Evaluating Hedge Fund Performance with Model Misspecification

Evaluating Hedge Fund Performance when Models are Misspecified David Ardia GERAD & HEC Montr al with Laurent Barras, Patrick Gagliardini, and Olivier Scaillet R/Finance - June 2022 David Ardia

Motivation Contribution Methodology Main Results Motivation Do hedge funds deliver superior performance to investors? Consistent with popularity of hedge funds size has increased from $40 billion in 1990 to more than $3 trillion today Hedge funds are more sophisticated, less constrained, and more incentivized than mutual funds Hedge fund performance is positive (e.g., Kosowski & al. (07) find an average alpha of 5% per year) David Ardia

Motivation Contribution Methodology Main Results Motivation A key issue: The misspecification of hedge fund models Hedge funds follow many alternative strategies to boost returns Any model to benchmark performance is likely misspecified It omits some alternative strategies that drive fund returns High alphas = hidden betas David Ardia

Motivation Contribution Methodology Main Results Motivation How misspecified are the standard hedge fund models? Hedge fund alphas are routinely measured using standard models Carhart (97) and Fung & Hsieh (04) models It is unclear if these models mitigate misspecification Little analysis of their ability to explain hedge fund returns They do not include recent factors (e.g., carry, variance) that are likely important for hedge funds (Pedersen (15)) David Ardia

Motivation Contribution Methodology Main Results Contribution In this paper: We mitigate misspecification by comparing models How does hedge fund performance vary across models? Focus on the performance difference with CAPM Do models have any ability to capture hedge fund strategies? We can then sharpen performance evaluation Choose models less prone to misspecification Identify relevant factors for hedge funds David Ardia

Motivation Contribution Methodology Main Results Contribution The two key features of our comparison approach We explicitly account for misspecification Crucial: models cannot be all correct Big impact on comparison tests because of estimation noise We examine the entire alpha distribution across funds Hedge fund investors only invest in a handful of funds David Ardia

Motivation Contribution Methodology Main Results Contribution Result 1: Standard models struggle to capture hedge fund returns Set of standard models includes Fama-French, Carhart, Fung-Hsieh Standard models = CAPM The alpha distributions are all the same (not just the mean) The standard factors explain little of hedge fund returns As a result, the estimated industry performance is high Average alpha is close to 2.5% per year More than 65% of the funds deliver positive alphas David Ardia

Motivation Contribution Methodology Main Results Contribution Result 2: A new model for sharpening hedge fund performance Built from new factors that plausibly capture hedge fund strategies (illiquidity, BAB, variance, carry, time-series (TS) momentum) New model largely reduces hedge fund performance Average alpha turns negative at -0.2% per year Only 50% of the funds deliver positive alphas New factors capture the fund exposures to alternative strategies David Ardia

Motivation Contribution Methodology Main Results Methodology Measuring hedge fund performance = ? ??,? ? ??,? ? Fund alpha: ?? ??,?is measured net-of-fees (investor s viewpoint) Benchmark depends on a set of trading strategies (factors) ?? ?= ?? ?[??] ? ??,? ) We focus on the entire cross-sectional alpha distribution (?? David Ardia

Motivation Contribution Methodology Main Results Methodology Case with well-specified model Suppose we know the correct model: + ?? ??+ ??,? ??,?= ?? ) Barras, Gagliardini, Scaillet (22) show how to estimate (?? David Ardia

Motivation Contribution Methodology Main Results Methodology In this paper: Focus on the misspecified case Two misspecified models 1 and 2 Each model omits some relevant factors in ?? 1), (?? 2) Each model produces its own alpha distribution (?? 1) and (?? 2) We show how to estimate and compare (?? 1, ?? 2(?=1, ,?) Using as inputs the estimated fund alphas ?? David Ardia

Motivation Contribution Methodology Main Results Methodology Theoretical analysis of misspecification ?) (?=1,2) Properties of the estimated alpha distribution ?(?? ?) consistently using estimated alphas ?? ? We can estimate (?? But misspecification largely increases estimation noise 1 ? ? ?? ? Illustration with the estimated average: ??= Precision does not depend on the number of funds ? Instead, it depends on the number of observations ? We have thousands of funds, but hundreds of observations David Ardia

Motivation Contribution Methodology Main Results Methodology Why such a high estimation noise? Because the factors omitted from model ? affect all funds Large realizations of the omitted factors drive the residuals of all funds simultaneously As a result, these realizations are not diversified away when the number of funds ? grows large Huge impact on model comparison tests It raises the bar for identifying differences between models David Ardia

Motivation Contribution Methodology Main Results Main Results Performance under the standard models Standard models produce the same alpha distribution as the CAPM For all characteristics (mean, std dev., proportions, quantiles) Few differences are significant David Ardia

Motivation Contribution Methodology Main Results Main Results Contribution of the Fung-Hsieh factors (relative to the CAPM) The standard factors do not capture hedge fund returns Contribution is low on average It is also small among the funds with the highest factor betas David Ardia

Motivation Contribution Methodology Main Results Main Results Performance under the new model The new model largely changes the shape of the alpha distribution Sharp reduction in hedge fund performance Stronger heterogeneity (driven by the worst funds) Differences are highly significant David Ardia

Motivation Contribution Methodology Main Results Main Results Contribution of the new factors (relative to the CAPM) The new factors do a good job at capturing alternative strategies For each factor, the majority of funds have positive betas The average factor contribution is economically large Most important factors are TS momentum, carry, variance David Ardia

Motivation Contribution Methodology Main Results To Conclude Measuring hedge fund performance is difficult Models are likely to be misspecified We propose a new approach for comparing models Help choose models less prone to misspecification Measure the economic importance of each factor We build a new model with economically-motivated factors Large performance reduction relative to the standard models David Ardia