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1 ANSWERS TO HOMEWORK QUESTIONS - HW #7 7. Suppose that you are given the following information about two callable bonds that can be called immediately: Estimated Percentage Change in Price if Interest Rates Change by: -100 basis points +100 basis points Bond ABC +5 -8 Bond XYZ +22 -16 You are told that both of these bonds have the same maturity and that the coupon rate of one bond is 7% and of the other is 13%. Suppose that the yield curve for both issuers is flat at 8%. Based on this information, which bond is the lower coupon bond and which is the higher coupon bond? Explain why. If both bonds were non-callable then bond XYZ would be the bond with the lower coupon rate of 7%. This is because ceteris paribus lower coupon bonds undergo greater changes in yields when interest rates change. However, since both bonds are callable, we have to first identify where the current rate is relative to y* which lies in the flatter region near 8%. Negative convexity for a callable bond implies that the price change is less when interest rates fall. This is the situation for bond ABC where its price only increases by +5 when there is a decrease of 100 basis points. Also, this bond would have less of price decrease when yield increase due to lying in its flatter region. Thus, it appears that bond ABC is the lower coupon bond. We could also conclude that bond ABC is the bond with the lower coupon rate by looking at bond XYZ, which behaves as if its coupon rate is above its flat region. For example, the difference between the coupon rate of 13% and the flat region of 8% indicates that regardless of the change in interest rates (assuming they are not extremely large), this bond will exhibit the behavior of a non-callable bond associated with positive convexity. Positive convexity means the bond will have greater price appreciation than price depreciation for a large change in yield. This describes the situation for bond XYZ further indicating it is the bond with the higher coupon rate of 13%. This implies that bond ABC is the bond with the lower coupon rate of 7%. 13. The current on-the-run yields for the Ramsey Corporation are as follows: Maturity (years) Yield to Maturity (%) Market Value 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. Answer the below questions. (a) Using the bootstrapping methodology, complete the following table:

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2 Maturity (years) Spot Rate (%) One-Year Forward Rate (%) 1 2 3 The one-year spot rate for year one is its annua1ized yield of 7.50%. Using this value and the yield to maturity for year 2, we can solve for the one-year spot rate for year two as shown below. We do this below using the bootstrapping methodology. The price of a theoretical 2-year zero-coupon security should equal the present value of two cash flows
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