In an article titled "Who gets the surplus?" (Pensions & Investments, Oct. 4), Mike Barry said, "Whoever bears the downside risk, gets the upside potential." He didn't need formulas to explain what he meant. A mound of research in behavioral finance indicates this is the way most people refer to their desired risk-return tradeoff. I believe we should incorporate the lingua franca of the man on the street in our attempts to measure the two most important concepts in investing, return and risk.
Our challenge is to figure out how to calculate these expressions in a way that is theoretically sound.
In the second-quarter ranking of mutual funds for P&I (July 26), I offered several examples; let me offer a few more.
The table above provides an example of how upside potential provides information not contained in the mean. Both Fund 1 and Fund 2 have the same mean, 9.6%. The mean cannot distinguish between them. However, Fund 1 was above the minimum acceptable return of 8% more often than Fund 2. This is added information, but the probability of success doesn't convey information about magnitude. Fund 1's upside probability of 70% doesn't tell the investor how high above the MAR Fund 1's returns were. Upside potential considers both frequency and magnitude. On average, Fund 2 was 2.5% above the MAR, while Fund 1 only had an average return of 1.8% above the MAR. In this simple illustration, it is clear Fund 1 never got more than 300 basis points above the MAR, while Fund 2 got as much as 700 basis points higher than the MAR. Investors looking for managers with upside potential should choose Fund 2. Notice that all returns below the MAR are set equal to zero (e.g., Fund 2's return in the first year was 4 percentage points, or 400 basis points below the MAR, so the upside is 0). Returns below the MAR are used in the downside risk calculation.
The minimal acceptable return the investor must earn in order to accomplish his or her goal is the dividing line between good outcomes and bad outcomes. The average return above the MAR captures the idea of upside potential, the deviations below the MAR capture the idea of downside risk. Because the mean is an average of all returns, the average return above the MAR will always be higher than the mean. (For formulas and theoretical foundation, please see the articles in the fall issues of The Journal of Portfolio Management and The Journal of Performance Measurement.)
The rankings on this page are from highest to lowest upside potential ratio. Windsor II had the highest ratio at 3.23. This means this manager's style should produce three units of upside potential for each unit of downside risk. An excellent risk-return tradeoff, in a language people intuitively understand. The U-P ratio is calculated from the manager's style data instead of directly from the manager's returns for the past five years. Why? Notice the R-squared indicates 97% of the manager's return is due to a style benchmark, or blend of passive indexes. I used the Independence Investment Associates indexes. Twenty years of data on the manager's benchmark provides a much more stable estimate of upside potential and downside risk than simply relying on the last five years of manager data.
But, knowing this manager's style is likely to be successful in the future does not tell us if the manager adds any value to his particular blend of passive indexes. That information is contained in the Omega excess return (the manager's risk-adjusted return minus the benchmark risk-adjusted return). The Omega excess for Windsor II is -1%. This means a passive blend of indexes produced 1% more than the active management. Presumably, if one could buy the blend of indexes for less than 1%, they could do better than the fund. Washington Mutual, on the other hand, beat its passive benchmark by a whopping 220 basis points, even though the R-squared was 96%.
Notice that some of the managers with the highest raw returns (unadjusted for risk) for the past five years (e.g., Janus Twenty which earned an average of 35%) are in the bottom quartile. Research indicates investing in the fund with the highest raw return in the past period produced a lower return than the average fund in subsequent periods.