5) Let the six-month interest rate be 8%. To satisfy no-arbitrage, assume the six month rate moves up or down by 25 bp each six-month period with equal probability. Build an interest rate tree and value a two-year, 8.2% callable bond that can be called for par ($100). What is the value of the embedded option?

5) Let the six-month interest rate be 8%. To satisfy no-arbitrage, assume the six month rate moves up or down by 25 bp each six-month period with equal probability. Build an interest rate tree and value a two-year, 8.2% callable bond that can be called for par ($100). What is the value of the embedded option?

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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1. Suppose that a 30-year Treasury bond offers a 5% coupon rate, paid semi-annually. The marketprice of the bond is $1,000, equal to its par value.a. What is the payback period for this bond?b. With such a long payback period, is the bond a bad investment?c. What is the discounted payback period for the bond assuming its 4% coupon rate is therequired return? What general principle does this example illustrate regarding a project’slife, its discounted payback period, and its NPV?
Assume that the real risk-free rate of return, k*, is 3%, and it will remain at that level far into the future. Also assume that maturity risk premiums (MRP) increase from zero for bonds that mature in one year or less to a maximum of 1%, and MRP increases by 0.2% for each year to maturity that is greater than one year-that is, MRP equals 0.2% for two-year bond, 0.4% for a three-year bond, and so forth. Following are the expected inflation rates for the next five years: Year Inflation Rate (%) 2017 5 2018 6 2019 7 2020 8 2021 9 a) Compute the interest rate for a one-, two-, three-, four-, and five-year bond. b) If inflation is expected to equal 9% every year after 2021, what should be the interest rate for a 10- and 20-year bond? c) Plot the yield curve for the interest rates you computed in part [a] and [b]. d) Based on the curve (in part c), interpret your findings.
Suppose for $1,000 you could buy a 10%, 10-year, annual payment bond or a 10%, 10-year, semiannual payment bond. They are equally risky. Which would you prefer? If $1,000 is the proper price for the semiannual bond, what is the equilibrium price for the annual payment bond?
Consider a bond that has a current value of $1,081.11, a face value of $1,000.00, a coupon rate of 10% and five years remaining to maturity.a. What is the bond’s yield-to-maturity today?b. If the bond’s yield does not change, what is its value one year from today? Please solve both parts
Consider a semi-annual bond that has a par value of 100, a 15-year maturity, a 5% coupon rate. Monthly interest rate is 0.412%. (a) Calculate the annualized semi-annual compounding yield. (b) What is the price of the bond (without calculation)? And explain why you can determine the price of the bond without calculation? (c) Using answers from (b), calculate the modified duration of this bond. (d) Using answers from (b) and (c), suppose that the bond’s yield to maturity decreases to 3.5%. How much will the bond price increase by applying the duration rule? (e) Do you agree with the following statement, and explain why? “If two bonds have the same duration, then the percentage change in price of the two bonds will be the same for a given change in interest rates.” (f) Discuss the problems with the traditional bond pricing approach by using the yield to maturity. (300 words Maximum)
Suppose a five-year face value of $1000 bond with a 9% coupon rate, and coupons are paid semi-annually. The yield to maturity of this bond is 7% (APR with semi-annual compounding). a) Is this bond trading at a discount, at par, or a premium? Explain. b) If the bond's yield to maturity rises to 8% (APR with semi-annual compounding), what price will the bond trade for?
Suppose the 1-year spot rate is 0.8%, and that a 2-year 1.5% annual coupon, a 3-year 2% annual coupon bonds are trading at par ($100). Calibrate a 2-year binomial interest rate model, assuming that interest rate volatility ?σ is 10%. What is the lowest rate at t=2?
Assume that K=61, St =65, t = 0.25 (i.e. time to expiry is 3 months), and the risk-free rate is 0.04. The current price of the put option is p = 4. If the price of the call option is 7.17, describe the arbitrage that would be possible, and calculate the profit that would result.
Consider a 3-month forward contract on a zero-coupon bond with a face value of $1,000 that is currently quoted at $1000, and assume a risk-free annual interest rate of 6%. Determine the price of the forward contract under the no-arbitrage principle.
Consider a three-year bond with annual coupons, a face value of 10,000$, and a 2% coupon rate. If the market interest rate is 3%, this bond's represent value is approximate $---?
Assume you can buy a bond that has a par value of $1000, matures in 10 years, yielding 6% and has a duration of 5. If you would like to use this bond to form a guaranteed investment contract “GIC” and offer a guaranteed rate of return to investors for certain years. a. what is the maximum yield you can offer? Why? Explain. b. For how many years would you make the guarantee? Explain.
Suppose that you buy a two-year 8% bond at its face value.(a) What will be your total nominal return over the two years if inflation is 3% in the first year and 5% in the second? What will be your total real return? (b) Now suppose that the bond is a TIPS. What will be your total two-year real and nominal returns?

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