The authors review the role of portfolio optimization in the construction of hedge fund portfolios and investable hedge fund indices. They address the challenge of dealing with abnormal hedge fund returns, which are a function of the various strategies. They find that using a semi-parametric statistical approach offers improved risk-adjusted portfolio performance.

The hedge fund market has grown and survived the 2007–09 financial crisis, which featured asset prices falling to their pre-crisis levels. This growth is attributable to an increase in both funds of hedge funds (FOF) and investable hedge fund indices. Portfolio optimization has played a central role in the growth. When including such alternative asset classes as hedge funds in mean–variance optimization, it is necessary to select risk and return metrics that take into account the nonnormal distribution of hedge fund returns. In statistics, a parametric model is a family of distributions that can be described using a finite number of parameters. The authors evaluate both the nonparametric and parametric approaches to portfolio optimization, discuss their advantages and disadvantages, and propose a semi-parametric approach to address the deficiencies of the two methodologies.

Hedge fund return distributions exhibit unique properties that lend themselves to alternative forms of examination. Namely, they display significant negative skewness and excess kurtosis. Consequently, portfolio optimization arrives at very different allocations. To address this phenomenon, the authors use different risk measures in the optimization process. These include mean–variance optimization, mean conditional value at risk (CVaR), mean conditional drawdown at risk (CDaR), and omega. The last measure, omega, is the probability-weighted ratio of gains to losses relative to a threshold return; it is designed to address the shortcomings of the Sharpe ratio.

The authors report the end-of-period value, annualized average return, standard deviation, maximum drawdown, CVaR, CDaR, Sharpe ratio, omega, information ratio, and portfolio turnover for a conservative investment strategy and for two aggressive strategies. One of the two aggressive strategies minimizes portfolio risk subject to a target return; the other maximizes portfolio return subject to a maximum risk constraint.

One drawback of the nonparametric approach is that a large dataset is needed to generate accurate estimates of the various optimization measures. Additionally, this methodology makes it difficult to incorporate such dynamic characteristics of hedge fund returns as autocorrelation and volatility clustering.

Despite its ease of implementation, the parametric approach suffers from a tendency toward significant estimation error, an inability to model tails and higher moments of the return distribution, and an inability to capture nonlinear relationships among returns.

The authors propose a semi-parametric approach to portfolio optimization. It addresses the shortcomings of both the parametric and nonparametric methods by preserving the time-series properties of returns, providing better forecasts of the return distribution tails, and accounting for (non) linear risks by filtering out the dynamics of autocorrelation and volatility clustering.

Portfolio managers, third-party manager researchers, and performance evaluators will find that the authors’ conclusions are a useful template for further study as well as a fresh look at this branch of the alternative asset universe.

The authors use monthly data from Hedge Fund Research on 10 hedge fund single-strategy indices: convertible arbitrage, distressed securities, event driven, equity hedge, emerging markets, equity market neutral, merger arbitrage, macro, relative value, and short-selling strategies. The benchmark is the fund-of-funds strategy index. The sample covers January 1990–January 2011. The statistical characteristics of the strategies are as varied as the strategies themselves. The authors use these data for different optimization approaches, including mean–variance, CVaR, CDaR, and omega. They apply the approaches to a conservative portfolio and two variants of an aggressive portfolio.

The CVaR, CDaR, and omega optimization models improve risk-adjusted performance versus the models used in a parametric mean–variance approach. Additionally, the semi-parametric estimation of these optimization models is superior to that of nonparametric estimation.

Finally, the authors confirm the robustness of the risk limits, return targets, and estimation periods for their research.

The unique strategies and risk–return attributes of hedge funds justify extraordinary methods of evaluation. Effective portfolio management that incorporates alternative assets and strategies must look at the hedge fund universe differently to avoid objective evaluation and missing opportunities for robust risk-adjusted returns. The authors recognize and apply a portfolio optimization strategy that improves on the deficiencies of the existing methodology.