QUESTION 2 Assume the yield curve is flat at 6.5% pa nominal. A cash and $duration-neutral butterfly is to be constructed by selling one thousand 7-year zero coupon bonds and purchasing q_s and q_l zero coupon bonds with maturities 4 and 14 years respectively. We assume that interest accrues semi-annually. We also assume each bond has a face value of $100.

(i) What is the standardized convexity of the 14-year bond? [ Select ] ["761.686", "40.839", "190.421", "None of the other answers is correct", "210.000"]

(j) What is the cash-neutral equation in the system of equations needed to find q_s and q_l? [ Select ] ["q_s*77.42+ q_l*40.84=63,905.64", "q_s*77.73+ q_l*41.41=64,350.62", "None of the other answers is correct", "q_s*40.84+ q_l*77.42=63,905.64", "q_s*41.41+ q_l*77.73=64,350.62"]

(k) What is the $Duration-neutral equation in the system of equations needed to find q_s and q_l? [ Select ] ["None of the other answers is correct", "q_s*299.95+ q_l*553.75=433,258.54", "q_s*571.75+ q_l*309.70=447,339.45", "q_s*553.75+ q_l*299.95=433,258.54", "q_s*309.70+ q_l*571.75=447,339.45"]

(l): It can be shown that the solution to the system of equations is: q_s = 577.77 and q_l= 469.44. The profit from this strategy if the yield curve shifts upwards by 1% at all maturities is closest to: [ Select ] ["57.81", "None of the other answers is correct", "43.69", "79.57", "68.59"]

(m): What is the modified duration of a portfolio comprising : q_s = 577.77 short-maturity bond and q_l= 469.44 long maturity bonds? [ Select ] ["None of the other answers is correct", "7.000", "13.559", "6.573", "6.780"]

(n): What is the standardized convexity of a portfolio comprising : q_s = 577.77 short-maturity bond and q_l= 469.44 long maturity bonds? [ Select ] ["134.894", "68.946", "None of the other answers is correct", "67.888", "138.360"]