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A company has a liability of $10, 000, 000 in three years time and wants to hedge this liability with the following semiannual bonds: The semiannually compounded 3 year rate is 5.0%. The company wants to hedge this liability by constructing a portfolio that is duration and convexity neutral. a. By differentiating the present value of the liability with respect to the 3-year semiannual rate, show that the modified duration and convexity of the liability are D_L = 3/1+0.025 C_L = 3 times 3.5/(1+0.025)^2 b. By computing the present values, durations and convexities, determine the three equations that must be satisfied by the weights W_2, w_5 and w_10 of the 2, 5 and 10 year bonds respectively. c. Express the equations in the matrix form: And solve for W_1, w_2 and w_3. d. Using the weights obtained in part (c), compute the corresponding units n_2, n_5 and n_10 of the bonds required for the hedge. A company has a liability of $10, 000, 000 in three years time and wants to hedge this liability with the following semiannual bonds: The semiannually compounded 3 year rate is 5.0%. The company wants to hedge this liability by constructing a portfolio that is duration and convexity neutral. a. By differentiating the present value of the liability with respect to the 3-year semiannual rate, show that the modified duration and convexity of the liability are D_L = 3/1+0.025 C_L = 3 times 3.5/(1+0.025)^2 b. By computing the present values, durations and convexities, determine the three equations that must be satisfied by the weights W_2, w_5 and w_10 of the 2, 5 and 10 year bonds respectively. c. Express the equations in the matrix form: And solve for W_1, w_2 and w_3. d. Using the weights obtained in part (c), compute the corresponding units n_2, n_5 and n_10 of the bonds required for the hedge