In late 1980, the U.S. Commerce Departmentreleased new data showing inflation was 15%. At the time, the prime rate of interestwas 21%, a record high. However, many investors expected the new Reagan administrationto be more effective in controlling inflation than the Carter administration hadbeen. Moreover, many observers believed that the extremely high interest rates andgenerally tight credit, which resulted from the Federal Reserve System’s attempts tocurb the inflation rate, would lead to a recession, which, in turn, would lead to a declinein inflation and interest rates. Assume that, at the beginning of 1981, the expected inflationrate for 1981 was 13%; for 1982, 9%; for 1983, 7%; and for 1984 and thereafter, 6%.a. What was the average expected inflation rate over the 5-year period 1981–1985? (Usethe arithmetic average.) b. Over the 5-year period, what average nominal interest rate would be expected to producea 2% real risk-free return on 5-year Treasury securities? Assume MRP = 0.c. Assuming a real risk-free rate of 2% and a maturity risk premium that equals 0.1 x(t)%,where t is the number of years to maturity, estimate the interest rate in January 1981 onbonds that mature in 1, 2, 5, 10, and 20 years. Draw a yield curve based on these data.d. Describe the general economic conditions that could lead to an upward-sloping yield curve.e. If investors in early 1981 expected the inflation rate for every future year to be 10%(i.e., It = It+1 = 10% for t = 1 to ∞), what would the yield curve have looked like?Consider all the factors that are likely to affect the curve. Does your answer here makeyou question the yield curve you drew in part c?
In late 1980, the U.S. Commerce Department
released new data showing inflation was 15%. At the time, the prime rate of interest
was 21%, 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 lead to a recession, which, in turn, would lead to a decline
in inflation and interest rates. Assume that, at the beginning of 1981, the expected inflation
rate for 1981 was 13%; for 1982, 9%; for 1983, 7%; and for 1984 and thereafter, 6%.
a. What was the average expected inflation rate over the 5-year period 1981–1985? (Use
the arithmetic average.)
b. Over the 5-year period, what average nominal interest rate would be expected to produce
a 2% real risk-free return on 5-year Treasury securities? Assume MRP = 0.
c. Assuming a real risk-free rate of 2% and a maturity risk premium that equals 0.1 x(t)%,
where t is the number of years to maturity, estimate the interest rate in January 1981 on
bonds that mature in 1, 2, 5, 10, and 20 years. Draw a yield curve based on these data.
d. Describe the general economic conditions that could lead to an upward-sloping yield curve.
e. If investors in early 1981 expected the inflation rate for every future year to be 10%
(i.e., It = It+1 = 10% for t = 1 to ∞), what would the yield curve 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?
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