Risk Measures for Hedge Funds: a Cross‐sectional Approach

This paper analyses the risk‐return trade‐off in the hedge fund industry. We compare semi‐deviation, value‐at‐risk (VaR), Expected Shortfall (ES) and Tail Risk (TR) with standard deviation at the individual fund level as well as the portfolio level. Using the Fama and French (1992) methodology and the combined live and defunct hedge fund data from TASS, we find that the left‐tail risk captured by Expected Shortfall (ES) and Tail Risk (TR) explains the cross‐sectional variation in hedge fund returns very well, while the other risk measures provide statistically insignificant or marginally significant results. During the period between January 1995 and December 2004, hedge funds with high ES outperform those with low ES by an annual return difference of 7%. We provide empirical evidence on the theoretical argument by Artzner et al. (1999) that ES is superior to VaR as a downside risk measure. We also find the Cornish‐Fisher (1937) expansion is superior to the nonparametric method in estimating ES and TR.     

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.     

Macroeconomic risk and hedge fund returns

This paper estimates hedge fund and mutual fund exposure to newly proposed measures of macroeconomic risk that are interpreted as measures of economic uncertainty. We find that the resulting uncertainty betas explain a significant proportion of the cross-sectional dispersion in hedge fund returns. However, the same is not true for mutual funds, for which there is no significant relationship. After controlling for a large set of fund characteristics and risk factors, the positive relation between uncertainty betas and future hedge fund returns remains economically and statistically significant. Hence, we argue that macroeconomic risk is a powerful determinant of cross-sectional differences in hedge fund returns.     

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.     

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.     

Incentives and risk taking in hedge funds

We study how incentive fees and manager’s own investment in the fund affect the investment strategy of hedge fund managers. We find that loss averse managers increase the risk of the fund’s investment strategy with higher incentive fees. However, risk taking is greatly reduced if a substantial amount of the manager’s own money (at least 30%) is in the fund. Using the Zurich hedge fund universe, we test the relation between risk taking and incentive fees empirically. Hedge funds with incentive fees have significantly lower mean returns (net of fees), while downside risk is positively related to the incentive fee level. Fund of funds charging large incentive fees achieve relatively high mean returns, but with significantly higher risk as well.     

The liquidity risk of liquid hedge funds

This paper evaluates hedge funds that grant favorable redemption terms to investors. Within this group of purportedly liquid funds, high net inflow funds subsequently outperform low net inflow funds by 4.79% per year after adjusting for risk. The return impact of fund flows is stronger when funds embrace liquidity risk, when market liquidity is low, and when funding liquidity, as measured by the Treasury-Eurodollar spread, aggregate hedge fund flows, and prime broker stock returns, is tight. In keeping with an agency explanation, funds with strong incentives to raise capital, low manager option deltas, and no manager capital co-invested are more likely to take on excessive liquidity risk. These results resonate with the theory of funding liquidity by Brunnermeier and Pedersen (2009).     

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.     

The risk in hedge fund strategies: Theory and evidence from long/short equity hedge funds

Theory suggests that long/short equity hedge funds' returns come from directional as well as spread bets on the stock market. Empirical analysis finds persistent net exposures to the spread between small vs large cap stocks in addition to the overall market. Together, these factors account for more than 80% of return variation. Additional factors are price momentum and market activity. Combining two major branches of hedge fund research, our model is the first that explicitly incorporates the effect of funding (stock loan) on alpha. Using a comprehensive dataset compiled from three major database sources, we find that among the three thousand plus hedge funds with similar style classification, less than 20% of long/short equity hedge funds delivered significant, persistent, stable positive non-factor related returns. Consistent with the predictions of the Berk and Green (2004) model we find alpha producing funds decays to “beta-only” over time. However, we do not find evidence of a negative effect of fund size on managers' ability to deliver alpha. Finally, we show that non-factor related returns, or alpha, are positively correlated to market activity and negatively correlated to aggregate short interest. In contrast, equity mutual funds and long-bias equity hedge funds have no significant, persistent, non-factor related return. Expressed differently, L/S equity hedge funds, as the name suggests, do benefit from shorting. Besides differences in risk taking behavior, this is a key feature distinguishing L/S funds from long-bias funds.     

Capturing hedge fund risk factor exposures: Hedge fund return replication with ETFs

We develop a new factor selection methodology of spanning the space of hedge fund risk factors with all available exchange traded funds (ETFs). We demonstrate the efficacy of the methodology with out-of-sample individual hedge fund return replication by ETF clone portfolios. This is consistent with our interpretation of ETF returns as proxies to risk factors driving hedge fund returns. We further consider portfolios of “cloneable” and “noncloneable” hedge funds, defined as top and bottom in-sample R² matches, and demonstrate that our ETF clone portfolios slightly outperform cloneable hedge funds out of sample.     

Liquidity shocks,size and the relative performance of hedge fund strategies

We examine whether the increase in the flow of capital to hedge funds over the period 1994–2005 had a negative impact on performance. More specifically, we study the relative performance of small versus large funds for each of the hedge fund strategies. Our results indicate that on an absolute return basis, small funds outperform large funds. On a risk-adjusted return basis, however, we find that large funds outperform small funds, and that large funds are also shown to hold less liquid assets and take on less systematic and idiosyncratic risk than small funds. Further, funds that experience positive liquidity shocks generally outperform those that experience negative liquidity shocks. We also find evidence that hedge fund managers that are aggressive in dealing with liquidity shocks perform better than hedge fund managers that are conservative in dealing with liquidity shocks.     

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.     

Short-term hedge fund performance

Hedge fund returns are often explained using linear factor models such as Fung and Hsieh (2004). However, since most hedge funds live only for 3 years, these linear regressions are subject to over-parameterization. I improve the out-of-sample accuracy of the linear factor model by combining cross-sectional and time series information for groups of hedge funds with similar investment strategies. The additional cross-sectional information allows more accurate estimates of risk exposures. I also propose a trading strategy based on this methodology for extracting substantially larger risk-adjusted returns.     

Do Hedge Fund Managers Misreport Returns? Evidence from the Pooled Distribution

We find a significant discontinuity in the pooled distribution of monthly hedge fund returns: The number of small gains far exceeds the number of small losses. The discontinuity is present in live and defunct funds, and funds of all ages, suggesting that it is not caused by database biases. The discontinuity is absent in the 3 months culminating in an audit, suggesting it is not attributable to skillful loss avoidance. The discontinuity disappears when using bimonthly returns, indicating a reversal in fund performance following small gains. This result suggests that the discontinuity is caused at least in part by temporarily overstated returns.     

The effect of downside risk reduction on UK equity portfolios included with Managed Futures Funds

The concept of asymmetric risk estimation has become more widely applied in risk management in recent years with the increased use of Value-at-risk (VaR) methodologies. This paper uses the n-degree lower partial moment (LPM) models, of which VaR is a special case, to empirically analyse the effect of downside risk reduction on UK portfolio diversification and returns. Data on Managed Futures Funds are used to replicate the increasingly popular preference of investors for including hedge funds and fund-of-funds type investments in the UK equity portfolios. The result indicates, however that the potential benefits of fund diversification may deteriorate following reductions in downside risk tolerance levels. These results appear to reinforce the importance of risk (tolerance) perception, particularly downside risk, when making decisions to include Managed Futures Funds in UK equity portfolios as the empirical analysis suggests that this could negatively affect portfolio returns.     

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.     

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.     

Speculative capital and currency carry trades

In this paper, we study a two-country general equilibrium model with partially segmented financial markets, where hedge funds emerge endogenously. Empirically, we show that the hedge fund investment strategy predicted by our model, which we call the “risk-adjusted carry trade” strategy, explains more than 16% of the overall hedge fund index returns and more than 33% of the fixed income arbitrage sub-index returns. The flow of new money to hedge funds affects market interest rates, exchange rates, and both the hedge funds’ contemporaneous and expected future returns as predicted by the model.     

The price of skill: Performance evaluation by households

Skilled investors make money off uninformed investors. By acting as intermediaries, they provide a hedge to the uninformed investors themselves. I present a model in which households have imperfect information about expected returns. Non-traded income shocks lead them to rebalance, sometimes at the wrong time. Active funds hedge this risk by trading on superior information. In equilibrium, they pay off when non-traded income disappoints, earning a premium that makes them appear to underperform index funds after fees. Empirical results using aggregate fund flows support the model. A corresponding asset pricing test can account for the apparent underperformance of active funds.     

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.