INTRODUCTION

Along with the rapid growth of the hedge fund industry and the emergence of hedge fund databases, scholars have started to study the persistence of hedge fund performance, analogously to the trend experienced in the mutual fund literature during the past 40 years. As can be judged from the abundant mutual fund literature over several decades, detecting performance persistence is challenging in mutual fund samples as a result of the many potential sources of bias (for a summary of potential biases in the context of mutual fund performance persistence studies, see Pätäri1). However, evaluating the persistence of hedge fund performance is even more challenging, as the diversity of hedge funds is even greater than it is among mutual funds. For example, hedge fund returns do not follow any conventional distributions, given the funds’ dynamic trading strategies and their holdings of derivative-type securities or agreements. In addition, the complexity of hedge fund strategies increases the risk of spurious persistence findings caused by model misspecification. Moreover, the higher attrition rate of hedge funds strengthens many of the biases documented in the mutual fund literature.

The evidence of performance persistence among hedge funds is mixed. Using annual return data and a sample of only offshore funds, Brown et al 2 find hardly any evidence of persistence after controlling for style effect, while the results of Agarwal and Naik3 show short-term persistence at the quarterly horizon in the traditional two-period framework but no persistence at the annual horizon in the multi-period framework. Harri and Brorsen4 find some evidence of persistence whose strength varies among hedge fund styles. The results show the greatest persistence for market neutral and for two funds of fund styles, and weaker persistence for the event driven, global and global macro styles. However, for some other styles no evidence of persistence is found. In this sense, the results of Harri and Brorsen are consistent with those of Agarwal and Naik,5 who also document that some hedge fund styles exhibit stronger performance persistence than others.

Controlling for look-ahead bias, Baquero et al 6 find a clear pattern of persistence in raw returns of hedge funds at the quarterly horizon but no statistically significant persistence at the annual horizon. Based on style-adjusted returns, the results show (on average) outperformance for top-decile funds of the preceding selection period at both the quarterly and annual horizons, though not significantly in the statistical sense. In addition, the authors note that persistence in hedge fund performance seems to be located in both the top and bottom parts of distribution. In this sense, the results of Baquero et al are in contrast with those of Capocci et al,7 who find that persistence, if any, is mostly located among medium performers. Gregoriou et al 8 show that fund portfolios made up of non-directional funds with the highest Information ratio and/or Sharpe ratio are likely to exhibit a remarkable persistence and continue to dominate the best fund of funds on the basis of the three performance metrics being examined (that is, the Sharpe ratio, 9-factor alpha and the corresponding Information ratio).

Kosowski et al 9 are the first to evaluate the persistence of hedge fund performance using Bayesian alphas. The Bayesian approach in the performance measurement context was first introduced in the mutual fund literature by Baks et al 10 and Pástor and Stambaugh,11 and Kosowski et al applied the Bayesian approach of Pástor and Stambaugh, which takes advantage of prior information in seemingly unrelated assets to overcome short sample problems, and to improve the precision of performance estimates. Their results show that hedge fund performance persists at annual horizons, and, further, that the prediction power of past alphas can be significantly improved by employing Bayesian alphas in forming the decile portfolios.

The parallel results of the improved predictive accuracy stemming from the use of Bayesian methods are also reported in many studies that examine persistence in mutual fund performance (for example, see Bollen and Busse,12 Busse and Irvine,13 Huij and Verbeek14). Many variants of the Bayesian estimation methods have been employed in the previous studies. This article contributes the existing literature in applying the so-called empirical Bayesian approach for the first time in the hedge fund context. Most of the Bayesian approaches require prior information related to such issues as funds’ expenses, investors’ beliefs about managerial skill, or benchmark pricing abilities, or the returns on other mutual funds, benchmark factors or non-benchmark factors, while the empirical Bayesian method is based entirely on a cross-section of fund returns within the sample period. The basic principle is to use cross-sectional data as prior information, in which case the resulting belief in managerial skill is no longer fully subjective, but instead, entirely data based. For example, Jones and Shanken,15 and Busse and Irvine13 demonstrate that the predictive accuracy of Bayesian alphas is greatly affected by the prior beliefs that are attributed to the investor. The empirical Bayesian approach was applied first in the mutual fund context by Huij and Verbeek,14 who document the superior prediction power of Bayesian alphas over standard OLS alphas.

We compare the prediction power of three performance metrics (that is, a standard frequentist style-adjusted 9-factor alpha, a corresponding Bayesian alpha and the Sharpe Ratio) to determine whether the performance persistence of hedge funds is dependent on the performance metrics employed. In addition, we use two complement methodologies in detecting the performance persistence of five different hedge fund styles (that is, convertible arbitrage, commodity trading advisor (CTA, henceforth), equity market neutral, event driven and global macro). First, we test the prediction power of the selection period performance on the holding period performance by means of cross-sectional regression. Second, we form top- and bottom-quartile portfolios based on selection period performance and test their holding period performance difference.

METHODOLOGY

Several models have been suggested to evaluate the performance of hedge funds. Typically, the multifactor models that are aimed to capture the common risk factors of diversified portfolios of hedge funds are employed for this purpose. The most widely used model of this type is the Fung-Hsieh 7-factor model, which includes the following factors: S&P 500 return in excess of the risk-free rate, Wilshire small cap minus large cap return, month-end to month-end change in the US Federal reserve 10-year constant maturity yield, corresponding change in the difference between Moody's Baa yield and the Fed's 10-year constant maturity yield, bond PTFS, currency PTFS, and commodity PTFS, where PTFS denotes primitive trend following strategy. While these seven factors can explain up to 80 per cent of monthly return variations for diversified hedge fund portfolios (see Fung and Hsieh16), their explanatory power with regard to returns of individual hedge funds is much lower. Therefore, we add two additional factors to the Fung-Hsieh model to improve its feasibility for hedge fund portfolio selection; first, as many hedge funds follow global stock investment strategies, we add a factor based on returns of Morgan Stanley Capital International world equities excluding US equities.17 Second, as we examine each hedge fund class separately, the style factor for each fund category is included in order to extract the funds’ true abnormal performance, that is, the performance beyond following a certain style. We use five different style factors for five corresponding hedge fund styles.

We employ three performance metrics in our comparative analysis: a standard frequentist style-adjusted 9-factor alpha, a corresponding Bayesian alpha and the Sharpe Ratio. At the outset of the study, the Fung-Hsieh 7-factor alpha was also employed, but was excluded from the comparative analysis, as the average adjusted coefficients of determination were remarkably higher for the 9-factor regression models including two additional factors than they were for the Fung-Hsieh 7-factor models.18 At the outset, we also employed several performance metrics that take account of skewness and kurtosis of fund return distributions. This was done because hedge funds frequently generate non-normal return distributions, and therefore the applicability of the Sharpe ratio to the evaluation of hedge funds particularly as the sole or the primary performance metric is questioned in many previous studies (for example, see Fung and Hsieh,19 Lo20 2002, Brooks and Kat,21 Gregoriou and Gueyie,22 Mahdavi,23 Sharma,24 Morton et al 25). However, the recent findings of Eling and Schuhmacher26 show that despite significant deviations of hedge fund returns from a normal distribution, the Sharpe ratio results in rank orders that are virtually identical to 12 other performance measures that are based on downside risk. In addition, the evidence from mutual fund markets indicates that performance rank orders are not very sensitive to the selection of risk measure (for example, see Ferruz et al 27 for a case of money market funds, and Ferruz et al 28 and Pätäri29 for a case of equity funds). We compared the rank orders produced by the Sharpe ratio with rankings based on one variant of the Sortino ratio, a modified Sharpe ratio that uses modified Value at Risk (VaR) as a risk metric (for details, see Favre and Signer30), and an adjusted Sharpe ratio that is closely related to a modified Sharpe ratio but that, in addition, can capture the occasional negative risk premiums and positive modified VaR figures that sometimes occurred in the sample employed. After numerous experiments, we came to the same conclusion as Eling and Schuhmacher26: for the sample employed, the hedge fund portfolios formed on the basis of performance metrics capturing downside risk were very similar to those based on the Sharpe ratio. Therefore, these approaches were not included in the comparative analysis, as they would have added hardly any value into it. In contrast, the results from the quartile portfolio approach based on the Sharpe ratio can, under these conditions, be generalized to also hold also for the above-mentioned performance metrics that put more emphasis on downside risk.

The purpose of the comparative analysis is to determine whether the investor would benefit from using more sophisticated methods while selecting a hedge fund portfolio based on past performance. We employ two different methodologies. First, we run a cross-sectional regression throughout the full sample period to determine whether the performance figures from the selection period explain those from the holding period. Second, to get a more in-depth view of the characteristics of the potential consistency in hedge fund performance, we form top-quartile portfolios and bottom-quartile portfolios based on selection period performance and compare their performance in the subsequent holding period in order to examine whether the performance difference between past outperformers and past underperformers remains. Taking account of implications of rebalancing, continuous, stacked time-series of monthly returns for quartile portfolios are generated throughout the sample period. In both methodologies, the selection period performance is based on time-series of 36 monthly returns and the holding period performance on subsequent 12-month period time-series of returns.

As a representative total risk-based performance metric, we employ the traditional Sharpe ratio as follows:

where R i =the average monthly return of a portfolio i; R f =the average monthly risk free rate of the return; σ i =standard deviation of the monthly excess returns of a portfolio i.

The 9-factor alpha represents the performance metrics that are based on the standard frequentist multi-factor model, and indicates the abnormal performance of the hedge fund/hedge fund portfolio i after controlling for its systematic risk exposures. The regression equation for calculating alpha is as follows:

where r t i is the fund i excess return at time t, α i is the intercept, β k i is the factor loading of hedge fund i on factor k, F k,t is the return of factor k at time t and ɛ t i is the error term.

In order to calculate the corresponding empirical Bayesian alphas, we first specify the cross-sectional distribution of alphas and betas as normal:

where θ i =(α i , β 1i ,…, β ki )′ μ is the (k+1) vector of the cross-sectional means of each estimate included in θ i , and Σ denotes a (k+1) by (k+1) covariance matrix of the previous OLS estimates. Under the assumption of independent and identically distributed (i.i.d.) normal error terms received using OLS regression, the posterior distribution of θ i is normal, with expected value given by

where θ̂ i denotes the OLS estimate, σ i 2 variance of the error terms, X i the excess return matrix of the benchmark factors including the intercept, and ((1/σ i 2)X i ′ X i +Σ −1)−1 denotes the corresponding covariance matrix.

The estimation of θ i * involves parameters (that is, μ, σ i and ∑) that cannot be estimated without knowing θ i *. This creates a recursive problem that Hu and Maddala31 overcome by using an empirical Bayesian approach. They calculate the parameters μ, σ i 2 and Σ iteratively using θ̂ i as initial estimation of θ i *:

where N is the number of funds, T i is the number of observations of fund i, y i is a vector containing the excess returns of fund i, and D denotes a diagonal matrix with small positive entries (for example, entries of 0.00001 can be used to improve the convergence in the iterative procedure). After calculating the parameters in (5), (6) and (7), θ i * is estimated again until the desired level of convergence of the parameters is obtained. Consistent with the previous studies employing the Bayesian estimation techniques, the Bayesian alphas are estimated only for selection periods, while the performance of holding period is determined on the basis of the Sharpe ratio and a standard frequentist 9-factor alpha only.

Statistical tests and adjustments

The statistical significances of differences between comparable pairs of the Sharpe ratios are given by P-values of the Ledoit-Wolf test,32 which is based on the circular block bootstrap method. We also test the statistical significance of differences between portfolio alphas by applying the alpha spread test as follows:

where α * is the alpha of portfolio*; SE α * is the standard error of portfolio*.

The degrees of freedom for the test statistic are given as

where v i and v j are the degrees of freedom determined on the basis of the number of time-series returns in samples i and j (v=n−1).

Throughout the study, we use Newey-West standard errors in statistical tests to avoid problems related to autocorrelation and heteroscedasticity. In addition, we performed the normality test by Jarque and Bera for regression residuals, but the assumption of their normality is not generally violated except for few random cases.

DATA

The sample data consist of monthly returns of 220 hedge funds (44 funds per each style) for the 1997–2006 period. In order to get as unbiased a sample as possible, the funds are selected randomly from the TASS database of those funds that have at least a 5-year return history. The minimum length requirement for the track record is set to 5 years, as we employ a 3-year selection period and follow the typical method used in hedge fund studies to eliminate backfill bias, which requires removing the first 12 monthly returns of every fund. To maintain better comparability between the two methodologies employed, we also require the full time-series of holding period returns from our sample funds, knowing that this raises some survivorship bias. However, because this kind of bias cannot be avoided in the cross-sectional sample by any means, we consider it a smaller trade-off than that stemming from the alternative consequence that the degree of survivorship bias would have varied in different persistence tests. On the other hand, as the attrition rate is highest among younger hedge funds (for example, see Brooks and Kat,21 Brown et al,33 Gregoriou,34 Amin and Kat35), it would not have made much difference if we had required only a 4-year return history instead.

The S&P 500 Composite Index, the Wilshire Small Cap Index, the Wilshire Large Cap Index, US Treasury securities at 10-year constant maturity and Moody's Baa Bond Index are from Datastream. The MSCI World ex US (Wexus) index is from the MSCI database and the 3-month US Treasury Bill is from the Federal Reserve database. Indices for PTFSs are from the web pages of the Fuqua School of Business.36 The hedge fund style indices are from the TASS database.

The first 3 years of data (that is, 1997–1999) are used only in evaluating selection period performance. Correspondingly, the stacked time-series of holding period returns for quartile portfolios ranges from the beginning of 2000 to the end of 2006, and includes 84 monthly observations throughout the 7-year period.

Table 1 reports the descriptive statistics of an average hedge fund within each fund style for a 36-month selection period and a 12-month holding period. Although there are great individual extreme values, the average values of descriptive statistics are surprisingly moderate. It is also noteworthy that skewness and kurtosis of return distributions are on average lower for shorter holding periods than for longer selection periods. Generally, the relatively low degree of average skewness and kurtosis may explain why the quartile portfolios formed on the basis of downside-risk variants of the Sharpe ratio did not deviate from those based on the standard Sharpe ratio. The rank order of hedge fund styles on the basis of average volatility of returns is the same for both periods; the returns of CTA-style funds are clearly the most volatile (their average annual volatility is 19.7 per cent in the selection period, and 18.6 per cent in the holding period), whereas those of equity market neutral-style are the least volatile. In addition, the lowest average minimum return and the highest maximum return are attributed to CTA style, whereas equity market neutral style gets the highest minimum and the lowest maximum return for both the selection and holding periods (on average).

Table 1 Descriptive statistics of the hedge funds for (a) the 3-year selection period (January 1997 – December 2005) and (b) the 1-year holding period (January 2000 – December 2006)
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THE RESULTS

Cross-sectional regression results

The strongest evidence of performance persistence is found within every hedge fund style when Sharpe ratios are used as input variables of regression analyses (Table 2). The results are highly significant for four hedge fund styles (that is, for convertible arbitrage, event driven, global macro and equity market neutral style at the 1 per cent level) and significant at the 10 per cent level for CTA style. However, the results are significant only for one style, that is, for equity market neutral at the 10 per cent level, when the regression is run with OLS alphas as input variables. When the Bayesian approach is applied to selection period alphas, the greatest difference in contrast to the regression that is based solely on cross-sections of OLS alphas is observed for CTA style; employing the Bayesian alphas turns the non-persistence finding based on OLS alphas into performance reversal, which is significant at the 10 per cent level. In contrast, regression results based on the Sharpe ratios indicate almost equally significant persistence for the same style. In conclusion, the cross-sectional results for CTA style are paradoxical, and should be interpreted with extreme caution.

Table 2 Cross-sectional regression results
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For the sample employed, the overall results of cross-sectional tests show that the Sharpe ratio is more sensitive detect performance persistence than are 9-factor alphas. For the pooled sample, 27.9 per cent of the variance of the holding period Sharpe ratio can be explained by its counterpart from the selection period, whereas for the other two factor-based performance metrics the explanatory power of past performance is virtually zero. For the fund style with the strongest persistence on the basis of cross-sectional results (that is, for equity market neutral), the explanatory power of past Sharpe ratios is double that of the average. However, it should be noted that except for convertible arbitrage and equity market neutral styles, the other coefficients of determination in style-specific cross-sectional regressions are also very low when cross-sectional tests are based on the Sharpe ratio.

In order to avoid spurious results stemming from the model misspecification bias,37 we also test the power of model-free performance metric (represented in this context by the Sharpe ratio) to predict the holding period performance evaluated by measures based on factor models and vice versa. The results of these tests indicate that for some fund styles, the cross-predictions are better than those based on the same performance metrics for both periods (Table 2). For example, for event-driven style, both standard and Bayesian alphas predict the holding period Sharpe ratio better than they predict the holding period alpha. In addition, for convertible arbitrage and CTA styles, Bayesian alphas predict the holding period Sharpe ratios better than they predict OLS alphas (and also significantly in the statistical sense). Furthermore, the pooled sample results show that the dependence of the holding period Sharpe ratio on the selection period Bayesian alphas is significant at the 1 per cent level. However, for equity market neutral style, the cross-prediction power between model-free and factor-based models is distinctly weaker than the corresponding prediction power when the same performance metrics are used for both periods. Again, it should be noted that the highest coefficient of determination in cross-prediction tests is only 3.8 per cent, indicating the relatively low explanatory power of these tests in general.

Quartile portfolio approach

When the performance difference of top- and bottom-quartile portfolios is used as a persistence criterion, the strongest evidence of performance persistence is found within event-driven style, for which every variant of the top and bottom portfolio performance comparison employed shows highly significant results (Table 3). However, none of the variants employed detect persistence within global macro style.38 For the three other hedge fund styles being examined, the results are somewhat mixed; for example, for CTA style, three out of six results are statistically significant and two other test statistics are also close to the 10 per cent significance level. For convertible arbitrage style, two significant results for persistence are documented when Bayesian alphas and the Sharpe ratio are employed as portfolio selection criteria, and the holding period performance is evaluated by the latter performance metric.

Table 3 Performance comparison of top- and bottom-quartile style portfolios
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For equity market neutral style only one out of six statistical tests indicates significant persistence. The only significant result for this style is obtained when the Sharpe ratio is used as a performance metric for the selection and holding periods. These results deviate from those obtained from cross-sectional regression tests that indicate the strongest persistence particularly for this fund style. The explanation as to why persistence is not observed using the quartile portfolio approach when alphas (either OLS or Bayesian) are used as performance metrics is given by the performance reversal effect in the bottom-quartile portfolio of equity market neutral style. The holding period alphas of bottom portfolios are positive in both cases, and in a case when portfolios are formed on the basis of OLS alphas, the bottom-portfolio alpha is even higher than the top-portfolio alpha, though not significantly. However, the reversal effect among bottom portfolio funds is not strong enough to mitigate persistence in cross-section tests of alphas when the full sample of equity market neutral funds is used as a basis of analysis. Thus, the results would indicate that for the sample employed, the persistence in equity market neutral style is concentrated on middle performers, parallel to the overall results of Capocci and Hübner39 and Capocci et al. 7

A comparison of the cross-sectional results for event-driven style with the corresponding results from top- and bottom-portfolio performance difference tests reveals a contrasting phenomenon to that observed among equity market neutral funds; while cross-sectional results do not indicate persistence when alphas are employed as input variables, the alpha spreads between top- and bottom-quartile portfolios based on both OLS and Bayesian alpha rankings are highly significant. This result indicates that for the sample employed, the persistence within event-driven style is concentrated on top- and bottom-quartiles (consistently with the overall findings of Baquero et al 6).

The alpha spread of top and bottom quartiles for the stacked holding period is statistically significant for two fund styles when the Bayesian alphas are used as a selection criterion (that is, for event driven and CTA styles; see Table 3, Panel B). Correspondingly, when quartile portfolios are formed on the basis of the 9-factor OLS alpha or the Sharpe ratio, the alpha spread is significant only for event-driven style. However, t-statistics are also quite close to the level of statistical significance for CTA style, particularly when portfolio selection is based on the Sharpe ratio (significance level in this case is 10.4 per cent; see Panel C). For global macro and equity market neutral styles, the results of the alpha spread tests are somewhat mixed, but none are statistically significant.

When the holding period performance is evaluated on the basis of the Sharpe ratio, the results are unanimous on the significant persistence within event-driven style. The Ledoit-Wolf test statistic is also significant for CTA style when either OLS or Bayesian alphas are employed as selection criteria. For convertible arbitrage style, the Sharpe ratio differences between top- and bottom-quartile portfolios are highly significant when fund portfolio selection is based either on the Sharpe ratio or the Bayesian alpha, but insignificant based on the OLS alpha criterion. It is also noteworthy that the use of the Sharpe ratio as a selection criterion leads to positive and significant top-quartile portfolio alphas in every fund style examined (Panel C).

The overall results give some evidence that the use of the empirical Bayesian method in determining selection period alphas slightly enhances the prediction power of past alphas within the hedge fund sample employed.40 Thus, it would be an interesting extension to study whether these findings hold also for larger samples of hedge funds. Moreover, applying the Bayesian approach has so far been applied only for the selection period (for example see Huij and Verbeek,14 Kosowski et al 9). However, as the empirical Bayesian method could be characterized as a shrinkage procedure of regression estimates (for example, see Huij and Verbeek41 for further details), it would be justified to treat both periods equally and apply the same procedure for performance evaluation of the holding period. In this way, the potential benefits of the Bayesian approach compared to those of the standard-frequentist approach could be revealed more transparently. This kind of approach can be motivated also by the fact that the holding period performance is often determined based on shorter time-series of returns than is the selection period performance. Given that one argument for using the Bayesian approach is to alleviate estimation problems stemming from a short sample, it would be even more justified to employ the Bayesian approach in determining performance for the shorter of evaluation periods. Although this issue is beyond the scope of this article, it provides an interesting topic for further research.

The overall results are consistent with those of Harri and Brorsen4 in the sense that performance persistence within event-driven style is found in both studies. In another sense, the results are contrasting because unlike Harri and Brorsen, we do not find evidence of persistence within global macro style. Parallel to the results of Capocci et al 7 or Kosowski et al,9 our cross-sectional results show persistence within equity market neutral style when the same evaluation criterion is used for both selection and holding periods, though significant persistence based on performance difference tests between top- and bottom-quartile portfolios within this style is found only when the Sharpe ratio is employed as a performance metric for both periods. However, the differences in results between studies may stem from several sources: the significance and even the direction of the results often depend on sample data, test period, and the length of selection and holding periods employed, in addition to the methodology, as shown in this article. The recent results of Gregoriou et al 8 support this conclusion.

CONCLUSIONS

We applied two complementary methodologies in detecting the performance persistence of five different hedge fund styles. First, we determined the prediction power of the selection period performance on the holding period performance by means of cross-sectional regression. Second, we formed top-and bottom-quartile portfolios based on selection period performance and tested their holding period performance difference based on both the Ledoit-Wolf test and the alpha spread test. In addition, we compared the results obtained by using model-free performance metrics to those obtained by using alphas of multifactor models. The 3-year selection period performance was evaluated with the Sharpe ratio, 9-factor OLS alpha and the corresponding Bayesian alpha, and the 1-year holding period performance was determined based on the first two of these.

Our results showed that both the degree and existence of performance persistence vary among hedge fund styles, and, in addition, depend on both methodology and performance metric employed. In comparison to the performance metrics that are based on factor models, model-free performance metrics such as the Sharpe ratio turned out to be more sensitive in detecting performance persistence within the sample employed. The evidence of this was particularly strong based on cross-sectional regression tests. This finding is not explained by the inability of the Sharpe ratio to cope with the non-normal return distributions, as at the outset of the study we formed quartile portfolios based on several other model-free performance metrics that take account of distributional non-normalities (including the Sortino ratio, modified Sharpe ratio and adjusted Sharpe ratio), and similar to the recent results of Eling and Schuhmacher,26 they all led to virtually identical portfolio compositions. Therefore, the main finding also holds for these alternative model-free performance metrics. However, one should be cautious in generalizing these results, as for some unknown reason the averages of both skewness and kurtosis were relatively low for this random sample compared to those reported in previous hedge fund studies. It is also noteworthy that the use of the Sharpe ratio as a selection criterion led to positive and significant top-quartile portfolio alphas in every fund style examined, indicating that the finding is somewhat robust to the choice of the holding period performance measure, and thus not a consequence of model misspecification bias. In addition, the overall results show that the Bayesian alphas are somewhat better predictors of future performance than are their OLS counterparts.

The strongest evidence of performance persistence was found among event-driven funds, for which 10 out of 12 persistence tests performed indicate significant results. Based on the cross-sectional regression tests of the Sharpe ratios, persistence is also strong among equity market neutral funds. The results between these two styles deviated from each other in that persistence within event-driven style is concentrated on top and bottom quartiles whereas among equity market neutral funds it is concentrated on middle performers. Although our sample includes only one directional fund style, our results are in line with those of Gregoriou et al,8 who report somewhat stronger persistence within non-directional styles (such as convertible arbitrage, equity market neutral or event driven) than within directional styles (such as global macro).