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By Martin L. Leibowitz

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Liability Returns 54 For simplicity and clarity, a single stable liability schedule was defined as a benchmark, as depicted previously in Figure 26. The present value of this Surplus Management liability stream depends on the interest rate used as a discounting factor, as shown in Figure 35. 00'/0 lnleresl Rate Figure 35. 2 As interest rates change, so will the liabilities cost. Thus, as shown in Figure 36, an interest-rate change from 8 percent to 7 percent would lead to an $11 million (11 percent) increase in the present value cost of these liabilities.

To gain insight into a more realistic pattern of liability returns, it is useful to explore the "performance" of an integrated benefits strueture consisting of a well-defined combination of both retired and active lives (see Figure 26). The present value of this combined flow comprises 60 percent retireds and 40 percent actives, based on their respective present values under a discount rate of 8 percent. Apply- Integrated Liability Returns R Nezo Pcr@rstivc on Assot Allocation ing the 10-year new A industrial rate as a discounting proxy to the integrated flaw illustrated in Figure 26 produces the performance results shown in Figure 27.

Range of duration values. Figure 33 shows the duration based on trailing 12-month returns for the S&P 500 for the period January 1980 through June 1986. The extraordinarily 1 I I I I I I 1981 1982 1983 ? 984 1985 1986 I , Year Figure 33. 982 t 983 1984 1985 1986 Year Figure 34. 90 years at the end of June 1986. 29 years. Moreover, the equation for transforming a given csrrelation into an empirical duration requires that only a high equity-to-bond volatility ratio-a rare occurrance-will produce equity durations as high as 6 years.

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