R ver the long term, equity investors have , -5 been richly rewarded for the risks that they have endured. For example, during the 1926-1987 period, the S&P provided an annual return advantage of 6.8%, compared with long-term corporate bonds. Over sh0rte.r periods, by contrast, stocks actually underperformed cash on a surprisingly frequent basis. In particular, stocks have underperformed Treasury bills over the past fifteen years in almost 35% of six-to eighteen-month time periods (see Salomon et al. [1990]).Few professional investors are able to observe callmly and passively while high volatility buffets their portfolio's value over the short run, and most fund sponsors control overall risk by adjusting the extent of their equity position. By adding cash or bonds and thereby lowering equity exposure, fund sponsors reduce portfolio volatility. At the same time, they give up a portion of the risk premium that equity offers; decreased exposure to equity leads to a reduction in expected returns.In this article we focus on the balance between risky and risk-free assets. Although we use equity as the proxy for all the risky assets in a portfolio, our methodology applies equally to any basket of risky assets. We offer a simple model of how to quantify risk tolerance and then use it to determine the maximal equity investment.We measure downside risk by the "shortfall probaldity" relative to a minimum return threshold. By specifymg both this threshold and a shortfall prob-,-ability, we can establish a "shortfall constraint" to determine the maximum allocation to risky assets. (See Leibowitz et al. [1990] for full details.)We also consider the sensitivity of the risky asset allocation to changes in voliltility, equity risk premium, return threshold, and shortfall probability. Finally, we show how this methodology can be applied to multi-year investment horizons.
THE EFFICIENT FRONTIER FOR AN EQUITYKASH PORTFOlLIOA portfolio manager with ,a well-established horizon always has a continuum clf choices between risky and riskless assets. For example, over a oneyear investment horizon, the oine-year Treasury STRIP provides a riskless return equal to its yield; that is, this "cash" asset has no return volatility. However, modern theory suggests that a holder of risky assets should be compensated for the associated volatility (risk) by means of a positive increment in expected returnthe so-called risk premium. Current estimates of the equity risk premium for U.S. equities range from a 4% expected return advantage to a 6% expected return advantage.Because cash does not have any return volatility, the volatility in an equitykash portfolio reflects entirely the proportion of equity in that portfolio, and the portfolio manager can control volatility risk by adjusting the equitykash balance. As the percentage of equity increases, so does both portfolio risk and expected return. Figure 1 illustrates the linear rela-MARTIN L. LELBOWITZ is Managing Director, and STANLEY KOGELMAN is Vice President, at S,alomon Brothers Inc in New York (I...
