Index Level T-Statistic Level T-Statistic Residual Total Strategy Alpha (Alpha) Beta (Beta) Volatility Volatility   Event driven 3.6% 1.77 0.25 6.55 5.4% 6.6% Equity long/short 3.1 0.86 0.52 7.65 9.5 12.3 Convertible arbitrage 4.8 2.60 0.04 1.17 4.9 5.0 Equity market neutral 5.0 4.59 0.10 4.83 2.9 3.3 Fixed income arbitrage 1.0 0.62 0.03 0.87 4.3 4.3 Tactical trading 1.1 0.36 -0.03 -0.47 8.2 8.2 Source: CSFB/Tremont. suggest that investors can achieve indexlike volatility without holding an exceptionally large number of hedge fund managers within each sector. However, to achieve these volatility levels, investors must also ensure that the correlation of returns across managers within each sector is relatively low. Consequently, our results also suggest that investors will need to rely on thoughtful portfolio construction tools to develop an initial hedge fund portfolio, and robust risk management systems to ensure that the hedge fund portfolio remains within its prescribed risk tolerances. What about historical performance? The objective of our analysis in this case is to verify whether a portfolio of hedge fund managers can achieve the implied hurdle rates shown in Figure 26.5. Those hurdle rates range between 100 and 125 basis points over cash rates, for allocations between 5 and 25 percent. One easy step we can take is to assess the historical performance for each hedge fund strategies index. For example, we can regress the historical performance (measured as excess return over cash) of each hedge fund on historical U.S. equity performance (also excess return over cash) and evaluate whether each hedge fund strategy added value after adjusting for the performance of the overall equity market. We'll call the performance after all the adjustments the strategy's "alpha." The results of this analysis, summarized in Table 26.5, are comforting. Over the period January 1994 through May 2001, the historical performance for each hedge fund strategy is positive, after adjusting for cash rates and market returns. (All return numbers are annualized.) In some sectors, the value added historically is quite high. For example, the alpha (or adjusted performance) for equity long/short is 310 basis points. Although each strategy's alpha is positive (and in some cases high), we can still ask whether it was generated by chance. To answer this question, we'll calculate the t-statistic for each adjusted performance. For a simple rule of thumb, we'll regard an alpha as statistically different from zero if the t-statistic is greater than two in absolute value.3 That is, when the alpha is positive and the t-statistic is greater than two, then we are more inclined to regard the historical performance as representing 3We are measuring statistical significance with a 95 percent confidence interval.