## Question

###### In late 1980 , the U.S. Commerce Department released new figures that showed that in flation was running at an annual rate of close to 15 percent. At the time, the prime rate of interest was 21 percent, a record high. However, many investors expected the new Reagan administration to be more effective in controlling inflation than the Carter administration had been. Moreover, many observers believed that the extremely high interest rates and generally tight credit, which resulted from the Federal

In late 1980 , the U.S. Commerce Department released new figures that showed that in flation was running at an annual rate of close to 15 percent. At the time, the prime rate of interest was 21 percent, a record high. However, many investors expected the new Reagan administration to be more effective in controlling inflation than the Carter administration had been. Moreover, many observers believed that the extremely high interest rates and generally tight credit, which resulted from the Federal Reserve System's attempts to curb the inflation rate, would shortly bring about a recession, which, in turn, would lead to a decline in the inflation rate and also in the interest rate. Assume that at the beginning of 1981 , the expected inflation rate for 1981 was 13 percent; for 1982,9 percent; for 1983,7 percent; and for 1984 and thereafter, 6 percent. a. What was the average expected inflation rate over the 5 -year period $1981-1985$ ? (Use the arithmetic average.) b. What average nominal interest rate would, over the 5 -year period, be expected to produce a 2 percent real risk-free rate of return on 5 -year Treasury securities? c. Assuming a real risk-free rate of 2 percent and a maturity risk premium that starts at 0.1 percent and increases by 0.1 percent each year, estimate the interest rate in January 1981 on bonds that mature in $1,2,5,10,$ and 20 years, and draw a yield curve based on these data. d. Describe the general economic conditions that could be expected to produce an upward-sloping yield curve. e. If the consensus among investors in early 1981 had been that the expected inflation rate for every future year was 10 percent (that is, $\mathrm{I}_{\mathrm{t}}=\mathrm{I}_{\mathrm{t}+1}=10 \%$ for $\mathrm{t}=1$ to $\infty$ ), what do you think the yield curve would have looked like? Consider all the factors that are likely to affect the curve. Does your answer here make you question the yield curve you drew in part c?