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Asia-Pacific Journal of Financial Studies (2009) v38 n1 pp1-33

Risk Measurement and Investment Myopia

in Hedge Fund Management*

Xun Li

Hong Kong Polytechnic University, Hong Kong, China

Zhenyu Wu∗∗

University of Saskatchewan, Saskatoon, Canada

This is one of the seven accepted papers among 76 papers that were submitted to the solicitation by

Asia-Pacific Journal of Financial Studies in the special “Call-for-Papers” event in 2008.

Abstract

Lo (2001) surveys the literature on risk management for hedge funds, and recommends a

dynamic and transparent risk measurement for the evolutionary hedge fund industry by

citing Albert Einstein’s comments. This study is to explore the feasibility and advantages

of adopting a dynamic absolute-deviation risk measurement in hedge fund management.

It does not only provide an optimal asset allocation strategy both analytically and nu-

merically in a dynamic mean-absolute deviation (DMAD) setting for hedge fund managers,

but also contributes to mitigation of potential investment myopia problems in their risk-

1. Introduction

In recent years, hedge funds have attracted financial economists and investors sig-

nificantly. As opposed to mutual funds, however, properties of hedge funds have not

been extensively examined. Research on risk management of hedge funds is still

emerging, and investor-fund manager agency conflicts have not been investigated in

depth. As suggested by Lo (2001), a seminal work in the literature on risk manage-

ment of hedge funds, developing a dynamic risk measurement with transparency is

important to this increasingly popular industry.

This study helps fill in this gap by applying a dynamic absolute-deviation risk

measurement to the evolutionary hedge funds industry, and adds to the literature on

dealing with investor-fund manger agency conflicts by comparing managers’ risk-

taking behaviors under different risk measurements. It does not only show the feasi-

bility of adopting a dynamic Mean-Absolute Deviation (DMAD) setting in the hedge

fund management by providing an optimal asset allocation strategy both analytically

and numerically, but also finds that the dynamic absolute-deviation risk measure-

ment helps mitigate fund managers’ potential investment myopia in their risk-taking

behaviors. It is well known that, while most of the investors are sufficiently wealthy

and therefore are considered risk-neutral, fund managers are usually risk-averse.

Due to the critical difference between the two parties, fund managers do not neces-

sarily act in the interest of the investors, but over-invest for short-term returns. Ap-

plications of the theoretical results derived in this study in the U.S. equity markets

are presented to illustrate the comparisons of investment behaviors based on differ-

ent risk measures.

Three major contributions are expected to be made to the finance literature and the

Asia-Pacific Journal of Financial Studies (2009) v38 n1

velops an alternative and efficient way to optimize portfolio selection in a dynamic

setting. It is also one of the few attempts to use real financial market data to assert

optimal solutions in dynamic settings. Third, it compares the effects of different risk

measurements on the risk-return trade-off and agency problems in fund managers’

risk-taking behaviors, respectively.

This article is structured as follows: In Section 2, we discuss the theoretical back-

ground for this study by surveying the literature on hedge fund management and op-

timal asset allocation. Section 3 describes the economy of a DMAD setting and pro-

vides analytical expressions of optimal investment strategies for hedge fund manag-

ers. Numerical applications of the optimal investment strategies in the DMAD model

and the effects of the absolute-deviation risk measurement on fund managers’ in-

vestment myopia problems are discussed in Section 4. We make conclusions in Sec-

2. Theoretical Background

This study attempts to show the feasibility and advantages of the DMAD risk mea-

surement in the hedge funds industry for risk transparency and to illustrate its role

in mitigating fund managers’ potential investment myopia problems in their risk-

taking behaviors. Therefore, we briefly survey two parts of the finance literature, risk

management and investment myopia in the hedge funds industry, and risk meas-

urements in portfolio selection and optimal asset allocation.

Risk Measurement and Investment Myopia in Hedge Fund Management

namic risk measurement to strengthen risk transparency and to mitigate the agency

conflicts between investors and fund managers. Although some incentive-related

studies, such as Brown et al. (2001), have considered the career concerns of fund ma-

nagers based on informational asymmetry, agency theory has not been substantially

applied to researches examining fund managers’ potential investment myopia prob-

lems in their risk-taking behaviors.

Whereas performance and risk-taking characteristics have become two of the most

popular issues in the field of hedge fund management, the risk measurement is still

on debate in the literature. As claimed by Lo (2001), traditional risk measurements,

such as mean-variance (MV), systematic risk, and value-at-risk (VaR) cannot repre-

sent the key features of hedge fund investments due to the incentive compensation

structure of hedge fund managers and the absence of regulations on their strategies.

Therefore, Lo (2001) suggests a dynamic risk analysis with transparency for hedge

fund investments. Furthermore, since a complete risk management system for hedge

fund management has to take into consideration both the principal (investors) and

the agent (fund managers), an appropriate risk measurement may help mitigate fund

managers’ investment myopia problems in their risk-taking behaviors.

According to the traditional corporate governance literature, fund managers may

behave myopically but not act in the interest of investors due to their personal con-

cerns and the informational asymmetry (e.g. Narayanan, 1985; Stein, 1988). Thus, a

performance-related incentive compensation package, consisting of both fixed man-

agement fee and incentive pay, needs to be appropriately constructed to mitigate the

conflict of interest between two parties: investors and fund managers. Since a

benchmark return, usually related to the industry average performance, is included

in the contract, this relative performance-based compensation structure is a typical

Asia-Pacific Journal of Financial Studies (2009) v38 n1

managers to take myopic behaviors since they can over-signal the market and the

investors so as to renegotiate for a better contract and/or pursue a better opportunity

in the labor market. Another factor which can potentially motivate these newly-hired

managers to do so is that they hold less fund assets than other fund managers; there-

fore, they have lower opportunity costs by taking myopic investment strategies.

Additionally, the risk exposures are complex in the hedge funds industry because of

its multi-dimensional organization structure. “Unregulated organization structure,

flexible investment strategies, relative sophisticated investors, substantial manage-

rial investment, and strong managerial incentives” (Ackermann et al. 1999, p. 834)

are incorporated into the investment partnerships and make traditional risk meas-

urements unsuitable. As claimed by Lo (2001), therefore, a dynamic risk measure-

ment is more appropriate than traditional static ones in risk management for the

hedge funds industry.

2.2 Risk Measurement in Portfolio Selection and Asset Allocation

In the past half a century, the Mean-Variance (MV) model proposed by Markowitz

(1952, 1959) has played an important role in the literature on portfolio selection and

optimal asset allocation. In fact, it has provided the basis for modern investment the-

ory (Chan, Karceski, and Lakonishok, 1999). Whereas it is a fundamental normative

model to study capital market theory and to develop hedging tools (e.g. Gourieroux,

Laurent and Pham, 1998; Biagini, Guasoni, and Pratelli, 2000) in the traditional fi-

nance literature, which risk measurement investors should choose is still on debate

in financial decision theory. Up until now, the most commonly used risk measure-

ments, such as semi-variance (e.g. Bond and Satchell, 2002), absolute deviation

Risk Measurement and Investment Myopia in Hedge Fund Management

most important contribution of this risk measurement is to replace the quadratic

program in the MV model by a linear program (Simaan, 1997). Konno and Yamazaki

(1991) prove the computational feasibility of a single-period MAD model, and Simaan

(1997) asserts its advantages based on utility maximization by comparing the MAD

model with the MV model. In the finance literature on capital market theory, its va-

lidity is empirically illustrated by Cornell and Dietrich (1978) on the CAPM model.

Unfortunately, the computational feasibility of the MAD model in a dynamic setting

has not been extensively explored.

3. A DMAD Economy and Optimization Results

In a DMAD economy, we consider a rational hedge fund manager who attempts to

minimize her risk measured by absolute deviation, given that the expected return of

her investments is not lower than the benchmark return written in her compensation