Assume the yield curve is flat shown as following table. A cash and $duration-neutral butterfly is to be constructed by selling one thousand 7-year coupon paying bonds and purchasing and coupon paying bonds with maturities 3 and 15 years respectively. More information on the bonds to be used in the strategy is given below: YTM Maturity (Years) Coupon Rate (%pa) Price Modified Duration Quantity (%pa) 3 8.00% 6.00% 105.42 -2.65 q_5 7 10.00% 6.00% 122.59 -5.24 -1000.00 15 10.00% 6.00% 139.20 -8.86 q_1 (f) What is the modified duration of the 15-year bond? (g) What is the cash-neutral equation in the system of equations needed to find q_s and q_1? (h) What is the $Duration-neutral equation in the system of equations needed to find q_s and q_l? (i): It can be shown that the solution to the system of equations is: q_s = 679.32 and q_I= 366.23. What is the profit from this strategy if the yield curve shifts upwards by 1% at all maturities? Assume the yield curve is flat shown as following table. A cash and $duration-neutral butterfly is to be constructed by selling one thousand 7-year coupon paying bonds and purchasing and coupon paying bonds with maturities 3 and 15 years respectively. More information on the bonds to be used in the strategy is given below: YTM Maturity (Years) Coupon Rate (%pa) Price Modified Duration Quantity (%pa) 3 8.00% 6.00% 105.42 -2.65 q_5 7 10.00% 6.00% 122.59 -5.24 -1000.00 15 10.00% 6.00% 139.20 -8.86 q_1 (f) What is the modified duration of the 15-year bond? (g) What is the cash-neutral equation in the system of equations needed to find q_s and q_1? (h) What is the $Duration-neutral equation in the system of equations needed to find q_s and q_l? (i): It can be shown that the solution to the system of equations is: q_s = 679.32 and q_I= 366.23. What is the profit from this strategy if the yield curve shifts upwards by 1% at all maturities