Complete the following problems from your textbook
6-1 YIELD CURVES Assume that yields on U.S. Treasury securities were as follows: Term Rate 6 months 4.69% 1 year 5.49 2 years 5.66 3 years 5.71 4 years 5.89 5 years 6.05 10 years 6.12 20 years 6.64 30 years 6.76 a. Plot a yield curve based on these data. b. What type of yield curve is shown? c. What information does this graph tell you? d. Based on this yield curve, if you needed to borrow money for longer than 1 year, would it make sense for you to borrow short term and renew the loan or borrow long term? Explain. 6-2 REAL RISK-FREE RATE You read in The Wall Street Journal that 30-day T-bills are currently yielding 5.8%. Your brother-in-law, a broker at Safe and Sound Securities, has given you the following estimates of current interest rate premiums: • Inflation premium = 3.25% • Liquidity premium = 0.6% • Maturity risk premium = 1.85% • Default risk premium = 2.15% On the basis of these data, what is the real risk-free rate of return? 6-3 EXPECTED INTEREST RATE The real risk-free rate is 2.25%. Inflation is expected to be 2.5% this year and 4.25% during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasury securities? 6-4 DEFAULT RISK PREMIUM A Treasury bond that matures in 10 years has a yield of 5.75%. A 10-year corporate bond has a yield of 8.75%. Assume that the liquidity premium on the corporate bond is 0.35%. What is the default risk premium on the corporate bond? 6-5 MATURITY RISK PREMIUM The real risk-free rate is 2.5% and inflation is expected to be 2.75% for the next 2 years. A 2-year Treasury security yields 5.55%. What is the maturity risk premium for the 2-year security? 6-19 INFLATION AND INTEREST RATES 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 × (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?