4. Why is the investor of a callable bond exposed to reinvestment risk? 5. What is negative convexity? 6. Does a callable bond exhibit negative or positive convexity? 8. The theoretical value of a...

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4. Why is the investor of a callable bond exposed to reinvestment risk? 5. What is negative convexity? 6. Does a callable bond exhibit negative or positive convexity? 8. The theoretical value of a noncallable bond is $103; the theoretical value of a callable bond is $101. Determine the theoretical value of the call option. 13. The current on-the-run yields for the Ramsey Corporation are as follows: Maturity (years) Yield to Maturity (%) Market Price 1 7.5 100 2 7.6 100 3 7.7 100 Assume that each bond is an annual-pay bond. Each bond is trading at par, so its coupon rate is equal to its yield to maturity. a. Using the bootstrapping methodology, complete the following table: Year Spot Rate (%) 1-Year Forward Rate (%) 1 2 3 b. Using the spot rates, what would be the value of an 8.5% option-free bond of this issuer? c. Using the 1-year forward rates, what would be the value of an 8.5% coupon option-free bond of this issuer? d. Using the binomial model (which assumes that 1-year rates undergo a lognormal random walk with volatility ), show that if is assumed to be 10%, the lower 1-year forward rate one year from now cannot be 7%. e. Demonstrate that if is assumed to be 10%, the lower 1-year forward rate one year from now is 6.944%. 14. Explain how an increase in expected interest-rate volatility can decrease the value of a callable bond.