By Martin L. Leibowitz

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Rsp~~ctive ow Asset Allocatin~z liabilities as the interest-rate sensitivity benchmark. When the total portfolio duration matches the liability duration, the surplus function is immunized with respect to interest-rate movements. Higher or lower total portfolio durations would entail different risk exposures to interest-rate changes. Portfolio Optimization The surplus function approach may be used to develop expected values of return as well as measures of both interest-rate and market variability.

In particular, active-lives projections clearly depend on a host of assumptions regarding future benefit-payroll statistics. Different active-lives schedules may be used for the same payroll for different actuarial and reporting purposes. Moreover, interactions with the inflation rate must be taken into account in any more refined duration calculations. The, flow of future contributions also may have a profound effect on interest-rate sensitivity. The fixed flow of nominal dollar payout, depicted in Figure 23, admittedly captures none of these important effects.

Figure 22. Retired-Lives Liability Schedule payments to a fixed pool of such retirees. Given a fixed pool, this pattern is typically frontloaded, with benefits declining exponentially in accordance with mortality tables. Active lives represent current employees who have vested (or accrued but unvested) interests in future benefits. For members of this class, the receipt of payments is deferred until some actuarially specified Liability Returns retirement time. Projected benefit payments for active lives begin to increase with those who are about to retire, then grow to a peak that represents the bulk of future retirement benefits.

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