Quantitative Research August 2013 Your Global Investment Authority Analytics A Quantitative Framework for Hedge Fund Manager Selection1 At PIMCO, we have developed a quantitative approach to hedge fund manager selection as a complement to – not a substitute for – traditional, time-intensive qualitative due diligence. Our framework is based on an econometric risk factor analysis that decomposes hedge fund manager returns into alpha and beta components. The most attractive managers exhibit statistically significant alpha and limited beta risk with only small exposures to traditional risk factors. A ranking methodology based on these criteria allows us to select hedge fund managers that significantly outperform their peers out of sample. Niels Pedersen, Ph.D. Senior Vice President Quantitative Research Analyst Client Analytics Quantitative screens for hedge fund manager selection Our ranking methodology uses three “screens” that identify managers with the following characteristics: Consistent high risk-adjusted returns across a set of relevant measures of overall risk as well as tail risk. Substantial and significant statistical alpha generation over time. We define alpha as a positive return component that may be the result of superior market timing abilities, relative value/security selection, or capabilities that allow funds to access and exploit special market opportunities. Limited exposures to the risk factors (“betas”) that drive volatility in multi-asset class portfolios, with only a small part of the return attributed to traditional risk factors. Figure 1 is a ranking of a random sample of 24 managers from One of the problems with a ranking of managers based on the Eurekahedge fund database based on the most commonly the Sharpe ratio is that it provides no sense of the types of used risk-adjusted return measure, the Sharpe ratio. For this set risk that the managers explicitly or implicitly take to generate of managers the Sharpe ratios range from -0.3 to 1.0 over the their returns. period from January 2006 to December 2012. The hedge fund That is, to what extent can a manager’s returns be viewed with the highest Sharpe ratio is manager “Event Driven-A,” as “pure alpha” (i.e., an expression of specialized and the fund with the lowest Sharpe ratio is “Multi- investment skills such as security selection, relative value Strategy-A.” The table also shows historical excess returns, trades or highly dynamic market timing ability) that investors volatilities, maximum drawdowns and the Calmar ratio. The should be willing to pay for? Or, to what extent is a Calmar ratio normalizes manager returns by their tail risk. It manager’s returns driven by exposures to broad asset classes is defined as the average annualized return divided by the or risk factors that investors could access at a lower cost maximum drawdown. The ranking of managers by Sharpe elsewhere or may want to control more explicitly? ratio is similar to the ranking by their Calmar ratio. More often than not these measures provide very similar rankings of the managers’ risk-adjusted performance. FIGURE 1. RANKING OF MANAGERS BASED ON SHARPE RATIO/CALMAR RATIO (JANUARY 2006 TO DECEMBER 2012) Manager Historical Historical Maximum Sharpe ratio Calmar ratio excess return volatility drawdown Event driven-A 4% 4% 5% 1.0 0.8 Multi-strategy-C 6% 7% 19% 0.9 0.3 Multi-strategy-B 7% 8% 15% 0.9 0.4 Long short equities-D 7% 10% 25% 0.7 0.3 Fixed income-E 6% 9% 22% 0.7 0.3 Long short equities-G 6% 9% 6% 0.6 1.0 Arbitrage-A 10% 18% 48% 0.6 0.2 Relative value-A 6% 12% 24% 0.5 0.3 Long short equities-E 2% 4% 5% 0.5 0.4 Macro-A 4% 10% 15% 0.4 0.3 CTA/managed futures-A 6% 17% 19% 0.4 0.3 Long short equities-F 8% 31% 71% 0.2 0.1 Long short equities-C 3% 14% 32% 0.2 0.1 Macro-B 3% 14% 30% 0.2 0.1 Long short equities-A 6% 29% 60% 0.2 0.1 Others-B 3% 19% 51% 0.2 0.1 Long short equities-B 5% 31% 76% 0.2 0.1 Others-A 1% 10% 26% 0.1 0.0 Long short equities-H 2% 28% 56% 0.1 0.0 Event driven-B 0% 12% 27% 0.0 0.0 Distressed debt-A -2% 16% 50% -0.1 0.0 Fixed income-F -1% 3% 7% -0.2 -0.1 Fixed income-D -4% 14% 43% -0.3 -0.1 Multi-strategy-A -5% 16% 32% -0.3 -0.2 Note: Hedge fund “screen 1” ranks managers according to the risk-adjusted historical return in excess of the risk-free rate (Sharpe ratio). The managers were selected at random from the Eurekahedge fund database with the following criteria: at least 100 USD MM assets under management (average), at least 6 years of return history and categorized as a flagship fund. 2 AUGUST 2013 | QUANTITATIVE RESEARCH Risk factor models for manager returns managers engage in. In practice it is therefore appropriate To answer these questions a risk factor based model of returns to consider several alternative model specifications. More must be estimated for each manager. We believe the following elaborate expanded risk factor models could, for instance, four-factor model for manager returns is a useful benchmark: include currency, volatility, liquidity, momentum, value and carry factors. Factors related to non-agency mortgages and ABS sectors may also have been important drivers of returns, where and represent the equity, especially in the period after the financial crisis of 2008. For some global macro managers and CTAs, exposures to specific duration, credit and commodity factor returns and α represents the alpha return component for each manager.2 macro-driven commodities such as oil and gold can also play Investors should be interested in their managers’ potential a dominant role. to diversify and generate returns relative to these four factors, Despite these caveats, we feel simpler models allow for better because these factors tend to dominate returns and volatility apples-to-apples comparisons across a broad range of funds. 3 in most broadly diversified multi-asset portfolios. The model Importantly, our results show that the simple four-factor specification may in some cases be too restrictive because it model can produce a quite robust ranking of managers. does not capture all the diverse strategies that hedge fund FIGURE 2. RANKING OF MANAGERS BASED ON ESTIMATED ALPHA T-STATISTIC (SIGNIFICANCE) Manager Estimated alpha T-alpha Appraisal ratio Sharpe beta Multi-strategy-B 6.6% 3.1 1.3 0.1 Multi-strategy-C 6.1% 3.0 1.3 0.1 Fixed income-E 5.1% 3.0 1.2 0.1 Event driven-A 3.6% 2.9 1.1 0.2 Long short equities-D 7.4% 2.6 0.8 -0.1 Arbitrage-A 9.7% 2.0 0.8 0.1 Long short equities-G 5.4% 1.8 0.6 0.1 Long short equities-E 1.7% 1.5 0.5 0.1 Macro-A 3.9% 1.1 0.4 0.0 Long short equities-A 7.4% 1.0 0.4 -0.1 CTA/managed futures-A 6.4% 1.0 0.4 -0.1 Long short equities-F 4.9% 1.0 0.3 0.1 Macro-B 1.7% 0.7 0.2 0.1 Long short equities-C 1.6% 0.5 0.2 0.1 Others-A 1.0% 0.5 0.1 0.1 Long short equities-B 0.4% 0.2 0.0 0.1 Others-B 0.1% 0.1 0.0 0.2 Long short equities-H 0.1% 0.0 0.0 0.1 Event driven-B -0.8% 0.0 -0.1 0.2 Relative value-A -0.9% -0.2 -0.1 1.0 Distressed debt-A -1.4% -0.2 -0.1 0.0 Fixed income-F -0.7% -0.2 -0.3 0.1 Fixed income-D -4.9% -0.7 -0.5 0.1 Multi-strategy-A -10.8% -1.1 -0.8 0.7 Note: Hedge fund “screen 2” ranks the sample set of managers according to their risk-adjusted alpha or equivalently the alpha t-statistic. The appraisal ratio normalizes the estimated alpha returns with historical alpha volatility. The Sharpe ratio of beta is calculated as the estimated beta return divided by the volatility of the beta return. Alpha is measured relative to the estimated four-factor model for returns. For each manager a general-to-specific modeling process is used to estimate the relevant risk factors and arrive at a final model specification. QUANTITATIVE RESEARCH | AUGUST 2013 3 Manager alpha a 5% significance level). A value below this threshold suggests that the manager’s actual alpha may be zero or even negative. Figure 2 shows the estimated alpha, â, for each manager, the t-statistic of the estimated alpha, as well as the manager’s In our randomly selected sample of 24 hedge funds more than appraisal ratio or risk-adjusted alpha. The managers have half of the managers have “insignificant” estimated alpha (i.e., been ranked according to the t-statistic of their estimated Talpha <1.645 ) and six of the managers have negative estimated alpha. Formally the alpha t-statistic is defined as alpha. These managers have failed to generate the positive, un-correlated returns that are required to improve the hedge T(alpha) = â std(â) fund investor’s overall risk-return profile. The hedge fund investor may consequently want to evaluate whether their fees This statistic is important because the magnitude of Talpha are justified and reconsider the allocation to these managers.