A Total Risk Measurement Framework for Hedge Funds and Funds of Funds

Abstract

This paper illustrates how qualitative analysis can be incorporated into quantitative risk measurement in order to construct an expected distribution of hedge fund returns that explicitly allows for market, residual and tail risk. We show how the combination of statistical criteria with out-of-sample model evaluation techniques, coupled with a qualitative understanding of the particular hedge fund strategy can lead to more robust risk factor models that capture the out-of-sample rather than the historical variation in hedge fund returns. Using Monte Carlo simulation techniques, that allow the most appropriate data generating process for each risk factor, we proceed to build a market risk based expected distribution of returns which is then adjusted for the presence of residual and tail risk. The residual risk distribution of expected returns is entirely based on the out-of-sample errors of the risk factor model and by using the out-of-sample explanatory power of the model as the weighting parameter we allow the model to ‘self correct’ when the actual returns deviate significantly from the model conditional expected returns. The tail risk distribution of returns and the correlation of these tails are solely based on qualitative analysis. We propose a methodology for the quantification of the potential impact of factors such as leverage, liquidity and concentration on the size and probability of excess losses due to tail risks. The proposed framework allows investors to explicitly measure, monitor and manage the modelable and non-modelable risks in a hedge fund portfolio.

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Electronic copy available at: http://ssrn.com/abstract=1546522

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A Total Risk Measurement Framework for Hedge
Funds and Funds of Funds





First draft: March 2009
This version: January 2010

Preliminary Draft
Comments welcome





Apostolos Katsaris, Caliburn Capital Partners LLP♣†
Ali Hegazi, Caliburn Capital Partners LLP
Martin Goulet, Caliburn Capital Partners LLP




♣ Contact: Apostolos Katsaris, Caliburn Capital Partners LLP, Time & Life Building, 1 Bruton Street, London, W1J 6TL, United
Kingdom, Tel: +44 (0) 207 518 2300, email: apostolos@caliburncapital.com, www.caliburncapital.com. The authors would like
to thank Chris Brooks, Phillip Xu, Gaurav Amin, Carol Alexander, and Ryan Davies for valuable comments and helpful
discussions. We would also like to thank Jacques Pezier, Simone Varotto, Emese Lazar and seminar participants at the ICMA
Centre, Henley Business School. We are responsible for any remaining errors.
† The views and opinions expressed in this document are those of the authors and are not necessarily those of Caliburn Capital
Partners LLP. Caliburn Capital Partners LLP accepts no liability over the content of the document. It is published for
informational purposes only and is not to be construed as a solicitation or an offer to buy or sell any securities or related financial
instruments.

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Electronic copy available at: http://ssrn.com/abstract=1546522

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“Quantitative models fail, human intuition fails. Models assist intuition and
conversely intuition facilitates the evolution of models. Without models hedge funds
could not provide services. Models need to grow and evolve or they will become
obsolete. However, without qualitative overlays to models; that is, a combination of
models and fundamental analysis, hedge funds can not survive unless they frequently
change their models to adapt to changing circumstances.”

Myron S. Scholes



Abstract
This paper illustrates how qualitative analysis can be incorporated into quantitative
risk measurement in order to construct an expected distribution of hedge fund returns
that explicitly allows for market, residual and tail risk. We show how the combination
of statistical criteria with out-of-sample model evaluation techniques, coupled with a
qualitative understanding of the particular hedge fund strategy can lead to more robust
risk factor models that capture the out-of-sample rather than the historical variation in
hedge fund returns. Using Monte Carlo simulation techniques, that allow the most
appropriate data generating process for each risk factor, we proceed to build a market
risk based expected distribution of returns which is then adjusted for the presence of
residual and tail risk. The residual risk distribution of expected returns is entirely
based on the out-of-sample errors of the risk factor model and by using the out-of-
sample explanatory power of the model as the weighting parameter we allow the
model to ‘self correct’ when the actual returns deviate significantly from the model
conditional expected returns. The tail risk distribution of returns and the correlation of
these tails are solely based on qualitative analysis. We propose a methodology for the
quantification of the potential impact of factors such as leverage, liquidity and
concentration on the size and probability of excess losses due to tail risks. The
proposed framework allows investors to explicitly measure, monitor and manage the
modelable and non-modelable risks in a hedge fund portfolio.

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1. Introduction
Over the last 60 years hedge funds have migrated from the fringes of the global
investment landscape to become one of the investment vehicles of choice for many
sophisticated investors. Underlying this increase in popularity has been the belief that
portfolio management skills, if properly compensated, combined with the use of non-
traditional investment methods and assets, can lead to superior risk-adjusted,
traditional-beta-independent returns. Hedge funds continue to develop and employ an
ever expanding range of strategies and today it is possible to access almost any area of
commercial activity through a hedge fund format. Hedge funds now invest or trade in
the complete spectra of markets, ranging from government related instruments or
currencies to the full capital structure of companies; from physical or real assets to
implied ones such as correlation and volatility.
Hedge fund investors often face significant liquidity and pricing risks since the most
abundant pricing inefficiencies, with the largest potential for superior risk-adjusted
returns, are often found in less mature, less competitive markets. At the same time,
full transparency does not always make the accurate measurement of risk using
traditional tools possible. This can be due to the complexity of assets found in many
hedge fund portfolios, combined with the fact that they can be invested across a range
of asset classes and instruments and may have a large number of positions2.
Furthermore, the difficulty may be compounded by the potential for rapid changes in
exposures and variations in leverage ratios that can make reliance on ‘portfolio
snapshots’ misleading.
The events of 2008-2009 resulted in a sharp increase in demand for more hedge fund
transparency and liquidity, as well as calls for increased regulation of hedge funds.
Despite this, the average hedge fund investor still faces limited transparency as many
hedge funds disseminate partial or non-standardised information regarding their
holdings. Often, hedge funds provide only stale or limited transparency to investors in
order to preserve a competitive research or informational edge that would otherwise
be at risk of being eroded. This situation is unlikely to change and, as a result,
investors that are unwilling to restrict themselves to a subset of simpler, less
competitive but fully transparent hedge funds need to adapt their risk management
tools to account for ‘known unknowns’ associated with this lack of transparency.
Several different methods for modelling the risk of a hedge fund portfolio have been
proposed in the academic literature with most approaches falling in one of two broad
categories. The first category tries to map hedge fund returns to observable risk
factors (see Ackermann, McEnally, and Ravenscraft (1999), Brown, Goetzmann and
Ibbotson (1999), Agarwal and Naik (2000) and Liang (2001) for single-factor models
and Fung and Hsieh (1997), Schneeweis and Spurgin (1999), Agarwal and Naik
(2004), Brealey and Kaplanis (2001), Edwards and Caglayan (2001) and Hasanhodzic
and Lo (2007) for multifactor models). The second category examines the returns of a
hedge fund or a hedge fund portfolio in isolation and recommends the calculation of
modified Value at Risk (VaR) estimates such as the Cornish-Fisher Modified VaR
(Zangari (1996)), Extreme Value Theory (EVT) based VaR (Braga (2009) and Gupta
and Liang (2005)), Jump-Diffusion Model based VaR (Derman (2006)), Johnson

2 For a summary of difficulties in hedge fund risk measurement, see Lo (2001)

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Distributions (Perez (2004)) and Skewed-t-Distribution VaR (Lyzanets and Senchyna
(2005)).
The major focus of many early papers on hedge fund risk factor modelling was the
problem of non-linearity of exposures of hedge funds to ‘traditional’ risk factors. In
order to account for this some researchers explicitly tried to include time-varying
exposures in the risk factor models (see Ferson, Kandel and Stambaugh (1987),
Kazemi and Schneeweis (2003), Billio, Getmansky and Pelizzon (2006), Goodworth
and Jones (2004), Alexander and Dimitriu (2005), and Coste, Douady and Zovko
(2009)) or calculate exposure to lagged market risk factors (see amongst others
Malkiel and Saha (2005)).
Other researchers have focused on the adaptation or expansion of asset pricing models
from the traditional investment space so as to capture the nonlinear return
characteristics of hedge fund returns (see amongst others Fung and Hsieh (2001),
Mitchell and Pulvino (2001), Agarwal and Naik (2004), Demaray and Luccioni
(2004), Kat and Miffre (2002) and Ranaldo and Favre (2005)). Finally, and perhaps
more popularly, researchers have recommended the inclusion of style-related risk
factors (see amongst others Fung and Hsieh (1997), Brown and Goetzmann (2001),
Lhabitant (2001), Amenc, Bied and Martellini (2003) and Huber and Kaiser (2004)).
Most of the papers outlined above focused on the quantitative measurement of risk
and limited the use of qualitative examination of hedge fund strategies to
classification, usually adopting style-based frameworks. Empirical papers that have
used qualitative information in the modelling of hedge fund risk have mostly been
focused on the examination of ‘death rates’ in the hedge fund industry (see for
example Getmansky (2004)). However, in hedge fund investing, a qualitative
understanding of the types of risks present is crucial. This is especially the case when
addressing idiosyncratic risks and unobserved tail risks, which correspond to events
that, despite their low probability of occurrence have a large adverse or even
catastrophic impact.
In this paper we extend the factor-based analysis of hedge fund returns to construct a
realistic and manageable methodology of total risk evaluation that combines
quantitative and qualitative information. The methodology considers the accuracy of
the risk factor model expectations in an out-of-sample setting and then, through the
use of Monte Carlo simulation techniques, adjusts the expected distribution of returns
for observed residual risk and previously unobserved tail risk that arises from the
particular characteristics of the hedge fund strategy. Previous studies add the in-
sample volatility of residuals to the volatility expected from the risk factor model to
form an estimate of ‘total’ risk. This can lead to the significant underestimation of risk
since it relies on market and residual risk to be present in the sample examined. Our
approach, mixes the risk factor based expected distribution of returns with a
distribution of residual risk that is based on the out-of-sample error of the model
conditional expectations of returns. In a portfolio setting, the residual risks of the
hedge funds are not assumed to be independent. Moreover, we extend the left tail of
the expected distribution of returns by adding a qualitatively derived expected excess
loss. The size, probability and, in a portfolio context, the correlation of this tail loss
depend solely on the qualitative understanding of the hedge fund’s strategy. This
probability weighted mixture of distributions is then used to sequentially adjust the
market risk based VaR of a hedge fund to incorporate residual and tail risk. This
approach allows the risk manager to target levels of market risk, residual risk and tail

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risk separately in hedge funds and hedge fund portfolios and thus allows the risk
manager to obtain a deeper understanding of the sources of risk in the portfolio and of
the possible ways to mitigate these risks.
The paper is organised as follows. Section 2 presents an account of the three main
types of hedge fund risk and an outline of how this paper addresses each category. In
the three sections that follow, each component is discussed in detail and in order. A
description is provided of how each part of the model corresponding to each type of
risk, is augmented by the next, leading to the final Total Risk Model which
incorporates market, residual and tail risk components. Empirical data is presented
that supports the underlying rationale of our approach and facilitates comparisons to
some existing Value at Risk approaches. Section 6 extends the approach to the risk
measurement of portfolios of hedge funds. Section 7 concludes.
2. Hedge Fund Risk
Hedge funds expose investors to a variety of risks that can be grouped into the
following three categories:
A. Market Risk
This is the risk of the hedge fund that is driven by the sensitivity of the
portfolio to market risk factors, both traditional and alternative, and can be
captured by risk factor return decomposition. Both the formulation of the risk
factors (whether they are simple indices of asset portfolios, specialised indices
or spreads between indices) and the structural form of the equation (whether it
is a linear, nonlinear or time dependent exposure) depend on the hedge fund or
portfolio of hedge funds being examined.
B. Residual Risk
This is the risk of a hedge fund that is driven more by its particular portfolio
holdings than the markets that the holdings belong to. The strategy pursued by
a fund is more important in determining this type of risk than the milieu of
investment. Some hedge funds have fairly stable exposures to risk factors
across time and hold large, liquid and diversified portfolios. Others, hold
concentrated portfolios in a particular area, sector, asset class, or change the
exposure of their portfolio very often, or both. In both cases the ‘divergence’
of the hedge fund portfolio from ‘visible’ diversified market portfolios results
in ‘alpha generation’ which is the compensation for non-market related
observed residual risk.
C. Tail Risk
This is the risk of a hedge fund investment that is associated with particular
strategy characteristics such as leverage, concentration and liquidity of
holdings etc. These characteristics have the potential to significantly affect
monthly returns even if their impact has not been observed in the past. In this
paper we distinguish Tail Risk from the more traditional market risk shock
definition.