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 sqand lqcoupon paying bonds with maturities 3 and 15 years respectively. More information on the bonds to be used in the strategy is given below: Maturity (Years) Coupon Rate (%pa) YTM (%pa) Price Modified Duration Quantity 3 8.00% 6.00% 105.42 -2.65 sq 7 10.00% 6.00% 122.59 -5.24 -1000.00 15 10.00% 6.00% 139.20 -8.86 lq Note that we are assuming all bonds pay interest semi-annually. (a) Explain how to interpret the modified duration of -8.86 corresponding to the 15-year maturity bond. (b) Write down the system of equations that needs to be solved in order to find sq andlq and verify that the solution to this system is sq= 679.32 andlq = 366.23. (c) Find the profit from this strategy if yield curve moves: (i) up to 8% pa and (ii) down to 5% pa. (d) Explain why in practice it may be difficult to profit from the cash and $duration neutral butterfly. (e) Explain the major differences between the 50-50 butterfly strategy and the cash and $duration neutral butterfly.