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.     

Optimal hedge fund portfolios under liquidation risk

We use an expected utility framework to integrate the liquidation risk of hedge funds into portfolio allocation problems. The introduction of realistic investment constraints complicates the determination of the optimal solution, which is solved using a genetic algorithm that mimics the mechanism of natural evolution. We analyse the impact of the liquidation risk, of the investment constraints and of the agent's degree of risk aversion on the optimal allocation and on the optimal certainty equivalent of hedge fund portfolios. We observe, in particular, that the portfolio weights and their performance are significantly affected by liquidation risk. Finally, tight portfolio constraints can only provide limited protection against liquidation risk. This approach is of special interest to fund of hedge fund managers who wish to include the hedge fund liquidation risk in their portfolio optimization scheme.     

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.     

A Time to Scatter Stones,and a Time to Gather Them: The Annual Cycle in Hedge Fund Risk Taking

Analyzing a sample of hedge fund daily returns from Bloomberg, we find a seasonal pattern in their risk taking. During earlier months of a year, poorly performing funds reduce risk. The reduction is stronger for funds with higher management fees, shorter redemption periods, and recently deteriorating performance, consistent with a managerial aversion to early fund liquidation. Toward the end of a year, poorly performing funds gamble for resurrection by increasing risk. It is largely achieved by increasing exposure to market factors, and can be linked to stronger indirect managerial incentives during the second half of a year.     

Capacity Constraints and Hedge Fund Strategy Returns

Hedge funds have generated significant absolute returns (alpha) in the decade between 1995 and 2004. However, the level of alpha has declined substantially over this period. We investigate whether capacity constraints at the level of hedge fund strategies have been responsible for this decline. For four out of eight hedge fund strategies, capital inflows have statistically preceded negative movements in alpha, consistent with this hypothesis. We also find evidence that hedge fund fees have increased over the same period. Our results provide support for the Berk and Green (2004) rational model of active portfolio management.     

Hedge Fund Regulation and Misreported Returns

This paper introduces a cross‐country law and finance analysis of the misreporting behaviour in the hedge fund industry in terms of smoothing returns so that a fund consistently generates positive returns. We find strong evidence that international differences in hedge fund regulation are significantly associated with the propensity of fund managers to misreport monthly returns. We find a positive association between wrappers and misreporting, particularly for funds that do not have a lockup provision. Also, we find some evidence that misreporting is less common among funds in jurisdictions with minimum capitalisation requirements and restrictions on the location of key service providers. We assess the robustness of our finds to a number of specifications, including, different specifications of misreporting bin widths, subsets of the data by fund type, as well as specifications controlling for collinearity and selection effects and other robustness checks. We show misreporting significantly affects capital allocation, and calculate the wealth transfer effects of misreporting and relate this wealth transfer to differences in hedge fund regulation.     

The Performance of Hedge Fund Strategies and the Asymmetry of Return Distributions

We present hedge fund performance estimates that adjust for stale prices, Fama‐French risk factors and skewness. We contrast these new performance estimates with traditional performance measures. Using three‐factor models to adjust for staleness in prices and to incorporate Fama‐French factors along with the Harvey‐Siddique (2000) two‐factor model that incorporates skewness, we find that for the period 1990–2003, all hedge fund categories achieve above average performance when measured against an aggregate market index. More significantly, however, when we estimate performance at the individual hedge fund level, we discover that only 40 to 47% of the funds are shown to achieve an above average performance over that time period depending on the model used. These results have important implications for investors, endowments and pensions when they choose hedge fund managers.     

Optimal Carried Interest: Adverse Selection in Islamic and Conventional Venture Capital and Private-Equity Funds

In an optimal carried interest model with adverse selection, the optimal profit-loss sharing ratio (PSR) explains how the risk aversion of the two parties can affect their bargaining powers by allowing investors to detect the true risk aversion of fund managers and not their true skills. The higher the management fee, the higher is the PSR. Our simulation exercise shows that when the fund manager is more risk averse than the investor for a higher invested capital and weaker expected net profit, the optimal negotiated profit-sharing ratio will be higher.     

Hedge fund strategies,performance &diversification: A portfolio theory & stochastic discount factor approach

For 5500 North American hedge funds following 11 different strategies, we analyse the stand-alone performance of these strategies using a stochastic discount factor approach. Employing the same data, we then consider the diversification benefits of each hedge fund strategy when combined with a portfolio of US equities and bonds. We compute the out-of-sample Black-Litterman portfolios, with Bayes-Stein, higher moments, simulations, desmoothed data and allowance for regimes as robustness checks. All but two hedge fund strategies out-perform the market as stand-alone investments; and all but one provide significant diversification benefits. The higher is an investor’s risk aversion, the more beneficial is diversification into hedge funds.     

Do hedge funds have enough capital? A value-at-risk approach

We examine the risk characteristics and capital adequacy of hedge funds through the Value-at-Risk approach. Using extensive data on nearly 1,500 hedge funds, we find only 3.7% live and 10.9% dead funds are undercapitalized as of March 2003. Moreover, the undercapitalized funds are relatively small and constitute a tiny fraction of total fund assets in our sample. Cross-sectionally, the variability in fund capitalization is related to size, investment style, age, and management fee. Hedge fund risk and capitalization also display significant time variation. Traditional risk measures like standard deviation or leverage ratios fail to detect these trends.     

Who benefits in a crisis? Evidence from hedge fund stock and option holdings

We use a unique data set of hedge fund long equity and equity option positions to investigate a significant lockup-related premium earned during the tech bubble (1999–2001) and financial crisis (2007–2009). Net fund flows are significantly greater among lockup funds during crisis and noncrisis periods. Managers of hedge funds with locked-up capital trade opportunistically against flow-motivated trades of non-lockup managers, consistent with a hypothesis of rent extraction in providing crisis era liquidity. The success of this opportunistic trading is concentrated during periods of high borrowing costs, in less liquid stock markets, and is enhanced by hedging in the equity option market.     

Consumption and Hedging in Oil‐Importing Developing Countries

We study the consumption and hedging strategy of an oil‐importing developing country that faces multiple crude oil shocks. In our model, developing countries have two particular characteristics: their economies are mainly driven by natural resources and their technologies are less efficient in energy usage. The natural resource exports can be correlated with the crude oil shocks. The country can hedge against the crude oil uncertainty by taking long/short positions in existing crude oil futures contracts. We find that both inefficiencies in energy usage and shocks to the crude oil price lower the productivity of capital. This generates a negative income effect and a positive substitution effect, because today’s consumption is relatively cheaper than tomorrow’s consumption. Optimal consumption of the country depends on the magnitudes of these effects and on its risk‐aversion degree. Shocks to other crude oil factors, such as the convenience yield, are also studied. We find that the persistence of the shocks magnifies the income and substitution effects on consumption, thus also affecting the hedging strategy of the country. The demand for futures contracts is decomposed in a myopic demand, a pure hedging term and productive hedging demands. These hedging demands arise to hedge against changes in the productivity of capital due to changes in crude oil spot prices. We calibrate the model for Chile and study to what extent the country’s copper exports can be used to hedge the crude oil risk.     

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.     

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.     

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.     

The fragile capital structure of hedge funds and the limits to arbitrage

During a financial crisis, when investors are most in need of liquidity and accurate prices, hedge funds cut their arbitrage positions and hoard cash. The paper explains this phenomenon. We argue that the fragile nature of the capital structure of hedge funds, combined with low market liquidity, creates a risk of coordination in redemptions among hedge fund investors that severely limits hedge funds' arbitrage capabilities. We present a model of hedge funds' optimal asset allocation in the presence of coordination risk among investors. We show that hedge fund managers behave conservatively and even abstain from participating in the market once coordination risk is factored into their investment decisions. The model suggests a new source of limits to arbitrage.     

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.     

Role of Managerial Incentives and Discretion in Hedge Fund Performance

Using a comprehensive hedge fund database, we examine the role of managerial incentives and discretion in hedge fund performance. Hedge funds with greater managerial incentives, proxied by the delta of the option-like incentive fee contracts, higher levels of managerial ownership, and the inclusion of high-water mark provisions in the incentive contracts, are associated with superior performance. The incentive fee percentage rate by itself does not explain performance. We also find that funds with a higher degree of managerial discretion, proxied by longer lockup, notice, and redemption periods, deliver superior performance. These results are robust to using alternative performance measures and controlling for different data-related biases.     

Diversification in the hedge fund industry

We provide evidence of a significant relation between diversification and performance in the hedge fund industry. Measuring diversification across four distinct dimensions, we find a significant positive relation between hedge fund performance and diversification across sectors and asset classes. We show that on a risk adjusted basis, hedge funds that diversify across sectors and asset classes outperform other funds by an average of 1.1% per year. However, diversification across styles and geographies exhibits a significant negative association with hedge fund returns. Funds that diversify across styles and geographies underperform other funds by an average of 1% per year. For fund of hedge funds, we find a significant positive relation between performance and diversification across sectors. However, diversifying across asset classes and geographies is found to exhibit a negative relation with fund performance. Finally, we find that the motive to engage in diversification is consistent with managerial incentive structure in the hedge fund industry.     

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.