FIN401-Ch.11Classnotes

Contingent immunization allows bond portfolio

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Contingent immunization allows bond portfolio managers to actively manage until the portfolio falls to a threshold level, after which the manager must immunize the portfolio.
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29 Net Worth Immunization Financial institutions need to match assets’ and liabilities’ maturity structures. Example: Consider a bank. Its bank liabilities are primarily the deposits owed to customers. These have very short maturities and, hence, low duration. On the other hand, bank assets are made up of outstanding commercial and consumer loans. These assets have longer duration than deposits. This means that the assets’ values are more sensitive to interest rate fluctuations.
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30 Net Worth Immunization In periods when interest rates increase unexpectedly, banks can suffer serious decreases in net worth. Their assets fall in value by more than their liabilities. Hence, banks need to do asset and liability management. One such technique is “gap management”: this is aimed at limiting the “gap” between asset and liability durations.
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31 Gap Management In gap management, the bank is trying to equate the durations of assets and liabilities to effectively immunize the overall position from interest rate movements. Because bank assets and liabilities are roughly equal in size, if their durations also are equal , any change in interest rates will affect the values of assets and liabilities equally.
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32 Target Date Immunization In contrast to banks, pension funds have to meet future commitments, rather than protecting current net worth. Such funds have to provide workers with a flow of income upon their retirements, and they must have sufficient funds available to meet these commitments. This means that the pension fund manager has to “immunize” the future accumulated value of the fund at some target date against interest rate movements.
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33 Immunization Example Suppose an insurance company issues a guaranteed investment contract for $10,000. GIC matures in five years with guaranteed interest rate of 8%. Insurance company is obligated to pay $14,693.28 in five years. What is the duration of the GIC? 5 ) 08 . 1 ( 000 , 10 $ 28 . 693 , 14 $ =
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34 Immunization Example Insurance company chooses to fund the obligation with $10,000 worth of 8% annual coupon bonds, selling at par, with 6 years to maturity. What is the duration of this investment? 8% Pmt PV Pmt w t*w 1 80 74.07 0.0741 0.0741 2 80 68.59 0.0686 0.1372 3 80 63.51 0.0635 0.1905 4 80 58.80 0.0588 0.2352 5 80 54.45 0.0544 0.2722 6 1080 680.58 0.6806 4.0835 1000 1 4.9927 years
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35 Immunization Example The insurance company has matched the duration of the asset and the liability. What if interest rates remain the same? Rate = 8% Pmt Number Yrs Remaining Accumulate Value 1 4 800*(1.08)^4 = 1,088.39 2 3 800*(1.08)^3 = 1,007.77 3 2 800*(1.08)^2 = 933.12 4 1 800*(1.08)^1 = 864.00 5 0 800*(1.08)^0 = 800.00 Sale of Bond 0 10,800/1.08 = 10,000.00 14,693.28
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36 Immunization Example What if interest rates fall to 7%? Rate = 7% Pmt Number Yrs Remaining Accumulated Value 1 4 800*(1.07)^4 = 1,048.64 2 3 800*(1.07)^3 = 980.03 3 2 800*(1.07)^2 = 915.92 4 1 800*(1.07)^1 = 856.00 5 0 800*(1.07)^0 = 800.00 Sale of Bond 0 10800/1.07 = 10,093.46 14,694.05
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37 Immunization Example What if interest rates rise to 9%?
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