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.     

Trapped in diversification – another look at the risk of fund of hedge funds

Recent literature implies that despite being more diversified, fund of hedge funds (FOFs) are exposed to tail risk. We propose an explanation for this phenomenon; tail risk is a systematic risk factor for hedge funds, which by construction, explains the higher portion of the returns in the diversified portfolios. Our study suggests that not only an additional tail risk factor improves the explanatory power of the factor model, the relative importance of tail risk factor increases with the number of underlying hedge funds in an FOF portfolio. Furthermore, we demonstrate that FOFs with a short history, higher management fees, leverage and requiring shorter lockup periods are more sensitive to tail risk.     

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.     

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 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.     

Hedge fund portfolio construction: A comparison of static and dynamic approaches

This article studies the impact of modeling time-varying covariances/correlations of hedge fund returns in terms of hedge fund portfolio construction and risk measurement. We use a variety of static and dynamic covariance/correlation prediction models and compare the optimized portfolios’ out-of-sample performance. We find that dynamic covariance/correlation models construct portfolios with lower risk and higher out-of-sample risk-adjusted realized return. The tail-risk of the constructed portfolios is also lower. Using a mean-conditional-value-at-risk framework we show that dynamic covariance/correlation models are also successful in constructing portfolios with minimum tail-risk.     

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.     

The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds

Abstract:  Current research suggests that the large downside risk in hedge fund returns disqualifies the variance as an appropriate risk measure. For example, one can easily construct portfolios with nonlinear pay-offs that have both a high Sharpe ratio and a high downside risk. This paper examines the consequences of shortfall-based risk measures in the context of portfolio optimization. In contrast to popular belief, we show that negative skewness for optimal mean-shortfall portfolios can be much greater than for mean-variance portfolios. Using empirical hedge fund return data we show that the optimal mean-shortfall portfolio substantially reduces the probability of small shortfalls at the expense of an increased extreme crash probability. We explain this by proving analytically under what conditions short-put payoffs are optimal for a mean-shortfall investor. Finally, we show that quadratic shortfall or semivariance is less prone to these problems. This suggests that the precise choice of the downside risk measure is highly relevant for optimal portfolio construction under loss averse preferences.     

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.     

Performance analysis of a collateralized fund obligation (CFO) equity tranche

This article examines the performance of the junior tranche of a collateralized fund obligation (CFO), i.e. the residual claim (equity) on a securitized portfolio of hedge funds. We use a polynomial goal programming model to create optimal portfolios of hedge funds, conditional to investor preferences and diversification constraints (maximum allocation per strategy). For each portfolio, we build CFO structures that have different levels of leverage, and analyze both the stand-alone performance as well as potential diversification benefits (low systematic risk exposures) of investing in the equity tranche of these structures. We find that the unconstrained mean-variance portfolio yields a high performance, but greater exposure to systematic risk. We observe the exact opposite picture in the case of unconstrained optimization, where a skewness bias is added, thus proving the existence of a trade-off between stand-alone performance and low exposure to systematic risk factors. We provide evidence that leveraged exposure to these hedge fund portfolios through the structuring of CFOs creates value for the equity tranche investor, even during the recent financial crisis.     

Factor-based,Non-parametric Risk Measurement Framework for Hedge Funds and Fund-of-Funds

Abstract

A factor-decomposition based framework is presented that facilitates non-parametric risk analysis for complex hedge fund portfolios in the absence of portfolio level transparency. This approach has been designed specifically for use within the hedge fund-of-funds environment, but is equally relevant to those who seek to construct risk-managed portfolios of hedge funds under less than perfect underlying portfolio transparency. Using dynamic multivariate regression analysis coupled with a qualitative understanding of hedge fund return drivers, one is able to perform a robust factor decomposition to attribute risk within any hedge fund portfolio with an identifiable strategy. Furthermore, through use of Monte Carlo simulation techniques, these factors can be employed to generate implied risk profiles at either the constituent fund or aggregate fund-of-funds level. As well as being pertinent to risk forecasting and monitoring, such methods also have application to style analysis, profit attribution, portfolio stress testing and diversification studies. This paper outlines such a framework and presents sample results in each of these areas.     

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.     

The performance and diversification benefits of funds of hedge funds

We examine the performance and diversification potential of 332 funds of hedge funds (FOHFs) for the period from January 1990 to May 2003. Consistent with prior studies, we find that FOHFs appear to underperform the hedge fund index on a risk-adjusted basis. However, FOHFs have characteristics that offset their apparent underperformance. Their returns do not suffer from negative skewness that is a feature of many hedge fund strategies. Relative to the hedge fund index, we find that FOHFs have lower correlations with stock indices in both bull and bear markets, making them a better diversification tool in equity portfolios. For bond portfolios, however, FOHFs have no diversification advantage over hedge fund indexing.     

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.     

On measuring nonlinear risk with scarce observations

We propose a methodology for estimating the risk of portfolios that exhibit nonlinear dependence on the risk driving factors and have scarce observations, which is typical for portfolios of investments in hedge funds. The methodology consists of two steps: first, regressing the portfolio return on nonlinear functions of each single risk driving factor and second, merging together the obtained estimates taking into account the dependence between different factors. Performing the second step leads us to a certain probabilistic problem, for which we propose an analytic and computationally feasible solution for the case where the joint law of the factors is a Gaussian copula. A typical practical application can be to estimate the risk of a hedge fund or a portfolio of hedge funds. As a theoretical consequence of our results, we propose a new definition of the factor risk, i.e., the risk of a portfolio brought by a given factor.     

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.     

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.     

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.     

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.     

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.