In an earlier post we addressed the question as to whether there is any bias in the delay between a fund's month end and the performance of that month. Our cynical theory is that managers with good news to report report it early and those with bad news to report report it late.

Since September, 2009, I've been sampling the reported monthly return of the BarclayHedge Hedge Fund Index. This is a simple average of the monthly returns of all funds that have reported to the group at that time. From time-to-time during each month I've sampled the main index's reported average monthly rate of return and the number of funds that have reported. You can find this data on my blog at the page Return Index Accumulation Report. The chart below is an analysis of the error, meaning the difference between the average monthly rate of return for the entire universe reporting on the sample date and that value finally reported at the end of the month. To gauge the average scale of the bias we fit a simple model by least squares:

Here B is the bias, or the average error between the sampled monthly rate of return and the final monthly rate of return; S is the scale we seek to estimate; and, p is the proportion of funds reported (i.e. the number in the sample divided by the final number of funds reporting in that month). Our estimate of the average scale of the error is (51 ± 8) bp/month.

Professional managers are fully awhere of the transient and random nature of the returns they create, whether actively or passively, and are real human beings with the behavioural biases and oddities that characterize us as a group. Thus, when we are presented with a month in which we do very well, we are aware that the future will likely hold periods of underperformance. Furthermore, it is likely that the month following a good month, the month during which we are preparing a formal summary of the prior returns that we know were good, we are more likely to underperform that recent history than outperform it. Nobody wants to write the letter:

Dear Investor, last month we did very well. However, as I write this I know that we're doing less well, so don't get too carried away with your newfound wealth that I've already lost.

Furthermore, a manager who is confessing to a particularly dire prior period of returns would greatly like to write:

Dear Investor, last month we did badly. However, as I write this I know that we're doing very well, so please do not distress too much over your losses, which have already been erased.

For an example of this latter tendency, I can simply refer to my prior post on the September, 2009, performance of our NASDAQ-100 futures trading system. Both these forces together, provide the incentive for outperforming managers to report their returns promply and for underperforming managers to linger a while before sending the letters out of the door. Thus, we can explain the tendency observed in our analysis of the incremental updates of the BarclayHedge data.