For many years now, my research efforts have focused on an alternative measure of risk called "downside risk." Now there's a new measure of return that I call "upside potential."
Behavioral Finance experts Mier Statman and Hersh Shefrin at Santa Clara University claim most investors do not seek the highest return for a given level of risk, as portfolio theory assumes. Instead, they say, investors seek upside potential with downside protection.
The protection part is measured well, I believe, by the downside risk measure. How to capture the upside potential is the focus here.
The accompanying graph illustrates the value of upside potential as a measure of return. It depicts the returns of three managers. The MAR line represents the return that must be earned at minimum in order to accomplish the financial goal. Manager A invested in securities perceived as safe, but that guaranteed the investor would not earn a return high enough to accomplish the stated goal. Therefore, manager A provided no upside potential. Manager B provided the highest chance of success; he was above the MAR more often than managers A or C. Yet most investors would prefer the upside results of manager C because, in addition to frequency, they value how far a manager's returns are above the MAR. To capture this idea of magnitude and frequency, I measure a manager's upside potential as "the average return above the MAR." This is more meaningful than simply using average return over time.
To illustrate the difference, look at "Upside vs. mean & chance." Funds 1 and 2 have the same average return over 10 years so the mean can't distinguish between them. However, Fund 1 earned a return greater than the MAR 80% of the time, while Fund 2 beat the MAR 40% of the time. Clearly, an investor seeking to maximize the chance of success would choose Fund 1. But it never beat the MAR by much, while Fund 2 has beaten the MAR by as much as 12%. Fund 2 clearly has more upside potential. In this example, the upside potential is calculated by adding all of the values above the 8% MAR and dividing by the number of observations, 10. Now we see Fund 2 has 31% more upside potential than Fund 1.
This example uses a discrete distribution. The LCG model used to make the calculations shown in the larger table above generates a continuous distribution for each fund, which requires integral calculus to calculate upside potential. Performance should never be measured by return alone. Risk must be taken into account. We prefer to use the downside risk of each fund's style benchmark. (For more information, see www.sortino.com.) Thus, the upside potential for success divided by the risk of failure is the upside potential ratio. The funds in the analysis are ranked by the upside potential ratio for that manager's style. For example, the T. Rowe Price Equity Income Fund's style has 5.8 times as much upside potential as downside risk. The next column is the Omega excess return, which measures the risk-adjusted return earned by a manager beyond a passive style benchmark. The Omega excess of 3.2 means this fund earned 320 basis points more on a risk-adjusted basis than a passive strategy that invested solely in a blend of indexes that attempts to replicate the manager's style. The R-squared of 92 means a set of passive indexes could capture 92% of this manager's style.