). So if consumers were to deposit $100
in a bank today, they would need to earn 8.15% to realize a
real return of 3%.
Putting this all together, we see that the 1-year nominal
interest rate can be calculated as follows:
rRF! (1 " r)(1 " I) # 1
! (1.03)(1.05) # 1! 0.0815! 8.15%
Note that this expression can be rewritten as follows:
rRF! r " I " (r $ I)
That equation is identical to our original expression for the
nominal risk-free rate except that it includes a “cross-term,”
r* $ I. When real interest rates and expected in" ation are
relatively low, the cross-term turns out to be quite small and
thus is often ignored. Because it is normally insigni$ cant we
disregard the cross-term in the text unless stated
otherwise.
One last point—you should recognize that while it may
be reasonable to ignore the cross-term when interest rates
are low (as they are in the United States today), it is a mistake
to do so when investing in a market where interest rates and
in" ation are quite high, as is often the case in many emerging
markets. In these markets, the cross-term can be signi$ cant
and thus should not be disregarded.
THE LINKS BETWEEN EXPECTED INFLATION AND INTEREST
RATES: A CLOSER LOOK