Type of Bond 1-year 2-year 3-year Yield 0.2% 0.3 0.5 Using the expectations theory, compute the expected one-year interest rates in (a) the second year (Year 2 only) and (b) the third year (Year 3 only). The bonds have no risk premiums. (L 5.3)
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- Consider the following two Treasury securities: Bond Price Modified duration (years) A $100 6 B $80 7 For a 25 basis-point change in interest rates, which bond has the greatest percentage change in price? A. Bond A B. Bond B C. Can't be determinedThe following information about bonds A, B, C, and D are given. Assume that bond prices admit noarbitrage opportunities. What is the convexity of Bond D?Cash Flow at the end ofBond Price Year 1 Year 2 Year 3A 91 100 0 0B 86 0 100 0C 78 0 0 100D ? 5 5 105The following information is about the spot rates on Treasury securities and BBB corporate bond: Spot 1 Year Spot 2 Year Spot 3 Year Treasury 3% 4.75% 5.5% BBB Corporate Debt 7.5% 9.15% 10.5% Question: Using the implied forward rates, estimate the annual marginal default probability for the one-year BBB corporate debt in year 3?
- You consider purchasing bonds today. There are three future time periods, t = 1, 2, 3, wherebonds can have payoffs. Consider the following 4 bonds: a) One amortizing bond paying $40 each period trading at a price of $104.95.b) One amortizing bond paying less in early periods and more in later periods. The bond pays $40 inperiod 1, $30 in period 2, and $20 in period 3. This bond is trading at a price of $80.61.c) One coupon bond with a 11% coupon rate trading at a price of $96.08.d) One zero coupon, which currently trades at a price of $77.22. Suppose you can take long or short positions in any bond, and also lend or borrow money. Is it possibleto construct an arbitrage trade where you pay nothing upfront, and get a certain payoff in period 1? If so,describe how you would do this trade.5. Look at the following data: i l-year bond, ti" t+1 5 percent premium = 0 i't +2 i't +3 5.78 percent 5.88 percent 5.65 percent premium = 0.10 premium = 0.22 premium = 0.33 Based on the data, do the following: a. Compute the interest rate on a 2-year, 3-year, and 4-year bond using expectations theory and then draw the corresponding yield curve. b. Compute the interest rate on a 2-year, 3-ycar, and 4-year bond using preferred habitat theory and then draw the corresponding yield curve.Suppose that a short-term government bond has a face value of $100. If the price of that bond is $95. What is the insterest rate of that bond? 5.3% 9.0% 10.0% 1.0%
- Suppose that the current one-year rate (one-year spot rate) and expected one-year government bonds over years 2, 3 and 4 are as follows: 1R1 = 4.80%, E(201) = 5.45%, E(3r1) = 5.95%, E(41) = 6.10% Assume that there are no liquidity premiums. To the nearest basis point, what is the current rate for the four-year-maturity government bond? < A. 5.57% B. 5.62% C. 5.83% D. 6.10%1. Bond prices and yields (S3.1) A 10-year bond is issued with a face value of $1,000, paying interest of $60 a year. If interest rates increase shortly after the bond is issued, what happens to the bond's a. Coupon rate? b. Price? c. Yield to maturity?3) Answer the below questions for bonds A and B. Bond A 8% 8% 2$100.00 $100.00 $100.00 $104.055 CouponYield to maturity Maturity (years) ParPrice Bond B 9% 8% (a) Calculate the actual price of the bonds for a 100-basis-point (1% annual) increase in interest rates. (b) Using (modified) duration, estimate the price of the bonds for a 100-basis- 5 point (1% annual) increase in interest rates.(c) Explain why your answers in parts (a) and (b) differ.
- The following table gives the prices of Treasury bonds: Bond Principal ($) Time to maturity (years) Annual Coupon* ($) Bond Price ($) 100 0.50 100 1.00 100 1.50 100 2.00 0.0 0.0 6.2 8.0 98 95 101 104 A. Calculate zero rates for maturities of 6 months, 12 months, 18 months, and 24 months. B. What are the forward rates for the periods: 6 months to 12 months, 12 months to 18 months, 18 months to 24 months? C. What are the 6-month, 12-month, 18-month, and 24-month par yields for bonds that provide semiannual coupon payments? D. Estimate the price and yield of a two-year bond providing a semiannual coupon of 7% per annum. PLEASE SHOW EXCEL WORK4. What is the carrying value of the bonds at the end of the second period (third number)? Premium 57,913.01 Carrying value (bonds) 432,913.01 Face Rate Market Rate Semiannual payments a. b. Cash Payment C. d. e. 14% 10% 0 or 1 2 or 3 4 or 5 6 or 7 8 or 9 Interest Expense Today Period #1 26,250.00 Period #2 26,250.00 Carrying value at end of second period (third number) ___________?__ 2. Disc. or Prem. Amort. 21,645.65 21,415.43 Disc. or Prem. 4,604.35 4,834.57 57,913.01 53,308.66 48,474.10 Face Value 375,000.00 375,000.00 375,000.00 Carrying Value 432,913.01 428,308.66 423,474.10Suppose that the current one-year rate (one-year spot rate) and expected one-year government bonds over years 2, 3 and 4 are as follows: 1R1 = 4.80%, E(2r1) = 5.45%, E(3r1) = 5.95%, E(4r1) = 6.10% Assume that there are no liquidity premiums. To the nearest basis point, what is the current rate for the four-year-maturity government bond? 5.57% 5.62% 5.83% 6.10%
