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Hedge funds: Market timing and the dynamics of systematic risk

**HEDGE FUNDS: MARKET TIMING AND THE**

**DYNAMICS OF SYSTEMATIC RISK**

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*are the daily excess returns on the individual security and the market portfolio respectively;

_{m,t}*β*

_{i,t}_{ }is the time-varying security beta;

*c*and

_{i,t}*c*are constants and;

_{m,t}*ε*and

_{i,t}*ε*are innovations or, error terms for the individual security and the market respectively.

_{m,t}The elements of the variance/covariance matrix of the two error terms follow a bivariate EGARCH model described by the following set of equations:

* σ*^{2}[ε_{i,t}] = exp{*α*_{i,0}* + **α*_{i,1}*(„ z _{i,t-1}„ - E„ z_{i,t-1}„ + *

*δ*

_{i}*z*

_{i,t-1}) +*φ*

_{i }*ln(*

*σ*

*(3)*

^{2}[ε_{i,t-1}]) } *σ*^{2}[ε_{m,t}]= exp{*α*_{m,0}* + **α*_{m,1}*(„ z _{m,t-1}„ - E„ z_{m,t-1}„ + *

*δ*

_{m}*z*

_{m,t-1})+*φ*

_{m}*ln(*

*σ*

*(4)*

^{2}[ε_{m,t-1}]} *σ*_{i,m,t}* = **ρ*_{i,m }*(**σ*^{2}[ε_{i,t}]* σ** ^{2}[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*are normalized innovations;

_{m,t}]*σ*

_{i,m,t}_{ }and

*ρ*are the conditional covariance and the conditional correlation coefficient; and

_{i,m}*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}/*

*σ*

*(6)*

^{2}[ε_{m,t}])**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.