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20 Jan 1981 Jan 1982 Jan 1983 Jan 1984 Figure 38.

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. With this quantification, the asset allocation problem may be formulated as an optimization problem, aimed at achieving the desired balance between return and risk as measured through the fund's surplus values. In this context, the difference between total portfolio duration and liability duration represents one risk measure. The effect of non-interest-rate factors constitutes a second dimension of risk.

This longer duration could be expected to lead to more Liability Retu~rzs volatile liability returns, and, as Figure 25 indicates, this expectation is met. 48 percent. 38 percent increase in surplus value, due primarily to the huge decline in the present value of the liabilities. In contrast, during 1982 the decline in interest rates caused the present value of the active-lives schedule to soar by almost 80 percent, a multiple of the returns available in either the S&P 500 or the BIG Index. It would have been virtually impossible, therefore, for any fund with a large active-lives component to avoid serious surplus erosion in 1982.

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