Hedge funds: Market timing and the dynamics of systematic risk

Thursday, 4 April 2013: 9:30 AM
Johan Knif, Ph.D. , Finance, Hanken School of Economics, Vaasa, Finland
Gregory Koutmos, Ph.D. , School of Business, Department of Finance, Fairfield University, Fairfield, CT
Dimitrios Koutmos, Ph.D. , Leeds University, Leeds, United Kingdom


            There is a growing body of literature dealing with the market timing abilities of hedge fund managers and the degree to which these managers can earn alpha returns, i.e., returns unrelated to general market movements. The assumption however is that the relationship of hedge fund returns to markets movements, the so-called beta parameter, is constant through over time.

            The purpose of this paper is to test the  market timing abilities of hedge fund managers and the possibility that beta coefficients are time-varying.  More specifically, this study attempts to provide answers to the following questions:

a)      Is the systematic risk (beta) of hedge funds with a variety of investment styles time varying?

b)     Is the systematic risk higher during market downturns (i.e., asymmetric)?

c)      Is time variation and/or asymmetry related to the particular investment style?

d)     What is the degree of persistence and predictability in systematic risk?

Data and Methodology

That data that will be used in this study are weekly returns on hedge funds with the following investment styles:

Convertible Arbitrage  

Dedicated Short Bias

Emerging Markets

Equity Market Neutral

Event      Driven

Fixed Income Arbitrage

Global      Macro

Long-Short Equity        

Managed   Futures

Multiple   Strategy

The data cover the period 9/12/2005 till 3/12/2012 for total of 340 weekly observations.

The model that is used  is a bivariate EGARCH model described by the following set of equations:

                                                Ri,t = ci + βi,t Rm,t + εi,t                                        (1)

                                                Rm,t = cm + εm,t                                                  (2)

where  Ri,t  and  Rm,t are the daily excess returns on the individual security and the market portfolio respectively; βi,t  is the time-varying security beta; ci,t and cm,t are constants and;  εi,t  and εm,t are innovations or, error terms for the individual security and the market respectively.

            The elements of the variance/covariance matrix of the two error terms follow a bivariate EGARCH model described by the following set of equations:

                             σ2i,t] = exp{αi,0 + αi,1(„ zi,t-1„  - E„ zi,t-1„  + δizi,t-1) + φi ln(σ2i,t-1]) }                   (3)

                          σ2m,t]= exp{αm,0 + αm,1(„ zm,t-1„  - E„ zm,t-1„ + δmzm,t-1)+ φm ln(σ2m,t-1]}                (4)

                                                         σi,m,t = ρi,m (σ2i,t] σ2m,t])1/2                                               (5)

where, ln(.) are natural logarithms, zi,t = εi,t/ σi,t]  and  zm,t = εm,t/ σm,t] are normalized innovations;  σi,m,t  and  ρi,m are the conditional covariance and the conditional correlation coefficient; and αi,0, αi,1, δi, φi, αm,0, αm,1, δm , φm are fixed parameters to be estimated. This version of the model assumes that the conditional correlation is constant but the conditional covariance is time-varying.  The beta of the individual hedge fund is given by

                                                            βi,t = (σi,m,t/ σ2m,t])                                                     (6)

Results/Expected Results

We expect to find that the beta parameter given by equation (6) is time varying and that the size of the alpha return is influenced by the time-variability of beta. Furthermore, we expect  the betas to be persistent but mean reverting.