5. Answer the following questions about convexity of coupon bonds. Briefly explain each answer. A. If two bonds are identical except one has a higher coupon, which has the higher convexity? B. If two bonds have the same coupon rate but one is $1m par and the other is $10m par, which has the higher convexity? C. What is the effect of an increase in yield on convexity? D. Does convexity always increase with maturity? 6. Portfolio A consists of a one-year zero-coupon bond with a face value of $2,000 and a 10-year zero- coupon bond with a par value of $6,000. Portfolio B consists of a 5.95-year zero-coupon bond with a face value of $5,000. The current yield on all bonds is 10% per annum (continuously compounded) (a) Show that both portfolios have the same duration. The duration approximation will therefore predict identical percentage changes for both portfolios when yield changes.) (b) Determine the actual percentage changes in the values of each of the two portfolios if the yield increases by 0.10%. They should be similar. (The percentage changes predicted using the duration approximation will be identical.) (c) Determine the actual percentage changes in the values of each of the two portfolios if the yield increases by 5%. In this case, the percentage changes for the two portfolios should not be that similar. (For a large yield change, the duration approximation is poor.) 5. Answer the following questions about convexity of coupon bonds. Briefly explain each answer. A. If two bonds are identical except one has a higher coupon, which has the higher convexity? B. If two bonds have the same coupon rate but one is $1m par and the other is $10m par, which has the higher convexity? C. What is the effect of an increase in yield on convexity? D. Does convexity always increase with maturity? 6. Portfolio A consists of a one-year zero-coupon bond with a face value of $2,000 and a 10-year zero- coupon bond with a par value of $6,000. Portfolio B consists of a 5.95-year zero-coupon bond with a face value of $5,000. The current yield on all bonds is 10% per annum (continuously compounded) (a) Show that both portfolios have the same duration. The duration approximation will therefore predict identical percentage changes for both portfolios when yield changes.) (b) Determine the actual percentage changes in the values of each of the two portfolios if the yield increases by 0.10%. They should be similar. (The percentage changes predicted using the duration approximation will be identical.) (c) Determine the actual percentage changes in the values of each of the two portfolios if the yield increases by 5%. In this case, the percentage changes for the two portfolios should not be that similar. (For a large yield change, the duration approximation is poor.)