something other than chance. In contrast, a positive alpha that is not statistically significant could be merely happy coincidence rather than manager skill.

In our case, two of the six strategies (convertible arbitrage and equity market neutral) have statistically significant historical alphas. For example, the equity market neutral alpha is 500 basis points and the t-statistic is 4.59. By contrast, the equity long/short alpha is 310 basis points, but the t-statistic is 0.86. On the basis of these figures, we are more inclined to regard the equity market neutral composite performance as representing something other than chance.

Index performance statistics are composites of many individual managers. The figures summarized in Table 26.5 suggest some historical variation across hedge fund strategies in producing alpha. However, even though the composite performance in a particular strategy does not have a statistically significant alpha, there may be managers in that strategy who have been able to generate significant outperformance.

A simple way to approach this issue is to do the same type of analysis that was done on each hedge fund index, except at the manager level. In other words, we can find the alpha for each manager in each strategy and determine whether the manager's alpha is positive and statistically different from zero. Just as with the analysis at the index level, we'll find the alpha for each manager by regressing the manager's historical performance on the performance of the U.S. equity market, after adjusting both for the level of cash returns. As before, when the alpha is positive and the t-statistic is greater than two, we are inclined to regard the historical performance as representing something other than chance.

In Table 26.6 we show the distribution of t-statistics for the alphas for the managers in each hedge fund strategy. We have focused on the t-statistics for only those managers who had positive alphas, since we want to know whether there are some managers who historically were able to add value through skill rather than chance. These alphas were estimated from the larger manager universe, and covered a longer time period. (Many managers reported returns over differing time periods, and most managers did not report returns over the entire time period indicated in Table 26.6.)

It is quite clear from Table 26.6 that some managers had statistically significant alphas. For example, in equity long/short 71 percent of the managers had positive

TABLE 26.6 Historical Manager-Specific Alpha (1/94-5/01)

% Managers % Managers Statistically

Number of with Positive Significant out of Those

Strategy Managers Alpha with Positive Alpha

Event driven 179 82% 59%

Equity long/short 622 71 33

Convertible arbitrage 71 80 77

Equity market neutral 177 62 49

Fixed income arbitrage 89 66 42

Tactical trading 1,355 57 12

Source: TASS Research.