Review of Econometric Models Applicable to Hedge Fund Returns Capturing Serial Correlation and Illiquidity

Abstract

Hedge Fund returns are often highly serially correlated mainly due to illiquidity exposures given that investments in such securities tend to be inactively traded and associated market prices are not always readily available. Following that, observed returns of such alternative investments tend to be smoother than “true” unobserved returns, which, in fact, turn out to underestimate risk measures such as volatility (i.e. standard deviation). In order to encompass for such serial correlation and illiquidity, we propose three econometric models. The first model referred to as the log-normally distributed random walk model with time varying parameters is largely used in the risk industry for Value-at-Risk4 purposes. Its main goal, in our context, is to derive specific characteristics of Hedge Fund returns by challenging and invalidating its assumptions (i.e. lognormality assumption and presence of autocorrelation between returns as well as their squares). The next two, referred to as the Blundell-Ward and the Getmansky, Lo and Markarovmodel respectively, both encompass an unsmoothing process and incorporate a predictive model for volatility. However, their mathematical background lies on a diametrically different perspective. Last but not the least, we propose for both an adequate model extension (i.e. a Markov-switching model for Blundell-Ward and conditional serial correlation for Getmansky, Lo and Markarov) that provide a superior volatility forecasting given the limitations arising within their actual standard mathematical formalism.