# Question

Suppose inflation currently is about 2 percent. Last year, the Fed took action to maintain inflation at this level. Now, the economy is starting to grow too quickly, and reports indicate that inflation is expected to increase during the next five years. Assume that the rate of inflation expected for the next year (Year 1) is 4 percent; the following year (Year 2) it is expected to be 5 percent; three years from now (Year 3) it is expected to be 7 percent; and every year thereafter, it is expected to settle at 4 percent.

a. What was the average expected inflation rate over the next five years (Year 1 through Year 5)?

b. What average nominal interest rate would be expected, over the five-year period, to produce a 2 percent real risk-free rate of return on five-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 on bonds that mature in one, two, five, 10, and 20 years, and then 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 had been that the expected rate of inflation for every future year was 5 percent (i.e., InflationYear1 InflationYear2 = 5% = . = InflationYear∞), what do you think the yield curve would have looked like? Consider all factors that are likely to affect the curve. Does your answer here make you question the yield curve you drew in part (c)?

a. What was the average expected inflation rate over the next five years (Year 1 through Year 5)?

b. What average nominal interest rate would be expected, over the five-year period, to produce a 2 percent real risk-free rate of return on five-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 on bonds that mature in one, two, five, 10, and 20 years, and then 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 had been that the expected rate of inflation for every future year was 5 percent (i.e., InflationYear1 InflationYear2 = 5% = . = InflationYear∞), what do you think the yield curve would have looked like? Consider all 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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