What difference does it make?
Is it true that one performance measure is as good as another? Do they all produce very similar results? The current quarter offers evidence that it ain't necessarily so.
Let's assume you're trying to select the best equity funds for a 401(k) plan your firm offers. You begin with a list of the 100 funds most used by defined contribution plans. Conveniently, these funds are listed in the March 23 issue of Pensions & Investments. To choose the best from this list, you decide to compare the results from three procedures for ranking performance for this most recent quarter on a risk-adjusted basis: the Sharpe ratio, the Omega return, and the Omega excess. (The latter two have been discussed at length in previous issues of P&I. For details, search for Omega on www.pionline.com or www.sortino.com.)
The results for these rankings are shown in the table titled "Risk-adjusted rankings" on page 26.
The Franklin Strategic Small Cap Fund is the first choice for both the Omega return and Omega excess. However, this fund does not even make the list based on the Sharpe ratio. In fact, seven of the top 10 choices based on the Sharpe ratio do not show up in either the Omega or the Omega excess top 10 lists.
There are two reasons for this. First, the Sharpe ratio assumes a good outcome is getting a return above the Treasury bill rate. The other procedures assume a good outcome is getting a return above some minimal acceptable return. Based on research conducted at the Pension Research Institute, we believe 8.6% is a reasonable estimate of the MAR for many investors. This is a higher hurdle than the T-bill rate, which is not an appropriate hurdle for most investors because merely beating it will never allow them to retire. Treasuries are free of default risk, but for most investors, they carry a high risk of not accomplishing the investors' goals.
The second reason for the difference in rankings has to do with what constitutes a bad outcome. The Sharpe ratio assumes that risk has to do with not achieving the mean, or average return. Thus high returns above the mean incur just as much risk as returns far below the mean. Omega and Omega excess returns consider only those that fall below the MAR as risky.
Three of the top 10 funds ranked by five-year Omega do not show up in the Omega excess return and the rankings are quite different. This could make a big difference in how much money is allocated to each manager. The difference has to do with what is measured. Omega return corrects for downside risk, the manager's style, and the investor's degree of risk aversion. It answers the question: "how does this manager's performance compare to all other managers when all these corrections are taken into consideration?"
The Omega excess begins with the calculation of the manager's Omega return. Then an Omega return is calculated for a passive strategy that attempts to replicate the manager's style. That style benchmark is subtracted from the manager's Omega return. The difference is the excess return, which tells how much the active manager earned relative to a passive strategy that charges lower fees?
Procedures for measuring performance do not all give the same answer, but they all give the right answer, depending on what question you are trying to answer. Fund data and statistics shown in this study were produced by the "Downstyle" model of LCG Associates, Atlanta, using Independence Investment Associates Inc. style data.
Frank Sortino is director of the Pension Research Institute, Menlo Park, Calif.
