Value at risk, GARCH modelling and the forecasting of hedge fund return volatility

This paper examines the conditional volatility characteristics of daily management style returns and compares the out-of-sample forecasts of different Value at Risk (VaR) approaches, namely, the normal, Cornish–Fisher (CF), and the so-called GARCH-type VaR. The examination of the conditional volatility of hedge fund styles and composite returns shows important differences concerning persistence, mean reversion and asymmetry in the period under consideration. Hedge fund returns exhibit significant negative skewness and excess kurtosis, which cannot be captured in the normal VaR whereas the CF-VaR results in a systematic downward shift of the conventional VaR. The GARCH-type VaR, however, includes the time-varying conditional volatility and is able to trace the actual return process more effectively. Since the forecast performance cannot detect which of the three VaR types can match the time-varying risk adequately, an adjusted hit ratio takes the size of the hits as well as the average VaR into account. According to this, the GARCH-type VaR outperforms the other VaRs for most of the hedge fund style indices.