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Insurance Company Immunization

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Accounting
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Boston University
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1) Liabilities: Year 3: 2.5 million Year 7: 4.2 million Year 20: 6.0 million Liabilities Time until payment Payment (in millions) 1 3 2.5 2 7 4.2 3 20 6.0 Total Liability: discount rate: 3.0% (3% discount) PV of CFs 2.288 3.415 3.322 9.02 million weights 0.254 0.378 0.368 1 2) In order to immunize the liabilities, the duration of the assets (ie. investment portfolio) must = the duration of The following formula will be able to solve for the weights: DL = XB * DB + XC * DC = DA DL < Duration of liabilities XB < weight of Stock B DB < Duration of Stock B = 7 XC < weight of coupon bond DC < Duration of coupon bond = 20 DA < Duration of assets 10.77 = (XB * 7) + ((1-XB) * 20) < use 1- the first weight, since there are only two investments in the p Solve algebraically for XB XB = 0.71 Therefore, XC = 1-0.71 = 0.29 Weight in the 30-year coupon bond: 29% Weight in stock B: 71% < annual expected return would be the yields of the investment portf Expected return: 13.34 % < (29% * 11%) + (71% * 14.3%) 3) Since the insurance company wants to protect its future cash obligations against fluctuations in interest rates, the based on Duration. In order to be perfectly ...
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