Problem 1.6. You start with $1,000 to invest. The current yield on all bonds is 5% per annum. (a) How much extra cash would you raise by shorting a 7-year zero-coupon bond with face value of $1,000? (b) You invest the total cash (original $1,000 and the cash raised from shorting the bond) in a two-year zero-coupon bonds and 10-year zero-coupon bonds. How much should you allocate to each bond to immunize your portfolio (the short position and the two long positions) against small interest rate changes? (c) Duration matching does not protect against large interest rate changes. Which of the following plots shows how the portfolio value changes with interest rate changes? Why? 1,020 A 1,010 Portfolio value ($) 1,000 990 - Plot 1 - Plot 2 Plot 3 Plot 4 980 N 3 7 00 4 5 6 Interest rate (%) Problem 1.6. You start with $1,000 to invest. The current yield on all bonds is 5% per annum. (a) How much extra cash would you raise by shorting a 7-year zero-coupon bond with face value of $1,000? (b) You invest the total cash (original $1,000 and the cash raised from shorting the bond) in a two-year zero-coupon bonds and 10-year zero-coupon bonds. How much should you allocate to each bond to immunize your portfolio (the short position and the two long positions) against small interest rate changes? (c) Duration matching does not protect against large interest rate changes. Which of the following plots shows how the portfolio value changes with interest rate changes? Why? 1,020 A 1,010 Portfolio value ($) 1,000 990 - Plot 1 - Plot 2 Plot 3 Plot 4 980 N 3 7 00 4 5 6 Interest rate (%)