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ACTSC 445 (24)

unit7 dedicated bond portfolio

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Actuarial Science
Jiahua Chen

ACTSC 445: Asset-Liability Management – Fall 2008 Department of Statistics and Actuarial Science, University of Waterloo Unit 7 – Dedicated Bond Portfolio: A Case Study References (recommended readings): Chap. 48 of Fabozzi. In this unit, we use an example based on a pension plan to illustrate the use of a dedicated bond portfolio for cash flow matching. The liabilities in this example are taken to be the expected benefit payouts to a closed block of current retirees, and a 35-year schedule is used. A few notes on liabilities: • Liability obligations must be projected accurately. • Sometimes, terminated vested participants (former employees who are vested in the pension plan and are entitled to benefit payouts commencing sometime in the future) are also included, and also active partcipants over the age of 50. When this is the case, various mortality, termination, and benefit assumptions must be reviewed periodically. The following table is an excerpt of the schedule of expected benefit payouts for this example (Exhibit 48-1 in Fabozzi). Retired lives liabilities Retired lives liabilities plus terminated vested Year Dollar Payout Dollar Payout 1992 1,250,000 2,000,000 1993 15,000,000 24,000,000 1994 14,916,015 24,519,000 1995 13,445,985 25,021,000 . . . . . . 2027 2,123,504 10,982,000 2028 1,337,297 9,869,000 Total 283,758,000 Once we have the liability schedule, the next step is to identify the portfolio’s constraints. A typical constraint is to force the portfolio to contain only bonds with low credit risk. Also, mortgages are usually undesirable because of the prepayment uncertainty. 1 The following table gives the constraints used for this example (Exhibit 48-2 of Fabozzi). Minimum Maximum Quality (Credit Rating) Treasury 20% 100% AAA 0 100% . . . . . . BBB 0 0 Sector Treasury 20% 100% Industrial 0 30% . . . . . . Concentration Max. in one issue 10% Min. in one issuer 10% Call Constraints on Corporate Securities Noncallable only Lot Size Conditional minimum $2,000,000 (par) Increment $1,000,000 (par) Maximum Unlimited Note: it is typical to not enforce a perfect match of the liability schedule. Because of that, we can have cash flows from the portfolio that need to be reinvested. Assumptions for the reinvestment rate are usually pretty conservative (3% in the example). Once the constr
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