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Homework 6 Multiple Choice Identify the choice that best completes the statement or answers the question. ____

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1. Suppose 1-year T-bills currently yield 5.00% and the future inflation rate is expected to be constant at 3.10% per year. What is the real risk-free rate of return, r*? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average. A. 1.90% B. 2.00% C. 2.10% D. 2.20% E. 2.30% 2. Suppose the real risk-free rate is 3.50% and the future rate of inflation is expected to be constant at 2.25%. What rate of return would you expect on a 1-year Treasury security, assuming the pure expectations theory is valid? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average. A. 5.25% B. 5.50% C. 5.75% D. 6.00% E. 6.25% 3. The real risk-free rate is 2.50%, inflation is expected to be 3.00% this year, and the maturity risk premium is zero. Taking account of the cross-product term, i.e., not ignoring it, what is the equilibrium rate of return on a 1-year Treasury bond? A. 4.975% B. 5.175% C. 5.375% D. 5.575% E. 5.775% 4. Suppose the real risk-free rate is 3.50%, the average future inflation rate is 2.25%, a maturity premium of 0.08% per year to maturity applies, i.e., MRP = 0.08%(t), where t is the years to maturity. Suppose also that a liquidity premium of 0.5% and a default risk premium of 0.85 applies to A-rated corporate bonds. How much higher would the rate of return be on a 10-year A-rated corporate bond than on a 5-year Treasury bond. Here we assume that the pure expectations theory is NOT valid? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average. A. 1.75% B. 1.80% C. 1.85% D. 1.90% E. 1.95% 5. Suppose the interest rate on a 1-year T-bond is 5.0% and that on a 2-year T-bill is 6.0%. Assuming the pure expectations theory is correct, what is the market's forecast for 1-year rates 1 year from now? A. 6.65% B. 6.74% C. 6.83% D. 6.92% E. 7.01%

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6. Keys Corporation's 5-year bonds yield 6.50%, and 5-year T-bonds yield 4.40%. The real risk-free rate is r* = 2.5%, the inflation premium for 5 years bonds is IP = 1.50%, the default risk premium for Keys' bonds is DRP = 0.50% versus zero for T-bonds, and the maturity risk premium for all bonds is found with the formula MRP = (t − 1)*0.1%, where t = number of years to maturity. What is the liquidity premium (LP) on Keys' bonds? A. 1.30% B. 1.40% C. 1.50% D. 1.60% E. 1.70% 7. Keys Corporation's 5-year bonds yield 6.50%, and 5-year T-bonds yield 4.40%. The real risk-free rate is r* = 2.5%, the default risk premium for Keys' bonds is DRP = 0.50% versus zero for T-bonds, the liquidity premium on Keys' bonds is LP = 1.7%, and the maturity risk premium for all bonds is found with the formula MRP = (t − 1)*0.1%, where t = number of years to maturity. What is the inflation premium (LP) on 5-year bonds? A. 1.50% B. 1.60% C. 1.70% D. 1.80% E. 1.90% 8. Keys Corporation's 5-year bonds yield 6.50%, and T-bonds with the same maturity yield 4.40%. The default risk premium for Keys' bonds is DRP = 0.40%, the liquidity premium on Keys' bonds is LP = 1.70% versus zero on T-bonds, inflation premium (IP) is 1.5%, and the maturity risk premium (MRP) on 5-year bonds is 0.40%. What is the real risk-free rate, r*? A. 2.10% B. 2.20% C. 2.30% D. 2.40% E. 2.50% 9. Suppose 1-year Treasury bonds yield 3.0% while 2-year T-bonds yield 4.5%. Assuming the pure expectations theory is correct and thus the maturity risk premium is zero, what should the yield be on a 1-year T-bond one year from now? A. 5.91% B. 6.02% C. 6.13% D. 6.24% E. 6.35% 10. Your uncle would like to limit both his interest rate price risk (the risk that rising rates will cause the value of his bonds to decline) and his default risk, but he would still like to invest in corporate bonds. He is considering the following bonds. Which of these bonds would best meet his criteria? A. AAA bonds with 10 years to maturity. B. BBB perpetual bonds. C. BBB bonds with 10 years to maturity. D. AAA bonds with 5 years to maturity. E. BBB bonds with 5 years to maturity.

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____ 11. Which of the following would be most likely to lead to a higher level of interest rates in the economy? A. Households start saving a larger percentage of their income. B. Corporations step up their expansion plans and thus increase their demand for capital. C. The level of inflation begins to decline. D. The economy moves from a boom to a recession. E. The Federal Reserve decides to try to stimulate the economy. ____ 12. A bond trader observes the following information: • • •

The Treasury yield curve is downward sloping. Empirical data indicates that a positive maturity risk premium applies to both Treasury and corporate bonds. Empirical data also indicates that there is no liquidity premium for Treasury securities but that a positive liquidity premium is built into corporate bond yields.

On the basis of this information, which of the following statements is most correct? A. A 10-year corporate bond must have a higher yield than a 5-year Treasury bond. B. A 10-year Treasury bond must have a higher yield than a 10-year corporate bond. C. A 5-year corporate bond must have a higher yield than a 10-year Treasury bond. D. The corporate yield curve must be flat. E. Since the Treasury yield curve is downward sloping, the corporate yield curve must also be downward sloping. ____ 13. The real risk-free rate is 3%. Inflation is expected to be 4% this coming year, jump to 5% next year, and increase to 6% the year after. According to the expectations theory, what should be the interest rate on 3-year, risk-free securities today? A. 18% B. 12% C. 6% D. 8% E. 10% ____ 14. Assume that the expectations theory holds, and that liquidity and maturity risk premiums are zero. If the 2-year Treasury bond rate is 10.5% and the 1-year Treasury bond rate is 12%, what does the market expect the 1-year Treasury bond rate one year from now will be? A. 8.68% B. 9.02% C. 9.56% D. 11.25% E. 13.48% ____ 15. One-year Treasury bills yield 6%, while 2-year Treasury notes yield 6.7%. If the expectations theory holds, what is the market's forecast of what 1-year T-bills will be yielding one year from now? A. 6.70% B. 7.40% C. 7.80% D. 8.00% E. 8.20%

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____ 16. One-year Treasury securities yield 5%, 2-year Treasury securities yield 5.5%, and 3-year Treasury securities yield 6%. Assume that the expectations theory holds. What does the market expect will be the yield on 1-year Treasury securities two years from now? A. 6.01% B. 6.51% C. 7.01% D. 7.51% E. 8.01% ____ 17. The real risk-free rate, r*, is 4%, and it is expected to remain constant over time. Inflation is expected to be 2% per year for the next three years, after which time inflation is expected to remain at a constant rate of 5% per year. The maturity risk premium is equal to 0.1(t − 1)%, where t = the bond's maturity. What is the yield on a 10-year Treasury bond? A. 8.1% B. 8.9% C. 9.0% D. 9.1% E. 9.9% ____ 18. You observe the following yield curve for Treasury securities: Maturity 1 year 2 years 3 years 4 years 5 years

Yield 5.5% 5.8 6.0 6.3 6.5

Assume that the pure expectations hypothesis holds. What does the market expect will be the yield on 4-year securities, 1 year from today? A. 6.00% B. 6.30% C. 6.40% D. 6.75% E. 7.30% ____ 19. Assume that r* = 2.0%; the maturity risk premium is found as MRP = 0.1%(t − 1), where t = years to maturity; the default risk premium for corporate bonds is found as DRP = 0.05%(t − 1); the liquidity premium is 1% for corporate bonds only; and inflation is expected to be 3%, 4%, and 5% during the next three years and then 6% thereafter. What is the difference in interest rates between 10-year corporate and Treasury bonds? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average. A. 0.45% B. 1.45% C. 2.20% D. 2.75% E. 3.25%

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____ 20. Three-year Treasury securities currently yield 6%, while 4-year Treasury securities currently yield 6.5%. Assume that the expectations theory holds. What does the market believe the rate will be on 1-year Treasury securities three years from now? A. 8.01% B. 8.51% C. 9.01% D. 9.51% E. 10.01% ____ 21. You observe the following yields on various Treasury securities: Maturity 1 year 3 years 6 years 9 years 12 years 15 years

Yield 6.0% 6.4 6.5 6.8 7.0 7.2

Using the expectations theory, forecast the interest rate on 6-year Treasuries, nine years from now. A. 6.70% B. 6.95% C. 7.20% D. 7.80% E. 8.00% ____ 22. Currently, 3-year Treasury securities yield 5.4%, 7-year Treasury securities yield 5.8%, and 10-year Treasury securities yield 6.2%. If the expectations theory is correct, what does the market expect will be the yield on 3-year Treasury securities seven years from today? A. 6.54% B. 7.14% C. 5.80% D. 4.58% E. 5.68% ____ 23. Three-year treasury securities yield 5%, 5-year treasury securities yield 6%, and 8-year treasury securities yield 7%. If the expectations theory is correct, what is the expected yield on 5-year Treasury securities three years from now? A. 5.09% B. 7.00% C. 6.71% D. 8.22% E. 6.03%

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____ 24. The real risk-free rate is expected to remain constant at 3%. Inflation is expected to be 4% a year for the next four years, and then 3% a year thereafter. The maturity risk premium is 0.1(t − 1)%, where t equals the maturity of the bond. A 7-year corporate bond has a yield of 9.8%. What is the yield on a 10-year corporate bond that has the same default risk premium and liquidity premium as the 7-year corporate bond? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average. A. 9.63% B. 9.73% C. 9.93% D. 10.03% E. 10.15% ____ 25. You read in The Wall Street Journal that 30-day T-bills are currently yielding 8%. Your brother-in-law, a broker at Kyoto Securities, has given you the following estimates of current interest rate premiums: • • • •

Inflation premium = 5%. Liquidity premium = 1%. Maturity risk premium = 2%. Default risk premium = 2%.

Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average. On the basis of these data, the real risk-free rate of return is A. 0% B. 1% C. 2% D. 3% E. 4%

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ID: A

Homework 6 Answer Section MULTIPLE CHOICE 1. ANS: A

TOP: Real risk-free rate, r* 2. ANS: C

TOP: Inflation and interest rates; no MRP; 1-year 3. ANS: D

TOP: Estimate the 1-year rate; with the cross-product term 4. ANS: A

TOP: Corporate vs. treasury bond yields 5. ANS: E

TOP: Estimating the 1-year forward rate

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ID: A 6. ANS: D

TOP: Liquidity premium (LP) 7. ANS: A

TOP: Inflation premium (IP) 8. ANS: E

TOP: Real risk-free rate, r* 9. ANS: B

TOP: Expectations theory 10. ANS: D TOP: Risk and return 11. ANS: B TOP: Interest rates 12. ANS: C TOP: Yield curve

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ID: A 13. ANS: D

4% + 5% + 6% = 5% . 3 rRF = r* + IP = 3% + 5% = 8%.

Average inflation =

TOP: Expected interest rates 14. ANS: B r1 = 1 year rate today = 1 year rate, one year from now 1r1 r2 = 2 year rate today (1 + r2)2 = (1 + r1)(1 + 1r1) (1.105)2 = (1.12)(1 + 1r1) 1r1 = 9.02% TOP: Expectations theory 15. ANS: B r1 = 1 year rate today = 1 year rate, one year from now 1r1 r2 = 2 year rate today (1 + r2)2 = (1 + r1)(1 + 1r1) (1.067)2 = (1.06)(1 + 1r1) 1r1 = 7.40% TOP: Expectations theory 16. ANS: C r2 = 2 year rate today r3 = 3 year rate today = 1 year rate, two years from now 2r1 (1 + r3)3 = (1 + r2)2(1 + 2r1) (1.06)3 = (1.055) 2(1 + 2r1) 2r1 = 7.01% TOP: Expectations theory 17. ANS: C IP is going to be the average inflation rate over the 10-year period. There will be 3 years of 2% inflation, then 7 years of 5% inflation. r

= r* + IP + MRP = 4% + (2% × 3 + 5% × 7)/10 + 0.1(10 − 1)% = 4% + (6% + 35%)/10 + 0.1(9%) = 4% + 4.1% + 0.9% = 9.0%.

TOP: Expected interest rates 3

ID: A 18. ANS: D r1 = 1 year rate today r = 4 year rate, one year from now 1 4 r5 = 5 year rate today (1 + r5)5 = (1 + r1)(1 + 1r4)4 (1.065)5 = (1.055)(1 + 1r4)4 1r4 = 6.75% TOP: 19. ANS: r* I1 IP10

r C10 T10

Expectations theory B = 2%; MRP = 0.1%(t − 1); DRP = 0.05%(t − 1); LP = 1% corporate only. = 3%; I2 = 4%; I3 = 5%; I4 and after = 6%. C10 − T10 = ? 3% + 4% + 5% + 6%(7) 54% = 5.4% . = = 10 10 = r* + IP + LP + DRP + MRP. = 2% + 5.4% + 1% + 0.05%(9) + 0.1%(9) = 9.75%. = 2% + 5.4% + 0% + 0% + 0.9% = 8.30%.

C10 − T10 = 9.75% − 8.30% = 1.45%. TOP: Expected interest rates 20. ANS: A r3 = 3 year rate today = 1 year rate, three years from now 3r1 r4 = 4 year rate today (1 + r4)4 = (1 + r3)3(1 + 3r1) (1.065)4 = (1.06) 3(1 + 3r1) 3r1 = 8.01% TOP: Expected interest rates 21. ANS: D r9 = 9 year rate today r = 6 year rate, nine years from now 9 6 r15 = 15 year rate today (1 + r15)15 = (1 + r9)9(1 + 9r 6)6 (1.072)15 = (1.068)9(1 + 9r6)6 9r6 = 7.80% TOP: Expectations theory

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ID: A 22. ANS: B r7 = 7 year rate today r = 3 year rate, seven years from now 7 3 r10 = 10 year rate today (1 + r10)10 (1.062)10 7r3

= (1 + r7)7(1 + 7r3)3 = (1.058)7(1 + 7r3)3 = 7.14%

TOP: Expectations theory 23. ANS: D r3 = 3 year rate today r = 5 year rate, three years from now 3 5 r8 = 8 year rate today (1 + r8)8 (1.07)8 3r5

= (1 + r3)3(1 + 3r5)5 = (1.05) 3(1 + 3r5)5 = 8.22%

TOP: Expectations theory 24. ANS: C rC7 = r* + IP7 + MRP7 + (DRP + LP) 9.8% 4%(4) + 3%(3) = 3% + + 0.1%(7 − 1) + (DRP + LP) 7 9.8% = 3% + 3.57% + 0.6% + (DRP + LP) 2.63% = DRP + LP. Now that we have solved for the default risk and liquidity premiums, we can carry the value forward and solve for the yield on a 10-year corporate bond. rC10 rC10 rC10

= r* + IP10 + MRP10 + (DRP + LP) 4%(4) + 3%(6) = 3% + + 0.1%(10 − 1) + 2.63% 10 = 3% + 3.4% + 0.9% + 2.63% = 9.93%.

TOP: Expected interest rates 25. ANS: D T-bill rate = r* + IP 8% = r* + 5% r* = 3%. TOP: Real risk-free rate of interest

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