Hedge funds: Market timing and the dynamics of systematic risk

HEDGE FUNDS: MARKET TIMING AND THE

DYNAMICS OF SYSTEMATIC RISK   Objectives

            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:

                                                R_i,t = c_i + β_i,t R_m,t + ε_i,t                                        (1)

                                                R_m,t = c_m + ε_m,t                                                  (2)

where  R_i,t  and  R_m,t are the daily excess returns on the individual security and the market portfolio respectively; β_i,t  is the time-varying security beta; c_i,t and c_m,t are constants and;  ε_i,t  and ε_m,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:

                             σ²[ε_i,t] = exp{α_i,0 + α_i,1(„ z_i,t-1„  - E„ z_i,t-1„  + δ_iz_i,t-1) + φ_i ln(σ²[ε_i,t-1]) }                   (3)

                          σ²[ε_m,t]= exp{α_m,0 + α_m,1(„ z_m,t-1„  - E„ z_m,t-1„ + δ_mz_m,t-1)+ φ_m ln(σ²[ε_m,t-1]}                (4)

                                                         σ_i,m,t = ρ_i,m (σ²[ε_i,t] σ²[ε_m,t])^1/2                                               (5)

where, ln(.) are natural logarithms, z_i,t = ε_i,t/ σ[ε_i,t]  and  z_m,t = ε_m,t/ σ[ε_m,t] are normalized innovations;  σ_i,m,t  and  ρ_i,m are the conditional covariance and the conditional correlation coefficient; and α_i,0, α_i,1, δ_i, φ_i, α_m,0, α_m,1, δ_m , φ_m 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

                                                            β_i,t = (σ_i,m,t/ σ²[ε_m,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.