Hedge funds : Quantitative insights

This primer on the analysis of hedge funds offers investors a more quantitative understanding of this topic, providing a complete guide to portfolio techniques, asset allocation, performance measurement and product selection in the alternative investment world. Hedge funds are the fastest growing sector of the financial industry, and yet the least understood, by market professionals. Examines and popularises the results of several quantitative studies that have so far been confirmed within academic circles.

Foreword by Mark Anson. Introduction. Acknowledgments. . Part 1: MEASURING RETURN AND RISK . 1 Characteristics of Hedge Funds. 1.1 What are hedge funds? 1.2 Investment styles. 1.2.1 The tactical trading investment style. 1.2.2 The equity long/short style. 1.2.3 The event-driven style. 1.2.4 The relative value arbitrage style. 1.2.5 Funds of funds and multi-strategy funds. 1.3 The current state of the hedge fund industry. 2 Measuring Return. 2.1 The difficulties of obtaining information. 2.2 Equalization, crystallization and multiple share classes. 2.2.1 The inequitable allocation of incentive fees. 2.2.2 The free ride syndrome. 2.2.3 Onshore versus offshore funds. 2.2.4 The multiple share approach. 2.2.5 The equalization factor/depreciation deposit approach. 2.2.6 Simple equalization. 2.2.7 Consequences for performance calculation. 2.3 Measuring returns. 2.3.1 The holding period return. 2.3.2 Annualizing. 2.3.3 Multiple hedge fund aggregation. 2.3.4 Continuous compounding. 3 Return and Risk Statistics. 3.1 Calculating return statistics. 3.1.1 Central tendency statistics. 3.1.2 Gains versus losses. 3.2 Measuring risk. 3.2.1 What is risk? 3.2.2 Range, quartiles and percentiles. 3.2.3 Variance and volatility (standard deviation). 3.2.4 Some technical remarks on measuring historical volatility/variance. 3.2.5 Back to histograms, return distributions and z-scores. 3.3 Downside risk measures. 3.3.1 From volatility to downside risk. 3.3.2 Semi-variance and semi-deviation. 3.3.3 The shortfall risk measures. 3.3.4 Value at risk. 3.3.5 Drawdown statistics. 3.4 Benchmark-related statistics. 3.4.1 Intuitive benchmark-related statistics. 3.4.2 Beta and market risk. 3.4.3 Tracking error. 4 Risk-Adjusted Performance Measures. 4.1 The Sharpe ratio. 4.1.1 Definition and interpretation. 4.1.2 The Sharpe ratio as a long/short position. 4.1.3 The statistics of Sharpe ratios. 4.2 The Treynor ratio and Jensen alpha. 4.2.1 The CAPM. 4.2.2 The market model. 4.2.3 The Jensen alpha. 4.2.4 The Treynor ratio. 4.2.5 Statistical significance. 4.2.6 Comparing Sharpe, Treynor and Jensen. 4.2.7 Generalizing the Jensen alpha and the Treynor ratio. 4.3 M2, M3 and GrahamHarvey. 4.3.1 The M2 performance measure. 4.3.2 GH1 and GH2. 4.4 Performance measures based on downside risk. 4.4.1 The Sortino ratio. 4.4.2 The upside potential ratio. 4.4.3 The Sterling and Burke ratios. 4.4.4 Return on VaR (RoVaR). 4.5 Conclusions. 5 Databases, Indices and Benchmarks. 5.1 Hedge fund databases. 5.2 The various biases in hedge fund databases. 5.2.1 Self-selection bias. 5.2.2 Database/sample selection bias. 5.2.3 Survivorship bias. 5.2.4 Backfill or instant history bias. 5.2.5 Infrequent pricing and illiquidity bias. 5.3 From databases to indices. 5.3.1 Index construction. 5.3.2 The various indices available and their differences. 5.3.3 Different indicesdifferent returns. 5.3.4 Towards pure hedge fund indices. 5.4 From indices to benchmarks. 5.4.1 Absolute benchmarks and peer groups. 5.4.2 The need for true benchmarks. . Part 2: UNDERSTANDING THE NATURE OF HEDGE FUND RETURNS AND RISKS . 6 Covariance and Correlation. 6.1 Scatter plots. 6.2 Covariance and correlation. 6.2.1 Definitions. 6.2.2 Another interpretation of correlation. 6.2.3 The Spearman rank correlation. 6.3 The geometry of correlation and diversification. 6.4 Why correlation may lead to wrong conclusions. 6.4.1 Correlation does not mean causation. 6.4.2 Correlation only measures linear relationships. 6.4.3 Correlations may be spurious. 6.4.4 Correlation is not resistant to outliers. 6.4.5 Correlation is limited to two variables. 6.5 The question of statistical significance. 6.5.1 Sample versus population. 6.5.2 Building the confidence interval for a correlation. 6.5.3 Correlation differences. 6.5.4 Correlation when heteroscedasticity is present. 7 Regression Analysis. 7.1 Simple linear regression. 7.1.1 Reality versus estimation. 7.1.2 The regression line in a perfect world. 7.1.3 Estimating the regression line. 7.1.4 Illustration of regression analysis: Andor Technology. 7.1.5 Measuring the quality of a regression: multiple R, R2, ANOVA and p-values. 7.1.6 Testing the regression coefficients. 7.1.7 Reconsidering Andor Technology. 7.1.8 Simple linear regression as a predictive model. 7.2 Multiple linear regression. 7.2.1 Multiple regression. 7.2.2 Illustration: analyzing the Grossman Currency Fund. 7.3 The dangers of model specification. 7.3.1 The omitted variable bias. 7.3.2 Extraneous variables. 7.3.3 Multi-collinearity. 7.3.4 Heteroscedasticity. 7.3.5 Serial correlation. 7.4 Alternative regression approaches. 7.4.1 Non-linear regression. 7.4.2 Transformations. 7.4.3 Stepwise regression and automatic selection procedures. 7.4.4 Non-parametric regression. 8 Asset Pricing Models. 8.1 Why do we need a factor model? 8.1.1 The dimension reduction. 8.2 Linear single-factor models. 8.2.1 Single-factor asset pricing models. 8.2.2 Example: the CAPM and the market model. 8.2.3 Application: the market model and hedge funds. 8.3 Linear multi-factor models. 8.3.1 Multi-factor models. 8.3.2 Principal component analysis. 8.3.3 Common factor analysis. 8.3.4 How useful are multi-factor models? 8.4 Accounting for non-linearity. 8.4.1 Introducing higher moments: co-skewness and co-kurtosis. 8.4.2 Conditional approaches. 8.5 Hedge funds as option portfolios. 8.5.1 The early theoretical models. 8.5.2 Modeling hedge funds as option portfolios. 8.6 Do hedge funds really produce alpha? 9 Styles, Clusters and Classification. 9.1 Defining investment styles. 9.2 Style analysis. 9.2.1 Fundamental style analysis. 9.2.2 Return-based style analysis. 9.2.3 The original model. 9.2.4 Application to hedge funds. 9.2.5 Rolling window analysis. 9.2.6 Statistical significance. 9.2.7 The dangers of misusing style analysis. 9.3 The Kalman filter. 9.4 Cluster analysis. 9.4.1 Understanding cluster analysis. 9.4.2 Clustering methods. 9.4.3 Applications of clustering techniques. . Part 3: ALLOCATING CAPITAL TO HEDGE FUNDS . 10 Revisiting the Benefits and Risks of Hedge Fun