Chapter 7, interest rates and bonds PDF

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Chapter questions, solutions and the formulas used if necessary....

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1. The possibility of a bondholder suffering losses when yields-to-maturity on similar bonds change is called a. b. c. d.

market yield risk" systematic risk" term structure risk" interest rate risk

2. A bond has 8 years remaining to maturity, pays annual coupons (yesterday) of $5, and has a face value of $100. The current price of the bond is $88.057 and the price next year is expected to be $89.221. (Interest rates are not expected to change over the coming year.) What is the yield to maturity on the bond?" 7%

3. Consider the treasury spot rate yield curve. That is, the yield curve constructed from zero coupon bonds issued by the Government with no default risk. If expected inflation rises in all future periods (by an equal amount), then the yield curve will: a. b. c. d.

shift down (parallel)" extend" shift up (parallel)" shift up (and get steeper)

4. A BBB corporate bond has 17 years remaining to maturity, pays annual coupons (yesterday) of $5, and has a face value of $100. The current price of the bond is $142.88 to yield 2%. What is the capital gain rate for the coming year if the yield to maturity remains constant?" -1.5%"

5. Consider a two-year coupon bond with a face value of $100 and a coupon rate of 8.5% (the next annual coupon is due in one year). The one-year spot rate is 5.5% and the two-year spot rate is 7.2357%. What is the expected holding period return if you buy the bond after the first coupon? (Assume no change in the economy.)" 9%

6. Springfield Nuclear Energy Inc. bonds are currently trading for $97.33. The bonds have a face value of $100, a coupon rate of 5 % with coupons paid annually, and they mature in 3 years. What is the yield to maturity of the bonds? 6%

7. What is the nominal yield on a 10-year government T-note if the real rate is 4%, the expected inflation is 5%, the liquidity premium is 1%, and the maturity risk premium is 1%? a. b. c. d.

not enough information" 1.0%" 1.5%" 2.0%"

8. What is the percentage change in price for a zero coupon bond if the yield falls by 1% from 5.5 % to 4.5%? The bond has a face value of $1,000 and it matures in 7 years. (Pafter#– Pbefore.)" 6.89%

9. Consider a two-year coupon bond with a face value of $100 and a coupon rate of 8% (the next annual coupon is due in one year). The one-year spot rate is 4%, the two-year spot rate is 5.9811%, and the bond is trading today for $103.846. What is the expected holding period return if you can sell the bond after the first coupon? a. b. c. d.

7%" 6%" 4% 5%"

10. What is the default risk premium of a corporate bond if the real rate is 4%, the expected inflation is 5%, the liquidity premium is 3%, the maturity risk premium is 1%, and the nominal yield of the bond is 15.7%?" 2.5%

11. The issuer of a zero coupon bond _________ money. The owner has a ________ position in the bond and the issuer has a _________ position. a. b. c. d.

lends; short; long" borrows; long; short lends; long; short" borrows; short; long"

12. What is the face value of a zero coupon bond? a. b. c. d.

The amount of money that the bond holder (owner) pays the issuer at the time of issue." The amount of money that the issuer pays the bond holder (owner) at the time of issue." The amount of money that the bond holder (owner) pays the issuer at maturity." The amount of money that the issuer pays the bond holder (owner) at maturity.

13. A U.S. Government 2-year T-Note has a face value of $100 and pays annual coupons of $7. The first coupon is due in one year. What is the correct price for the coupon bond today? Use the term structure of interest rates shown in the table."

a. b. c. d.

$99 $98" $96" $97"

14. A U.S. Government T-bond matures in 30 years and has a face value of $100. The bond has a coupon rate of 8% and the next (annual) coupon is due in one year. You bought the bond today for $92. If you can re-invest the coupons at 3.7220%, then what is your total return (per annum) on the bond? (The total return is the interest rate that grows the investment to the future value of the bond’s proceeds at maturity.)" 6%

15. If the nominal rate of interest is 7.12% and the real rate of interest is 3% , what is the expected rate of inflation?" 4%

16. As the maturity date of a bond approaches, a. b. c. d.

the bond will always sell at a premium." the bond will always sell at a discount." default risk decreases." the price of the bond approaches its face value.

17. A newly issued U.S. Federal T-Bond matures in 24 years. The coupon rate is 4% and coupons are paid semi-annually. The bond is priced at $86.11 (FV = $100) and yields 5%. The economy is slowing and many forecasters predict a recession. You expect that the monetary authorities to lower interest rates. You expect the yield to fall to 4.26. You want to earn $1M by investing in bonds to profit from the interest rate change, how many bonds do you buy? 100,000 bonds

18. The main difference between a coupon bond and a zero coupon bond is that a. b. c. d.

the zero coupon bond has no coupons and pays its face value at maturity. the zero coupon bond pays all of its coupons and its face value at maturity." a coupon bond only pays coupons and a zero only pays a face value." the zero coupon bond has no coupons or face value."

19. The _______ of a bond varies daily as the bonds are bought and sold.# a. b. c. d.

coupon rate" face value" price maturity"

20. The 10-year T-note has a Bloomberg price quote of 98-26. What is the price as a percentage of face value? a. b. c. d.

98.71875" 98.0625" 98.8215 98.46875"

21. You are comparing a 10-year, 3% U.S. government zero coupon bond (which is priced to yield 4%) to a 10-year, 3% coupon bond issued by the Aerocar Motor Co. (which is priced to yield 5%). The difference between the two yields is due to:" I. maturity premium" II. default premium" III. liquidity premium" a. III only" b. II and III c. II only" d. I only" " 22. Assume that the 4-year spot rate is k4=2.437% and the 3-year spot rate is k3#= 2.25%. What is the forward rate in the fourth year?" 5%

23. Which bond's price is least sensitive to changes in interest rates?"

a. b. c. d.

A" B" C" D

*Least amount of time to mature" 24. The ‘yield spread’ is defined as the difference in yields between a U.S. Treasury and an otherwise equivalent Baa rated corporate bond. The yield spread is the compensation to investors for bearing default risk and it varies over time, peaking in recessions. Following the financial crisis, the spread peaked in the Fall of 2008 at 611 basis points (bps) or 6.11%. If you had anticipated that the spread had peaked, then what positions would you have taken in the two bonds to profit from the decline in the spread after the Fall of 2008? a. b. c. d.

short treasuries, short Baa" short treasuries, long Baa long treasuries, long Baa" long treasuries, short Baa"

25. Suppose you purchase a zero coupon bond with a face value of $1,000, maturing in 8 years, for $858.31. What is the implicit interest in the first year of the bond's life?" $16.55

26. Consider an annual coupon bond with a face value of $ 100, 13 years to maturity, and a price of $90. The coupon rate on the bond is 3%. If you can reinvest coupons at a rate of 4.038 % per annum, then how much money do you have if you hold the bond to maturity?" $150

27. Rudy purchased a 7.5% coupon rate bond one year ago for its face value of $100. He bought the bond just after the coupon date. Yesterday the bond paid its annual coupon. The bond currently has 15 years until maturity and has a yield to maturity of 9.44%. If Rudy sells the bond today, then what is his return for the last year?" -7.74%

28. Combs-R-Us Corp. bonds have been downgraded by Standard and Poor's because of the growing number of men who shave their heads. Which of the following should result from this development? a. b. c. d.

the yield to maturity will fall" the maturity date will change" the coupon yield will fall" the bond price will fall

29. A U.S. Government 3-year T-Note has a face value of $100 and pays annual coupons of $8. The first coupon is due in one year. What is the correct price for the coupon bond today? Use the term structure of interest rates shown in the table." "

a. b. c. d.

$96" $98" $99 $97"

30. The table below shows market prices for three zero coupon bonds with three different terms: one, two, and three years. The bonds all have a face value of $1,000. Calculate the yields on the zero coupon bonds and graph the yield curve. What is the shape of the yield curve?"

a. upward sloping" b. flat" c. downward sloping" 31. Consider a 2-year coupon bond with a face value of $100 and a coupon rate of 8% (the next annual coupon is due in one year). The one-year spot rate is 8%, the two-year spot rate is 9.0964%, and the bond is trading today for $98.148. What is the expected price for the coupon bond after the first coupon? a. $99" b. $100" c. $98 d. $97" " 32. The real rate of interest is 1% and the expected rate of inflation is 2.97%. What is the nominal rate of interest?" 4%

33. What is the price of a bond with 8 years to maturity, a 3% coupon rate (annual coupons), and $100 face value if the yield to maturity is 4.517%?" $90.00"

34. The "price value of a basis point" (PVBP) measures the change in the price of a bond if the yield changes by one basis point (one one-hundredth of a percent—0.01%). PVBP is expressed as the absolute value of the change in price. For example, if the yield on a bond rises from 8% to 8.01% and the bond price falls by $0.3992 (on a $1,000 face), then the PVBP is 0.3992. Drawing on your knowledge of the price-yield properties of coupon bonds, which of the following bonds has the highest PVBP? a. b. c. d.

20 years, 8% coupon" 25 years, 8% coupon" 10 years, 8% coupon" 15 years, 8% coupon"

35. Which of the following is not a fixed feature of a bond? a. b. c. d.

the maturity date" the coupon" the price of the bond the coupon dates"

36. The "price value of a basis point" (PVBP) measures the change in the price of a bond if the yield changes by one basis point (one one-hundredth of a percent—0.01%). PVBP is expressed as the absolute value of the change in price. Consider a coupon bond with a face value of $100, an annual coupon rate of 4%, and 19 years to maturity. What is PVBS if the yield rises from 4% to 4.01%?" $0.13

37. A U.S. Government T-bond matures in 21 years and has a face value of $100. The bond has a coupon rate of 3% paid semi-annually (the next coupon is due in 6 months). The yield on the bond is 9%. If coupons are re-invested at 3.7033% per annum, then how much interest is earned on re-invested coupons over the life of the bond? Calculate the interest as a percentage of the total cash flows received by the bondholder. a. b. c. d.

19%" 16% 18%" 17%"

38. Assume that the one-year spot rate is 1% (k1=1%) and the expected future spot rate is 3.01% (E(k1) = 3.01%). What two-year spot rate is consistent with these values under the expectations theory and what is the shape of the yield curve? a. b. c. d.

k2=2%, upward sloping k2=3.01%, upward sloping" k2=2%, flat" k2=2%, downward sloping"

39. Consider the two bond quotes in the table:#a two-year U.S. Government bond and a twoyear U.K. Government bond. Which bond has greater interest rate risk?"

a. US government b. UK government" 40. Consider two zero coupon bonds. Both have face values of $100. Bond A pays its face value in 8 years, and Bond B pays its face in 2 years. If interest rates change from 9% to 6%, what is the percentage change in the long maturity bond's price minus the percentage change in the short maturity bond's price?" 19.28%

41. The 1-year spot rate is 1%. The 1-year spot rate expected for next year is 5.0396% and the 1-year spot rate expected in two years is 6.0292%. What are the 2-year and 3-year spot rates predicted by the pure expectations theory?" 2-year spot rate = 3%" 3-year spot rate = 4%

42. Use the information in the table to calculate the expected spot rate in year 2."

4.5%"

43. Investors who purchase bonds at a discount will:" a. receive lower coupon payments than from those bonds sold at face with the same coupon rate." b. be able to sell the bond at a premium if interest rates rise above their current level." c. fare worse than those investors who bought the same bond at a premium if the borrower defaults." d. earn a capital gain if they hold the bond to maturity. 44. Holding the yield to maturity and the coupon rate of a bond constant, as the maturity date moves further into the future (time to maturity increases): a. the value of the bond will fluctuate less for any change in market yields" b. the discounted face value of the bond represents a larger percentage of the bond's total value than the total present value of the interest payments" c. the discount factor used to calculate the present value of the principal increases" d. the sum of the present value of the coupon payments represents a larger share of the total bond value than the present value of the principal 45. The yield to maturity on a bond a. is the effective yield earned only from coupon payments." b. is approximately equal to the return the bond investor will earn if they pay the price and hold the bond to maturity. c. remains fixed over its life." d. is the discount rate that equates the face value of a bond with the present value of all its future cash flows." 46. Three-month commercial paper has ________ yield than three-month T-bills. a. the same" b. a lower c. a higher" 47. City Wok Inc. bonds trade for a price of $88.298. The bonds have 10 years to maturity and a yield to maturity of 3.4 %. The bonds pay annual coupons (the next coupon is due in one year) and the face value is $100. What is the coupon rate of the bond? a. b. c. d.

2.0% 5.0%" 3.0%" 4.0%"

48. Tegridy Farms Inc.’s semi-annual coupon bonds are currently trading for $103.78. The bonds have a face value of $100, a coupon rate of 4%, and they mature in 6 years. What is the yield to maturity of the bonds?" 1.65%"

" 49. The 1-year spot rate is 3% and the expected spot rate next year is 5.0097%. What is the 2year spot rate predicted by the expectations theory?" 4%

50. A bond that sold for $900 three months ago is selling for $1,000 today. Which of the following must be true? a. b. c. d.

The coupon rate must have decreased over the last three months." Interest rates must have increased over the last three months." Interest rates must have decreased over the last three months. The coupon rate must have increased over the last three months."

51. Most zero coupon bonds trade in the _________ market. a. money b. bond" c. secondary" d. capital" " 52. You just bought a strip bond with a face value of $1,000 and 12 years to maturity. You paid $556.84. What is the yield on the bond?" 5%

53. Assume that the one-year spot rate is 2% (k1=2%) and the expected future spot rate is 3.01% (E(k1) = 3.01%). Investors don’t like long-term investments, so the two-year bond yield includes a maturity risk premium of 1%. Answer the questions that follow." " Part 1: What two-year spot rate is consistent with these values under the maturity preference hypothesis?" a. 2.5%" b. 3.01%" c. 3%" d. 3.5% " Part 2: Using the two-year spot rate from Part 1, calculate the forward rate. The resulting forward rate is _______ the expected future spot rate." a. larger than b. the same as" c. smaller than"

54. A Ford Motor Co. coupon bond has a face value of $100, a coupon rate of 3%, and pays annual coupons. The next coupon is due tomorrow and the bond matures 12 years from tomorrow. The yield on the bond issue is 4.070 %. What is the fair price for the bond today?" $93

55. A 9% coupon bond has a yield of 9.75%. The bond is selling at a price that is ______ par. a. higher than" b. equal to" c. lower than 56. Use the information in the table to calculate the one-year forward rate starting two years from today."

5%

57. Without doing any calculations, which of the bond price quotes is incorrect?"

a. Amtrak" b. Boeing" c. US Government " 58. Without doing any calculations, which of the bond price quotes is incorrect?" $339.99

59. Hooli Inc. bonds trade for a price of $109.197. The bonds have a coupon rate of 6% (annual) and a yield to maturity of 4.6 %. The face value is $100. How many years until the maturity of the bond? a. b. c. d.

12 years" 6 years" 10 years" 8 years

60. Consider the information on various bonds in the table and answer the question that follows."

" The yield on the Texas State Highway Bond exceeds the yield on a 10-year U.S. Government TNote because of:" a. b. c. d.

liquidity risk" inflation risk" maturity risk" credit or default risk"

61. In this question you will compare three investment strategies in a situation where interest rates are expected to rise. Many investors consider the lock-in to be inferior when rates rise because of interest rate risk. What you will see in this example is that anticipated rate increases are priced into the yield curve and so all strategies are equivalent. However, with unanticipated rate increases, there is a dominant investment strategy. Use the data in the table for zero coupon bonds below to complete parts (1) through (6)."

Part 1: " The lock-in: If you buy the two-year bond at its quoted price and hold to maturity, then what return do you earn (per annum) over the two years? (Enter your answer in percentage form rounded to one decimal place.)" 30.5% Part 2: What is the expected spot rate in year 2? (Enter your answer in percentage form rounded to one decimal place.)" 54.1%

Part 3: If you had bought the two-year bond at t=0 and the spot rate had risen to 54.12% at t=1 as expected, then what could you have sold the bond for? (Round your answer to two decimal places.)" $64.88 Part 4: If you had bought the two-year bond at t=0 and the spot rate had risen to 54.12% at t=1 as expected, and then you had sold your two-year bond in order to buy a new one-year bond, what compound average return would you have earned over the two years? (Enter your answer in percentage form rounded to one decimal place.)" 30.5%" Part 5: The roll-over: Assume that you buy 0.6488 of a one-year bond at t=0. Assume that bond matures at t=1 and you use the proceeds to buy the new bond at t=1. Assume that the interest rate rises at t=1 to 54.12% as expected. How much money do you have at t=2 and what is your compound average return? (Enter your answer in percentage form rounded to one decimal place.)" 30.5%" Part 6: Which strategy generates the highest average compound return over the two years when interest rates are expected to rise?" a. b. c. d.

They are all the same Start with lock-in, sell it at t=1, and buy the new 1-year bond" Roll-over" Lock-in"

62. Tegridy Farms Inc.’s semi-annual coupon bonds are currently trading for $103.78. The bonds have a face value of $ 100, a coupon rate of 4%, and they mature in 6 years. What is the yield to maturity of the bonds?" 3.3%...