Hedge Fund Tail Risk: An Investigation In Stressed Markets, Extended Version With Appendix

Hedge Fund Tail Risk: An Investigation In Stressed Markets, Extended Version With Appendix

Monica Billio

Ca Foscari University of Venice – Dipartimento di Economia

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Lorenzo Frattarolo

Ca Foscari University of Venice – Dipartimento di Economia

Loriana Pelizzon

Ca Foscari University of Venice – Dipartimento di Economia

January 18, 2016

University Ca’ Foscari of Venice, Dept. of Economics Research Paper Series No. 01/WP/2016


This paper develops several risk measures that captures the tail risk of single hedge fund strategies and the tail risk contribution of these hedge fund strategies to the overall portfolio tail risk, conditional on the level of market distress. We show that, during the recent global financial crisis, all the different hedge fund strategies are contributing to the tail risk of the portfolio of hedge funds, mostly because of the hedge fund strategies’ exposure to liquidity and credit risk.

Hedge Fund Tail Risk: An Investigation In Stressed Markets, Extended Version With Appendix – Introduction

The financial industry has witnessed several crises in the past, some of which have had a major global impact. Although hedge funds are expected to have the capability to at least avoid the impact of such crises by hedging against market movements, the LTCM crisis in 1998 and the global meltdown in 2008 showed otherwise. In both cases, most hedge funds suffered from large losses. In fact, almost all Dow Jones Credit Suisse hedge fund indexes experienced huge losses. These systemic losses of hedge funds have been associated with mostly large, simultaneous liquidation by market participants, causing a liquidity freeze that crippled hedge funds and also spilled over to the general economy (see Brown et al. (2009), Buraschi et al. (2014) and for a Lo et al. (2015). The experiences from these crises motivate investors, academics and also regulators to better understand systematic risk in hedge funds and these funds’ contribution to the overall risk of a portfolio (see Billio et al. (2012a)).

In this study, we concentrate on the risk of a portfolio of hedge funds, from the investor’s point of view. In this respect, our paper is generally related to Brown et al. (2012), who investigate over-diversification in funds of hedge funds that could generate tail risk and Heuson et al. (2014), who investigate hedge fund performance when returns are skewed. As funds of hedge funds primarily invest in hedge funds, it is important to develop a risk measurement technique that captures the risk exposure of the individual hedge funds and the risk contribution of these hedge funds toward the overall portfolio risk, especially in light of the 1998 and 2008 hedge fund crises. As documented by several studies, hedge funds follow dynamic trading strategies. As a result, the risk exposures and thus the risk contributions of hedge funds are expected to change significantly over time. To capture the dynamic nature of hedge funds, we apply a Markov regime-switching approach, which allows us to estimate time- and state-dependent risk exposures.

There are several ways to measure the risk of a financial asset or portfolio. The common ones include volatility, semi-variance, value-at-Risk and Expected Shortfall. Different studies suggest the use of one or the other of these tools to measure the risk of financial assets and make optimal portfolio choices. The mean-variance framework of Markowitz (1952) uses volatility (or variance) to understand the risk and select an optimal portfolio. Others, like Roy (1952), suggest a safety first approach, which accounts for the possibility of surprises, that is, returns below a certain, acceptable threshold. These ideas of using downside risk measures are developed further by Bawa (1978), and Fishburn (1977) suggests semi-variance and other partial moments as alternative risk measures. Currently, value-at-risk (VaR) and expected shortfall (ES) are the popular measures of downside/tail risk, VaR being the most widely used. While VaR is used to determine the capital requirements of banks and other financial institutions, it is shown to have some faults, including failing to be coherent. As a result, the academic literature seems to favor ES over VaR. See Artzner et al. (1999) and Inuia and Kijima (2005).

These measures provide different pieces of information about the risk of a portfolio and the contribution of the different hedge fund strategies to the risk of a portfolio. Measuring the risk using these different measures helps one to better diversify the portfolio with respect to “normal”and “extreme events”. It is in fact the case that the contributions of an asset to the portfolio volatility and to the tail risk are not necessary the same when the asset’s returns are not normally distributed.

Tail Risk

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