QUESTION 5. A company has a liability of $10,000,000 in three years time and wants to...

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QUESTION 5. A company has a liability of $10,000,000 in three years time and wants to hedge this liability with the following semiannual bonds: Maturity Face Value Coupon Yield 2 100,000 5% 4.8% 5 100,000 6% 5.0% 10 100,000 7% 5.2% 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 D₁ 3 1+0.025' 3x3.5 CL (1+0.025)² b. By computing the present values, durations and convexities, determine the three equations that must be satisfied by the weights w2, ws and W₁0 of the 2,5 and 10 year bonds respectively. c. Express the equations in the matrix form: aaa b 21 22 23 W₂ b₁₂ W And solve for W₁, W₂ and w₁. d. Using the weights obtained in part (c), compute the corresponding units n₂, ns the bonds required for the hedge. and n10 of QUESTION 5. A company has a liability of $10,000,000 in three years time and wants to hedge this liability with the following semiannual bonds: Maturity Face Value Coupon Yield 2 100,000 5% 4.8% 5 100,000 6% 5.0% 10 100,000 7% 5.2% 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 D₁ 3 1+0.025' 3x3.5 CL (1+0.025)² b. By computing the present values, durations and convexities, determine the three equations that must be satisfied by the weights w2, ws and W₁0 of the 2,5 and 10 year bonds respectively. c. Express the equations in the matrix form: aaa b 21 22 23 W₂ b₁₂ W And solve for W₁, W₂ and w₁. d. Using the weights obtained in part (c), compute the corresponding units n₂, ns the bonds required for the hedge. and n10 of

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a To find the modified duration and convexity of the liability we differentiate the present value of the liability with respect to the 3year semiannua... View the full answer