The following is excerpted from a paper done by Bernardo Kuan, which I referenced in P&I 2/99.

 Research on the Excess Omega Return

by

BERNARDO B. KUAN

San Francisco, California

December 1998

ABSTRACT

In an effort to apply style analysis to downside risk, Sortino, Miller, and Messina [1997] developed a performance measure called the omega excess return. The purpose of this research project was to conduct an empirical investigation to compare the omega excess return with other performance measures. The methodology consisted of collecting monthly returns on twenty-eight mutual funds between 1978 and 1996. The Pension Research Institute Style Evaluator program was used to make the necessary calculations. The study indicates that the omega excess return was superior to other performance measures in predicting future performance. Also, selecting funds on the basis of the omega excess return proved to be a superior strategy to holding all of the funds or always investing in the fund with the highest return in the previous year

ANALYSIS AND RESULTS

Ranking Correlation:

The Schwab Center for Investment Research study separated mutual funds by style and then ranked them by eight different measures: Sharpe Ratio, Geometric Sharpe Ratio, Selection Sharpe Ratio/Information Ratio, Return/Risk Ratio, Jensen’s Alpha, Benchmark Jensen’s Alpha, Holding Period Alpha, Appraisal Ratio and the Modigliani risk-Adjusted Performance. This study found that the rankings tend to be very similar irrespective of the measure used, concluding that the investor should not be concerned about which of these measures to use. 

Similarly, to see whether the Excess Omega Returns produces similar rankings to the one obtained by using the Sharpe ratio and Sortino ratio, the Spearman rank-correlation coefficient was used.

The statistic takes on values between +1 and –1, where +1 indicates they are identical and –1 indicates the rankings are reversed. The Spearman rank correlation is computed using the following formula:

x_i = the rank of the i^th item using a single variable, y_i = the rank of the I^th item using a different variable, and n = number of items being ranked.

Ex-Omega – Sortino = Spearman rank correlation between the Excess Omega and the Sortino rankings.

Ex-Omega – Sharpe = Spearman rank correlation between the Excess Omega and the Sharpe rankings.

Sortino – Sharpe = Spearman correlation between the Sortino and Sharpe rankings.

Consistency

Another question regarding the results calculated was: How consistent were the rankings obtained from one year to the next?

To study the consistency of the excess omega returns, the following two methods were proposed.

Method 1:

Quartile Consistency

The mutual funds were ranked by the excess omega returns (See Exhibit 5), and the Sharpe and Sortino ratios from 1981 to 1996. Then, I measured the frequency that funds moved or stayed in a given quartile from one year to the next using a three and five year intervals (See Exhibit 6).

The results show a better quartile consistency ranking than that obtained using the Sharpe or Sortino measurements. If a fund started in the first quartile, there was a 61% chance that it will remain in the first quartile in the next year ranking. Likewise, If a fund was in the lowest quartile rank it was very likely it would have stayed in the 4th quartile in the following year (62%). Increasing the time interval from three to five years produced very similar results (71% and 67% respectively). In contrast, the Sortino and Sharpe rankings showed a 38% and 42% chance on remaining in the first quartile and a 29% and 38% probability of staying in the 4th quartile (See Exhibit 10).

Almost every fund had a similar ranking fluctuation, except the Magellan and IDS New Dimensions funds that consistently ranked in top quartile and the Dreyfus fund staying frequently in the lowest quartile from 1981 to 1996 (See Exhibit 6).

Method 2:

Consistency as ranking variation:

A variation of method 1 is how far a fund changed ranking from one year to the next. A fund was deemed consistent If its ranking didn’t changed more than three ranking positions. The total number of times that a fund stayed within ±3 ranking positions (± 10%) from one year to the next was 169, which is more than 40% of the time. In contrast the Sortino and Sharpe rankings had a grand total of 92 (21.9%) and 98 (23.3%) respectively (See Exhibit 11).

Looking at individual funds under the excess omega ranking the Fidelity Contrafund and the Keystone Small Co Growth proved to be the more consistent, having a 73% and 80% consistency respectively. By contrast, the more consistent funds under the Sortino ranking were the Kemper Small Cap Equity and the Fidelity Puritan, both with a 40% consistency. The highest rank under the Sharpe ranking was the Fidelity Contrafund with a 60% consistency. The Sortino and Sharpe rankings produce consistencies as low as 0%. The average consistencies for the Excess Omega, Sortino and Sharpe rankings were: 40.2%, 21.9% and 23.3% respectively (See Exhibit 12).

These two methods showed that the excess omega returns produce a more consistent ranking from one year to the next than the rankings by the Sortino ratio or the Sharpe ratio.

Excess Omega Return Statistics:

The Excess Omega Return Statistics from 1981 to 1996 ranged from a maximum of 31.20% for Fidelity Magellan to a minimum of –22.90% for Keystone Small Co Growth. With a few exceptions, like Fidelity Magellan and Janus, the average manager’s contribution to the total return was 0.9%. This indicates the average manager was able to produce higher risk adjusted returns than a set of passive indexes. However, the average excess returns exhibited a downward trend, from positive excess omegas in the early 80s to negatives in the later years of our study. This may indicate that the markets are become more efficient with respect to the Omega Excess return (See Exhibit 7).

                                                                                                                   Exhibit 7

The descriptive statistics suggest that on average the manager’s skills contribute a small percentage of the total performance return of the fund. However, there were a few funds that significantly and consistently outperfomed or underperformed all other funds, and those are the ones that evaluation services should be trying to identify. The Omega Excess appears to hold greater promise for accomplishing this than any of the performance measures in the Schwab study.

The use of the Excess Omega Return as an investment strategy:

To see if the Excess Omega Returns can be used by an investor as an investment strategy, I developed a simple strategy. At the end of each year, the fund with the highest Omega Excess return was purchased. This Omega Excess strategy was compared to a naïve strategy of holding a portfolio of all the funds and a strategy of buying the fund with the highest raw return.

The Omega Excess strategy earned a cumulative return of 1444.15% for the period 1/1980 to 12/1996) with an average annual return of 21.5%. Over this same interval, the naïve strategy holding all funds produced a total cumulative return of 868.8%, with an annual average of 17.0% (See Exhibit 13-14). The worst performaing strategy was that of buying the top mutual fund ranked by raw returns, which produced a cumulative total return of 796.6%, with a average yearly return of 16.6%. If one held the top quartile of funds based on their Omega Excess, the cumulative return dropped to 943.9%, with an average annual return of 17.8% (See Exhibit 14), which is still better than the naïve strategy.

Because the funds ranked by excess omega returns remain in the top quartile more consistently than if they were ranked by unadjusted total returns, the number of transactions would be far less than buying the fund with the highest raw return each year. (See Exhibit 8).

CONCLUSION

In this study, mutual funds were ranked on the basis of 3-year risk and style adjusted returns using the Excess Omega returns. The Excess Omega rankings are not highly correlated with the Sharpe ratio, and therefore, according to the Schwab study, not highly correlated with the information ratio, alpha etc. Also, the consistency of ranking produce by the Omega Excess returns is far more stable than the one obtained using the Sharpe ratio or the Sortino ratio. From the investor's perspective, the use of the Omega Excess Returns as an investment strategy (buying the top fund) is superior to holding all funds or just investing in the fund with the highest raw return each year. This study suggests that the Omega Excess returns may provide unique information about funds that would be valuable to investors.