Should hedge funds be cautious reporting high returns?

In a recent article, Schuster and Auer (2012) show that fund managers with a certain positive performance need to be aware of the fact that too high prospective excess returns can lower the empirical Sharpe ratio of their funds. In this note, we investigate the empirical relevance of this effect. We analyse whether hedge funds being evaluated on the basis of the Sharpe ratio negatively influence their performance by reporting too high returns. Our results show that a economically significant number of hedge funds listed in the CISDM hedge fund database has at least once reported a high return causing this effect.     

Does the choice of performance measure influence the evaluation of hedge funds?

The Sharpe ratio is adequate for evaluating investment funds when the returns of those funds are normally distributed and the investor intends to place all his risky assets into just one investment fund. Hedge fund returns differ significantly from a normal distribution. For this reason, other performance measures for hedge fund returns have been proposed in both the academic and practice-oriented literature. In conducting an empirical study based on return data of 2763 hedge funds, we compare the Sharpe ratio with 12 other performance measures. Despite significant deviations of hedge fund returns from a normal distribution, our comparison of the Sharpe ratio to the other performance measures results in virtually identical rank ordering across hedge funds.     

HEDGE FUNDS: WHAT DO WE KNOW?

Hedge funds are attracting increased attention because of their reputation for earning superior (risk-adjusted) returns. Hedge Fund Research Inc. estimates that in 2001 there were about 7,000 hedge funds with investor capital of about $600 billion. And yet the diversity of hedge funds, combined with a general lack of transparency, makes the hedge fund industry something of a "black box."
This article provides an overview of the legal structure of hedge funds, the various fund investment strategies, and the existing research on overall hedge fund performance. Without uniform and comprehensive reporting requirements, it is difficult to ascertain the size and scope of hedge fund investments. Nonetheless, current research provides persuasive evidence that hedge funds earn positive risk-adjusted returns, on average, in contrast to their counterparts in the mutual fund industry. In an attempt to explain these higher returns, the authors begin by noting that hedge funds are subject to considerably less regulation than other investment institutions because their client base is limited to wealthy individuals and institutions. Hedge funds can thus employ investment strategies that mutual funds and pension funds are prohibited from pursuing, such as short selling, high leverage, derivatives, concentrated holdings, and limited redemptions. As a result, the funds may be able to earn excess returns by operating in illiquid and specialized markets where there is a shortage of arbitrage capital. At the same time, and perhaps even more important, hedge funds are in a better position than conventional mutual funds to attract skilled managers because of their use of performance-based incentive fee structures.     

The low return distortion of the Sharpe ratio

This article formalizes the undesirable property of the Sharpe ratio that a fund with a certain poor performance can increase its Sharpe ratio in a prospective period by generating a sufficiently negative excess return. Specifically, we set out the conditions that a fund must meet to be exposed to this kind of effect. Furthermore, we provide a formal statement of the excess return value that needs to be deceeded to obtain a higher Sharpe ratio. In an empirical application, we investigate the practical relevance of this kind of distortion. We find that an economically significant number of funds listed in the CISDM hedge fund database have at least once reported a sufficiently negative return, causing an increased Sharpe ratio fund performance.     

Emerging Market Exposures and the Predictability of Hedge Fund Returns

We examine emerging market and global macro hedge funds and find a significant positive relation between hedge funds’ future returns and their exposure to both emerging market equities and emerging market currencies. We present evidence that the strong predictive power of emerging market betas is related to the superior market‐timing ability of these fund managers. Results are robust after controlling for commonly used hedge fund factors, the emerging market equity index, lagged fund returns, liquidity risk, and fund characteristics. Our results suggest that hedge funds can earn positive excess returns by timing their exposure to emerging market securities.     

Zur Risikoanalyse von Hedgefonds: Ein datenanalytischer Ansatz

Hedge fund returns have a number of specific features compared to traditional investments which result in problems when applying traditional methods of risk analysis (Markowitz portfolio selection theory, Sharpe Ratio, value at risk calculation based on normal returns). These problems have to be considered adequately by insurance companies when constructing internal risk models and performing risk management for hedge funds in their investment.The present paper has its focus on the departure of hedge fund returns from the normality hypothesis, especially with respect to the statistical quantities skewness and kurtosis (fat tail problem). A statistical analysis of hedge fund index returns gives evidence that the majority of hedge fund returns show substantial departures from normality. In addition, the analysis shows that hedge fund returns are adequately represented by the family of GH-distributions developed in exploratory data analysis. Following this result a risk analysis of hedge fund strategies is performed on the basis of the GH-value at risk.     

Hedge funds and optimal asset allocation: Bayesian expectations and spanning tests

This paper analyzes the contribution of hedge funds to optimal asset allocations between 1993 and 2010. The preferences of specific institutional investors are captured by implementing a Bayesian asset allocation framework that incorporates heterogeneous expectations regarding hedge fund alpha. Mean-variance spanning tests are used to infer the ability of hedge funds to significantly enhance the mean-variance efficient frontier. Further, a novel democratic variance decomposition procedure sheds light on the dynamics in the co-movement of hedge fund returns with a set of common benchmark assets. The empirical findings indicate that portfolio benefits of hedge funds are time-varying and strongly depend on investor optimism regarding hedge funds’ ability to generate alpha. In general, allocations to hedge funds improve the global minimum variance portfolio even after controlling for short-selling restrictions and minimum diversification constraints. However, due to dynamics underlying the composition of the aggregate hedge fund universe, the factor structure of hedge fund returns has become more similar to the benchmark assets over time.     

Quantile regression analysis of hedge fund strategies

Extending previous work on hedge fund pricing, this paper introduces the idea of modelling the conditional quantiles of hedge fund returns using a set of risk factors. Quantile regression analysis provides a way of understanding how the relationship between hedge fund returns and risk factors changes across the distribution of conditional returns. We propose a Bayesian approach to model comparison which provides posterior probabilities for different risk factor models that can be used for model averaging. The most relevant risk factors are identified for different quantiles and compared with those obtained for the conditional expectation model. We find differences in factor effects across quantiles of returns, which suggest that the standard conditional mean regression method may not be adequate for uncovering the risk-return characteristics of hedge funds. We explore potential economic impacts of our approach by analysing hedge fund single strategy return series and by constructing style portfolios.     

Who Charges More: Hedge Funds or Mutual Funds?*

Explicit mutual fund fees are typically less than 1% of the assets under management. By comparison, the typical hedge fund charges a base fee of 2% plus a performance fee equal to 20% of net profits. Thus, hedge funds appear to charge far more for even comparable performance—unless one takes account of the following:

• ? For most mutual funds, a very high percentage of performance is driven by its passive exposure to the market, even though the fee is applied to the total fund.
• ? Many hedge funds are designed to provide returns that are completely independent of market performance.

Using these two assumptions, the author provides a simple example that shows that a representative mutual fund's performance can be replicated by combining an index fund, which represents the mutual fund's passive component, with a hedge fund, representing the mutual fund's active component. When analyzed in this way, the fee of the combined fund turns out to be remarkably close to the actual fee of the mutual fund. This in turn suggests that the implicit fee for the mutual fund's small active component is comparable to the fees of the hedge fund.     

Systematic risk and the cross section of hedge fund returns

This paper investigates the extent to which market risk, residual risk, and tail risk explain the cross-sectional dispersion in hedge fund returns. The paper introduces a comprehensive measure of systematic risk (SR) for individual hedge funds by breaking up total risk into systematic and fund-specific or residual risk components. Contrary to the popular understanding that hedge funds are market neutral, we find that systematic risk is a highly significant factor explaining the dispersion of cross-sectional returns while at the same time measures of residual risk and tail risk seem to have little explanatory power. Funds in the highest SR quintile generate 6% more average annual returns compared with funds in the lowest SR quintile. After controlling for a large set of fund characteristics and risk factors, systematic risk remains positive and highly significant, whereas the relation between residual risk and future fund returns continues to be insignificant. Hence, systematic risk is a powerful determinant of the cross-sectional differences in hedge fund returns.     

Share restrictions and asset pricing: Evidence from the hedge fund industry

This paper presents evidence on the relation between hedge fund returns and restrictions imposed by funds that limit the liquidity of fund investors. The excess returns of funds with lockup restrictions are approximately 4–7% per year higher than those of nonlockup funds. The average alpha of all funds is negative or insignificant after controlling for lockups and other share restrictions. Also, a negative relation is found between share restrictions and the liquidity of the fund's portfolio. This suggests that share restrictions allow funds to efficiently manage illiquid assets, and these benefits are captured by investors as a share illiquidity premium.     

Beyond the Sharpe ratio: An application of the Aumann–Serrano index to performance measurement

We propose a performance measure that generalizes the Sharpe ratio. The new performance measure is monotone with respect to stochastic dominance and consistently accounts for mean, variance and higher moments of the return distribution. It is equivalent to the Sharpe ratio if returns are normally distributed. Moreover, the two performance measures are asymptotically equivalent as the underlying distributions converge to the normal distribution. We suggest a parametric and a non-parametric estimator for the new performance measure and provide an empirical illustration using mutual funds and hedge funds data.     

Convertible Bond Arbitrage: Risk and Return

Abstract:  This paper specifies a simulated convertible bond arbitrage portfolio to characterise the risks in convertible bond arbitrage. For comparison the risk profile of convertible bond arbitrage hedge fund indices at both monthly and daily frequencies is also examined. Results indicate that convertible bond arbitrage is positively related to default and term structure risk factors. These risk factors are augmented with the simulated convertible bond arbitrage portfolio, mimicking a passive investment in convertible bond arbitrage, to assess the risk and return of individual hedge funds. We provide estimates of the performance of two hedge fund indices (an equally weighted and value weighted index) and a sample of convertible bond arbitrage hedge funds using a factor model methodology. Lagged and contemporaneous observations of the risk factors are specified, controlling for illiquidity in the securities held by funds. Our results cover two time periods. Initially we find evidence of abnormal risk adjusted returns in the individual hedge fund data and the equally weighted hedge fund index and no evidence of abnormal risk adjusted returns in the value weighted hedge fund index. When we examine performance during the credit crisis of 2007 and 2008 we find evidence of negative abnormal returns amongst individual hedge funds and the hedge fund indices.     

Higher risk,lower returns: What hedge fund investors really earn

The returns of hedge fund investors depend not only on the returns of the funds they hold but also on the timing and magnitude of their capital flows in and out of these funds. We use dollar-weighted returns (a form of Internal Rate of Return (IRR)) to assess the properties of actual investor returns on hedge funds and compare them to buy-and-hold fund returns. Our main finding is that annualized dollar-weighted returns are on the magnitude of 3% to 7% lower than corresponding buy-and-hold fund returns. Using factor models of risk and the estimated dollar-weighted performance gap, we find that the real alpha of hedge fund investors is close to zero. In absolute terms, dollar-weighted returns are reliably lower than the return on the Standard & Poor's (S&P) 500 index, and are only marginally higher than the risk-free rate as of the end of 2008. The combined impression from these results is that the return experience of hedge fund investors is much worse than previously thought.     

Hedge fund allocation: Evaluating parametric and nonparametric forecasts using alternative portfolio construction techniques

We propose a model for constructing Asian funds of hedge funds. We compare the accuracy of forecasts of hedge fund returns using an ordinary least squares (OLS) regression model, a nonparametric regression model, and a nonlinear nonparametric model. We backtest to assess these forecasts using three different portfolio construction processes: an “optimized” portfolio, an equally-weighted portfolio, and the Kelly criterion-based portfolio. We find that the Kelly criterion is a reasonable method for constructing a fund of hedge funds, producing better results than a basic optimization or an equally-weighted portfolio construction method. Our backtests also indicate that the nonparametric forecasts and the OLS forecasts produce similar performance at the hedge fund index level. At the individual fund level, our analysis indicates that the OLS forecasts produce higher directional accuracy than the nonparametric methods but the nonparametric methods produce more accurate forecasts than OLS. In backtests, the highest information ratio to predict hedge fund returns is obtained from a combination of the OLS regression with the Fung–Hsieh eight-factor variables as predictors using the Kelly criterion portfolio construction method. Similarly, the highest information ratio using forecasts generated from a combination of the nonparametric regression using the Fung–Hsieh eight-factor model variables is achieved using the Kelly criterion portfolio construction method. Simulations using risk-adjusted total returns indicate that the nonparametric regression model generates superior information ratios than the analogous backtest results using the OLS. However, the benefits of diversification plateau with portfolios of more than 20 hedge funds. These results generally hold with portfolio implementation lags up to 12 months.     

Jumping over a low hurdle: personal pension fund performance

This paper provides a comprehensive analysis of the annual and of the long-term performance of personal pension funds relative to their Primary Prospectus Benchmarks (PPBs) and T-bills. The study covers 9659 personal pension funds from across all 30 ABI investment sectors that operated in the UK in the 1980–2009 period. Of these, 4531 pension funds are compared against their PPBs. The performance measured by ordinary excess returns over the UK T-bills and over PPBs, as well as the Sharpe ratio, Sharpe ratio adjusted for skewness and kurtosis, Sortino ratio in relation to the UK T-bills and PPBs, and the Modigliani–Modigliani measure are calculated for arithmetic, geometric and log returns. We find convincing evidence that pension funds lack challenging long-term performance targets. We argue that the existing PPBs are easy to outperform given that funds are allowed to diversify in assets not included in their PPBs. We discuss policy implications of our findings.     

The Cost of Capital for Alternative Investments

Traditional risk factor models indicate that hedge funds capture pre‐fee alphas of 6% to 10% per annum over the period from 1996 to 2012. At the same time, the hedge fund return series is not reliably distinguishable from the returns of mechanical S&P 500 put‐writing strategies. We show that the high excess returns to hedge funds and put‐writing are consistent with an equilibrium in which a small subset of investors specialize in bearing downside market risks. Required rates of return in such an equilibrium can dramatically exceed those suggested by traditional models, affecting inference about the attractiveness of these investments.     

Conditionally fitted Sharpe performance with an application to hedge fund rating

We define a battery of Sharpe performance measures, which differ by the information taken into account in their computation, but also by the potential use of the fund by the investor. Four advantages of Sharpe performance based rating are especially important for the investor. First, the performance measures correspond to the standard measures used for mutual funds and known by retail investors. Second, we can compare the numerical results, even if they are obtained with different assumptions. Third, the rankings are based on regression analysis and easy to compute. Fourth, we can easily use these performance measures in the design of an optimal basket of hedge funds. Finally, we can use the performance measures to partition the set of funds into homogenous segments.     

Conditional Properties of Hedge Funds: Evidence from Daily Returns*

Using daily returns on a set of hedge fund indices, we study (i) the properties of the indices' conditional density functions and (ii) the presence of asymmetries in conditional correlations between hedge fund indices and other investments and between hedge fund indices themselves. We use the SNP approach to obtain estimates of conditional densities of hedge fund returns and then proceed to examine their properties. In general, a nonparametric GARCH(1,1) model appears to provide the best fit for all strategies. We find that the conditional third and fourth moments are significantly affected by changes in the current volatility of returns on hedge fund indices. We examine changes in the conditional probability of tail events and report significant changes in the probability of extreme events when the conditioning information changes. These results have important implications for models of hedge fund risk that rely on probability of tail events. We formally test for the presence of asymmetries in conditional correlations to determine if there is contagion between hedge funds and other investments and between various hedge fund indices in extreme down markets versus extreme up markets. We generally do not find strong evidence in support of asymmetric correlations.     

Hedge Fund Indices: Reconciling Investability and Representativity

Following a growing concern among investors about the quality of hedge fund index return data, this paper addresses the question of whether designing hedge fund indices that fulfil the usual requirements (in particular representative and investable) is or not a feasible task, given a variety of features that are specific to that industry. To test whether or not investability should necessarily come at the cost of representativity, we use a well‐known methodology in the asset pricing literature based on the concept of factor replicating portfolios. Our results suggest that it is actually possible to construct representative indices based on a limited number of funds that are open to new investments, except perhaps in the case of equity market neutral strategies, provided that: i) these funds are suitably selected and ii) a portfolio is constructed with the objective of replicating the common trend in hedge fund returns for a given strategy. A range of robustness tests are performed that show that high correlation of the factor replicating portfolios with the common factor of returns for each strategy is remarkably stable with respect to modifying the number of funds in the replicating portfolio or changing the frequency of rebalancing.