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1 March 1988 Financial Analysts Journal Volume 44, Issue 2

Portfolio Optimization Within a Surplus Framework

  1. Martin L. Leibowitz, PhD
  2. Roy D. Henriksson

Portfolio optimization aims to achieve the asset mix that offers the highest expected return at a given level of risk. This process eliminates sources of portfolio risk that do not provide an expected return premium for investors.

Portfolio optimization can also be applied to the asset allocation decision when the investor has both assets and liabilities. The liabilities can be treated as a short position within the overall portfolio. Return and risk are then measured in terms of changes in the surplus of the asset value over the liability value. In this surplus framework, the optimal asset mix may differ drastically from the mix that is optimal when assets only are considered.

One dimension of the riskiness of pension liabilities is their sensitivity to interest rates. This source of risk can be neutralized by creating an “immunized bond fund” that precisely funds the liabilities. This immunized fund takes the place of cash as the riskless asset. Cash, with zero duration, cannot offset changes in liability values resulting from interest rate changes and carries a high surplus risk. The addition of equities to the immunized fund, however, increases portfolio expected return and risk, just as the addition of equities to an all-cash portfolio does in the assets-only framework.

Furthermore, in the surplus framework, bonds with durations longer than the liability duration represent substantial diversification potential when the effective duration of equities is less than that of the liabilities. Their value will tend to rise by more than the liability value when interest rates decline, potentially creating surplus growth; short-duration bonds, cash and most equities will tend to generate surplus losses under this condition. In effect, such bonds are negatively correlated with equity; they may be used in conjunction with an equity/immunized fund mix to achieve the highest expected return at a given risk level.

In practice, the asset allocation decision may be much more complex. It will require a more detailed and expanded set of potential assets. It may be necessary to incorporate other dimensions of risk for liabilities. Investors may have multiple objectives. However, even with these added complications, portfolio optimization can still be a valuable tool in the asset allocation decision.

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