In this section we report the results of experiments that test various procedures for selecting potential future winners from among each year's LS100 funds. In no small measure, this is an exercise in data mining -- one of the more serious sins in empirical investigation. Not surprisingly, if enough procedures are tested, one can invariably find some that would have "worked" in at least some periods. But this hardly guarantees that they will work in the future. Studies of this sort are subject to a potentially huge selection bias.
Despite these caveats, our findings are of some interest. To allow the reader to fully evaluate them, we summarize the results for all the methods that were tested. However, even this can provide a deceptive view, since the methods analyzed were chosen, to at least an extent, because they were similar to procedures that others had proposed, based on analyses of data from some of the years that we utilize.
As with any empirical study of this type, the reader is advised to proceed at his or her own peril.
A passive manager provides investors with style. An active manager provides both style and selection. Since we are interested in the possibility of selecting active managers who will be successful in the future, we focus on selection returns.
Initially, we concentrate on the ability of a group of funds to produce superior average selection returns. Later we analyze the abilities of various groups to produce selection returns with desirable mean/standard deviation ratios, often termed Sharpe Ratios (for a discussion of the latter, see William F. Sharpe, "The Sharpe Ratio," Journal of Portfolio Management, Fall 1994, pp. 49-58.). In each case we utilize monthly selection returns.
Each experiment begins by choosing a selection criterion, implemented using data available in December of each year. The LS100 funds to be used in the following year are ranked on the basis of this "selector", then grouped into four portfolios, each with 25 funds. Within each of the resulting four quartile portfolios, funds are weighted in accordance with their net asset values at the end of November. The performance of each such portfolio is calculated over each of the next twelve months, with each fund position held throughout the year. The entire process is repeated each year.
For each strategy we compute our two performance measures (average selection return and selection return Sharpe Ratio) for (1) the 120 months in the entire period from January 1985 through December 1994 and (2) the 60 months from January 1990 through December 1994. We refer to these as the "10 Year" and "5 Year" periods, respectively.
The performance of the aggregate index of all the LS100 funds is shown below.
10 Yrs 5 Yrs
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Mean -.04 -.01
Sharpe Ratio -.17 -.04
All results are based on monthly returns, expressed in percentage terms. Thus the average selection return for the LS100 over the 10 year period was -.04, or -.04% (4 basis points) per month, approximately equal to 0.48% per year.
Overall, the funds offered performance that was better (less b ad) in the last 5 years than it was in the last 10 years. In the last 5 years the average performance was approximately -.01% per month, somewhat better than that associated with a typical index fund, which is closer to -.02% per month (-.20% per year).
Our first experiment utilized size (total net asset value) as a selector. The table below shows the average selection returns over each of the periods for each of four portfolios. Portfolio 1 comprised the 25 funds with the largest total net asset values, portfolio 2 the next 25, portfolio 3 the next, and portfolio 4 the 25 funds with the smallest total net asset values. As in all the experiments, within each portfolio funds were weighted in accordance with their net asset values.
10 Yrs 5 Yrs
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1: Largest -.04 -.02
2 -.08 -.06
3 -.04 .04
4: Smallest -.01 .03
These results suggest that over the entire 10-year period, there was not a significant relationship between size and performance. Over the last five years there was a tendency for the smaller funds within the LS100 to do better than larger funds. Given the statistics for the full ten-year period, the pattern in the first five years must have been reversed.
These results provide no support for the thesis that the larger LS100 funds are likely to outperform the smaller ones. If anything, the evidence is mildly supportive of the opposite thesis. Economies of scale may well give larger funds comparative advantages over smaller ones up to a point, but that point may be reached at a size below that of the smallest LS100 fund.
The table below shows the average selection returns over each of the periods for the "Quartile 1" portfolios based on three different selection criteria. In each case, the 25 funds with the largest prior average selection returns were selected each year. The first row shows the results obtained when the funds were chosen each year on the basis of their average selection returns in the prior 12 months. The second row shows the results when the criterion was the funds' average selection returns in the prior 24 months. The last row shows the results obtained when the criterion was the average selection returns over the prior 36 months.
10 Yrs 5 Yrs
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12 Prior Months .07 .07
24 Prior Months .04 .03
36 Prior Months .03 -.02
This set of experiments suggest that the most recent prior performance (12 months) may be the most relevant for predicting future performance.
Taken alone, the results show that this method worked as well in the last 5 years as over the entire period. However, the average performance of the LS100 was better in the latter five years. Relative to the average performance of the 100 funds, the quartile 1 funds' performance declined. For example, the funds selected on the basis of the prior 12 months' selection returns outperformed the LS100 by 0.11 percent per month for the overall period, but only .08 percent per month in the latter five years:
10 Yrs: .07 - (-.04) = .11
5 Yrs: .07 - (-.01) = .08
To further illustrate the value of the prior 12 months' average selection returns as a predictor of future performance, we show below the average selection returns for each of the four quartile portfolios over each of our ex post measurement periods.
10 Yrs 5 Yrs
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1 (Best) .07 .07
2 -.08 -.01
3 -.06 -.05
4 (Worst) -.11 -.04
The progression from quartile 1 through quartile 4 is fairly regular, lending added credence to the earlier results. Note, however, that the spread between the performance of the best and worst quartiles was somewhat lower in the last five years than it was for the overall ten-year period:
10 Yrs: .07 - (-.11) = .18
5 Yrs: .07 - (-.04) = .11
We next examine the performance of the top-quartile portfolios selected on the basis of the Sharpe Ratios of prior selection returns. The table below shows the average selection returns over each of the periods for strategies in which funds were chosen based on the Sharpe Ratios of selection returns. The first row shows results obtained when 12 months of prior selection returns were used, the next row when 24 months were used, and the last row when 36 months were used.
10 Yrs 5 Yrs
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12 Prior Months .06 .06
24 Prior Months .02 .01
36 Prior Months .04 -.02
The results are similar but slightly inferior to those found when funds were selected on the basis of prior average selection returns. As before, the shorter the period used for prediction purposes, the better.
Thus far we have utilized only ex post average selection returns as a measure of the actual performance of each of the strategies analyzed. For completeness, we turn now to the ex post Sharpe Ratio of the strategies' selection returns. Specifically, we consider only the Sharpe Ratios for the aggregate portfolios, not the Sharpe Ratios for the individual funds.
Each of the next two tables shows the ex post selection return Sharpe Ratios for six strategies, defined by the selection criterion (prior average selection ratio or prior selection return Sharpe Ratio) and the period (12, 24 or 36 months) over with the measures utilized for the selection were computed.
Selection return Sharpe ratios for the entire ten-year period were as follows:
Prior
Prior Sharpe
Average Ratio
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12 Prior Months .15 .17
24 Prior Months .07 .04
36 Prior Months .06 .08
while those for the last five years covered were:
Prior
Prior Sharpe
Average Ratio
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12 Prior Months .14 .16
24 Prior Months .05 .02
36 Prior Months -.04 -.04
The selection return Sharpe Ratio predicted the future selection return Sharpe Ratio better than did the historic average selection return, although the differences were relatively slight. As before, the shortest historic period was the best and both predictors did a better job for the last five years than for the overall period.
While these results offer at best presumptive evidence on the subject of predicting future winners, some tentative implications may be offered.
For predicting future performance, relatively recent prior performance appears to be more relevant than longer-term performance. Both the average of the last 12 month's selection returns and the Sharpe Ratio of those returns provided useful information about future performance over the period analyzed.
The average selection return from a strategy based on prior average selection returns was slightly better than that of one based on the Sharpe Ratio of prior selection returns. On the other hand, the ex post Sharpe Ratio of selection returns was higher for a strategy based on the prior Sharpe ratio of such returns. When making predictions, it appears to be slightly better to use a past value of the measure being predicted rather than an alternative measure.
During the periods analyzed, strategies based on both average prior selection returns and those based on the Sharpe Ratio of prior selection returns produced portfolios of funds that outperformed their styles. This was the case for both the full ten-year period and the last five years of that period. A fortiori, such strategies outperformed the LS100 funds, taken as a whole.
These results can be seen in the next two figures, which show the cumulative monthly selection returns (uncompounded) for four strategies.
In the graph below, the MnQ1 and MnQ4 curves show the performance of the first (best) and fourth (worst) quartiles of 25 funds each year, ranked on prior 12-month mean (average) selection returns. The curve labeled "All" shows the performance of the full set of 100 funds. The curve labeled "Passive" reflects the results associated with an index fund with overall costs of 0.20% per year. It is included as an indication of a reasonable performance for a fund that engages in no active management and minimizes expenses accordingly.
The next graph shows the same results for the LS100 ("All") and the passive alternative, along with the first and fourth quartiles ranked on the Sharpe Ratios of prior 12-month selection returns.
Do winners repeat? If so, can Style Analysis help find winners in advance? If the last ten years are indicative of the next ten years, one might be tempted to answer both questions in the affirmative. However, closer examination of the record of the last two or three years could lead to at least a neutral position on the issues. Either way, the evidence is far from conclusive, statistically or economically. Perhaps the only safe conclusion is that there is little support for the thesis that within this group of funds, past losers "are due" and likely to outperform past winners.
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