Suppose the term structure of annualized interest rate is flat at 5%. Consider the following three bonds with face value $100: Bond 1: a 10-year zero coupon bond; • Bond 2: a 1.5-year semi-annually paid floating rate bond with zero spread; • Bond 3: a 3-year annually paid coupon bond, with coupon rate 6%. 1) What are the current prices for the three bonds? 2) Compute the Duration and Convexity for each of the three bonds. 3) Assume that you have 10 units of Bond 3, how to conduct delta hedge and convexity hedge using Bond 1 and Bond 2?

Suppose the term structure of annualized interest rate is flat at 5%. Consider the following three bonds with face value $100: Bond 1: a 10-year zero coupon bond; • Bond 2: a 1.5-year semi-annually paid floating rate bond with zero spread; • Bond 3: a 3-year annually paid coupon bond, with coupon rate 6%. 1) What are the current prices for the three bonds? 2) Compute the Duration and Convexity for each of the three bonds. 3) Assume that you have 10 units of Bond 3, how to conduct delta hedge and convexity hedge using Bond 1 and Bond 2?

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Assume you have a bond with a semi-annual interest payment of $50, a par value of $1 comma 000, and a current market price of $870. What is the current yield of the bond?
Suppose that the prices of zero-coupon bonds with various maturities are given in the following table. The face value of each bond is $1,000. Maturity (Years) 1 2 3 4 5 Price $983.78 865.89 797.92 732.00 660.24 Required: a. Calculate the forward rate of interest for each year. b. How could you construct a 1-year forward loan beginning in year 3? c. How could you construct a 1-year forward loan beginning in year 4?
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(2r₁) = 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%
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Consider the situation where zero rates, measured with continuous compounding, are as in the below table. Suppose that a two-year bond with a principal of $100 provides coupons at the rate of 8% per annum semiannually. What is the theoretical price of the bond. Maturity (years) Zero rate (%) with continuous compounding 0.5 5 1.0 6 1.5 7 2.0 8 $99.60 $99.25 $99.02 $99.89
The outstanding bonds of Winter Tires Inc. provide a real rate of return of 3.2 percent. If the current rate of inflation is 2.1 percent, what is the actual nominal rate of return on these bonds?
Consider a one-year discount bond that has a present value of P1,500. If the rate of discount is 4 percent, the future value of the bond (the amount the bond pays in one year) is * P1,560.00 P1,540.00 P1,440.00 P1,442.31
Consider the following bonds: •Bond A: A 2-year zero-coupon bond with a face value of $100 and 6% YTM. •Bond B: A 2-year par-value bond with a face value of $100 and 6% coupon rate. *Bond C: A 2-year par-value bond with a face value of $100 and 7% coupon rate. Suppose the yield curve shifts upwards by one percent. Which bond among bonds A, B, and C will experience the largest percentage price change? Which will have the lowest percentage price change? O a. Bond A; Bond C O b. Bond A; Bond B O c. Bond B; Bond C O d. Bond C; Bond B
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(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%
Suppose that all bonds have $1,000 of face value. The current prices of zero coupon bonds are as follows: $960 for a one-year bond; $910 for a two-year bond; $850 for a three-year bond. a. What is the price of a three-year bond with 8% annual coupon payment? b. What is the YTM of the two-year zero coupon bond? c. Consider the following two-year bonds: (i) a zero coupon bond as above; (ii) a bond with 6% annual coupon payment. Whose YTM is higher?
Assume that the real, risk-free rate of interest is expected to be constant over time at 3 percent, and that the annual yield on a 6-year corporate bond is 8.00 percent, while the annual yield on a 10-year corporate bond is 7.75 percent: you may assume that the default risk and liquidity premium are the same for both bonds. Also assume that the maturity risk premium for all securities can be estimated as MRP, (0.1%) *(t-1), where t is the number of periods until maturity. Finally assume that inflation is expected to be constant at 3 percent for Years 1-6, and then constant at some rate for Years 7-10 (4 years). Given this information, determine what the market must anticipate the average annual rate of inflation will be for Years 7-10. 2.583% O 1979% 2.281% 1.375 % O 1.677 % 4
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%

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