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immunization - Chapter 44 of H of Fixed-Income Securities...

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Chapter 44 of H. of Fixed-Income Securities Chapter 3 of Financial Economics Immunization Theory Notes by Prof. K.S. Tan/Actsc445/845 Immunization – p. 1/60
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Immunization F.R. Redington (1952): “the investment of the assets in such a way that the existing business is immune to a general change in the rate of interest” Fisher and Weil (1971): “A portfolio of investment is immunized for a holding period if its value at the end of the holding period, regardless of the course of rates during the holding period, must be at least as it would have been had the interest rate function been constant throughout the holding period If the realized return on an investment in bonds is sure to be at least as large as the appropriately computed yield to the horizon, then that investment is immunized.” An immunization strategy is a risk management technique designed to ensure that a portfolio of debt instruments (eg. T-bills, bonds, GICs etc) will cover a liability (or liabilities) coming due at a future date (or over a period in the future) Notes by Prof. K.S. Tan/Actsc445/845 Immunization – p. 2/60
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Topics Immunization for single-period liability Target Date Immunization Immunization for multi-period liabilities Generalizations of classical immunization theory Other immunization techniques asset allocation problems Notes by Prof. K.S. Tan/Actsc445/845 Immunization – p. 3/60
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Immunization: Single Period Case Example I: Suppose an insurance company faces a liability obligation of $1 million in 5 years. The available market instruments are: 3-year, 5-year and 7-year zero-coupon bonds, each yields 6% annual effective rate. Portfolio A: Invest $747,258.17 in the 5-year zero coupon bond Portfolio B: Invest the same amount (i.e. $747,258.17) in 3-year zero. maturity value in year 3 is $889,996.44 Portfolio C: Invest $747,258.17 in 7-year zero. maturity value in year 7 is $1,123,600.00 Are these immunized portfolios? Scenario 1: No change in yields; i.e. ytm remains at 6%. What will be the impact? Notes by Prof. K.S. Tan/Actsc445/845 Immunization – p. 4/60
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Example I Cont’d Scenario 2: What if, immediately after the portfolio is acquired, the yield changes instantaneously to ˆ y and remains constant at that level ? What will be the impact on the portfolios? Portfolio A: Portfolio B and Portfolio C Notes by Prof. K.S. Tan/Actsc445/845 Immunization – p. 5/60
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Ex. I Cont’d: Impact of Scenario 2 on Portfolio B Recall that the maturity value of Portfolio B is $889996.44 Value of Portfolio B Capital Gain Implied ˆ y (%) in year 0 in year 5 in year 0 Yield (%) 4.00 791203.5944 962620.1495 43945 . 4215 5.20 5.00 768812.3874 981221.0751 21554 . 2146 5.60 5.90 749377.0511 998114.0975 2118 . 8782 5.96 6.00 747258.1729 1000000.0000 0.0000 6.00 6.10 745147.2753 1001887.6824 2110 . 8975 6.04 7.00 726502.2044 1018956.9242 20755 . 9684 6.40 8.00 706507.8685 1038091.8476 40750 . 3044 6.80 Remarks: Notes by Prof. K.S. Tan/Actsc445/845 Immunization – p. 6/60
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Ex. I Cont’d: Impact of Scenario 2 on Portfolio C Recall that the maturity value of Portfolio C is $1123600.00 Value of Portfolio C Capital Gain Implied ˆ y (%) in year 0 in year 5 in year 0 Yield (%) 4.00 853843.6549 1038831.3609 106585 . 4820 6.81 5.00 798521.5425 1019138.3220 51263 . 3697 6.40 5.90 752211.5711 1001889.4658 4953 . 3982 6.04 6.00 747258.1729 1000000.0000 0.0000 6.00 6.10 742342.0181 998115.8742 4916 . 1548 5.96 7.00 699721.6100 981395.7551 47536 . 5629 5.60 8.00 655609.8081 963305.8985 91648 . 3647 5.21 Remarks: Notes by Prof. K.S. Tan/Actsc445/845 Immunization – p. 7/60
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Summary
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