Lecture_17

Lecture_17 - Immunization ProfessorRuslan Goyenko...

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Immunization Professor Ruslan  Goyenko
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General Principles of  Asset/Liability Management Ø A liability is a cash outlay that must be made at a specific time to satisfy the contractual terms of an issued obligation. Ø An institutional investor is concerned with both the amount and timing of liabilities, because its assets must produce the cash to meet any payments it has promised to make in a timely way.
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Immunization of a Portfolio to  Satisfy a Single Liability v An immunization strategy refers to the investment of the assets in such a way that the existing business is immune to a general change in the rate of interest. è Suppose that a life insurance company sells a GIC that guarantees an interest rate of 6.25% every six months (12.5% on a bond-equivalent yield basis) for 5.5 years (11 six-month periods). Also suppose that the payment made by the policyholder is $8,820,262. è Then, the value that the life insurance company has guaranteed the policyholder 5.5 years from now is $8,820,2621(1.06252)11 = $17,183,033 è When investing the $8,820,262, the target accumulated value for the portfolio manager of the life insurance company is $17,183,033 after 5.5 years, which is the same as a target yield of 12.5% on a bond-equivalent basis.
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Immunization of a Portfolio to Satisfy a  Single Liability (continued) è Suppose that the portfolio manager buys $8,820,262 par value of a bond selling at par with a 12.5% yield to maturity that matures in 5.5 years. è Will the portfolio manager be assured of realizing the target yield of 12.5% or, equivalently, a target accumulated value of $17,183,033? è To demonstrate this, we will suppose that immediately after investing the $8,820,262 in the 12.5% coupon 5.5-year maturity bond, yields in the market change and stay at the new level for the remainder of the 5.5 years.
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  Accumulated Value and Total Return After 5.5 Years: 5.5- Year 12.5% Bond Selling to Yield 12.5% Investment horizon (years): 5.5; Coupon rate: 0.125; Maturity (years): 5.5; Yield to maturity: 0.125; Price: 100; Par value purchased: $8,820,262; Purchase price: $8,820,262; Target accumulated value: $17,183,033 After 5.5 years New Yield a Coupon Interest Interest on Interest Price of Bond b Accumulated Value Total Return 0.160 $6,063,930 $3,112,167 $8,820,262 $17,996,360 0.1340 0.155 6,063,930 2,990,716 8,820,262 17,874,908 0.1326 0.145 6,063,930 2,753,177 8,820,262 17,637,369 0.1300 0.140 6,063,930 2,647,037 8,820,262 17,521,230 0.1288 …. …. …. …. …. …. 0.065
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Lecture_17 - Immunization ProfessorRuslan Goyenko...

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