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sol6 - ACTSC 445 Asset-Liability Management Department of...

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Unformatted text preview: ACTSC 445: Asset-Liability Management Department of Statistics and Actuarial Science, University of Waterloo Solutions for Unit 6 Exercises 1. (i) We will find one portfolio based on 2 and 4-year zero-coupon bonds (Portfolio A), and one portfolio based on 2 and 5-year zero-coupon bonds. So in both cases, we have two different maturities t 1 and t 2 , and we need to solve 1 . 05- t 1 x + 1 . 05- t 2 y = 4000000(1 . 05)- 3 t 1 1 . 05- t 1 x + t 2 1 . 05- t 2 y = 3 × 4000000(1 . 05)- 3 where x and y represent the cash-flows at time t 1 and t 2 , respectively. For portfolio A, we find x = 1727675(1 . 05) 2 = 1904761 . 7 and y = 1727675(1 . 05) 4 = 2100000. For portfolio B, we get x = ((2 / 3)4000000(1 . 05)- 3 )1 . 05 2 = 2539682 . 5 and y = ((1 / 3)4000000(1 . 05)- 3 )1 . 05 5 = 1470000. (ii) We get Δ y Portfolio A Portfolio B t = 0 t = 3 t = 0 t = 3-1% 3,556,148 4,000,183 3,556,312 4,000,367 1% 3,358,628 4,000,180 3,358,778 4,000,358 2. (i) Let x and y be the asset cash-flows (in millions) at time 1 and 6, respectively. We need to solvebe the asset cash-flows (in millions) at time 1 and 6, respectively....
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sol6 - ACTSC 445 Asset-Liability Management Department of...

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