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
Related Book For
Statistics And Data Analysis For Financial Engineering
ISBN: 9781461427490
1st Edition
Authors: David Ruppert
Posted Date:
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