In previous posts we've suggested that the returns of dynamic traders, such as hedge funds, are equivalent to the profits that arise from writing options on a trading risk premium. We've shown data from the spread between the VIX and a model of S&P 500 volatility which explains some of the variance of hedge fund returns, and which represents the profitability of option writing. We've also estimated a hedge fund index returns factor and shown that the data (the indices from Barclay Hedge) are consistent with the hypothesis that most of the profits arise from exposure to the dynamic trading risk factor, but that a small style alpha does exists.

Of course, an extremely interesting question is then whether the dynamic trading risk factor is entirely random or whether it can be conditionally forecast. (We can easily see that it has a non-zero mean!) To put it simply: do hedge fund returns trend; do they revert; or, are they conditionally random?

I use a very nice time series analysis program called RATS. This program has a command specifically designed to perform a Box-Jenkins ARIMA analysis. Below are the results of fitting a parsimonous AR(1) model to the estimated factor returns data. The results of fitting an AR(1) model are shown below.

The answer is "yes, hedge fund returns trend strongly." The autocorrelation function, with the expected ACF for an AR(1) model, is shown below and suggests that this month-on-month trending is a sufficient model for the data.

This allows us to forecast a factor return of 54 b.p. for January, 2009.