It's time to update our forecasts of the monthly returns of hedge funds, based on our analysis of the Dynamic Trading Risk Factor — the underlying factor we hypothesize drives the returns of all funds engaged in systematic trading activity.

In our last post on this topic, we forecast a July 2010 return of +7 bp. The realized return was +2.53%. Based on our model, we now forecast a total return for August 2010 of +1.27%.

Following on from May's difficult trading, we forecast a continued loss for the Dynamic Trading Risk Factor of 65 bp for June, 2010, and similar returns for correlated typical hedge funds. Early indications are that the numbers are coming in at a rate of −87 bp — marginally worse than the expectation. However, our early forecast for July, 2010, is now a slight gain of 7 bp.

Andrew Hall's Astenbeck Commodities Fund II is all over the news today. This is because Mr. Hall's relationship with, and compensation from, Citigroup became controversial during the global financial crisis and because Mr. Hall apparently lost around 10% during this past May.

My interpretation of the thrust of the reporting is that we are being directed to conclude that Mr. Hall's feet are in fact made of clay, and that Citi did the right thing to purge itself of this business. Furthermore, commentary has suggested that we should attribute Mr. Hall's prior out-performance to the access to cheap funding from Citi and the use of innapropriate levels of leverage to enhance returns.

However, most hedge funds, as exhibited by common indices and also by the Dynamic Trading Risk Factor, can be assumed a priori to have lost money to some degree or other during the last month. So the fact that Astenbeck had a losing month this month is not interesting, although the size of the losses might be. I have estimated the historic returns of Astenbeck for analysis from publicly available sources, and the data is available from this blog.

Above is the summary chart from our now standard comparative analysis. With the small dataset available, let's propose two hypotheses to test:

1. Astenbeck has outperformed the typical fund i.e. α > 0; and,
2. Astenbeck uses excessive levels of leverage i.e. β > 1.

The null hypothesis for the both tests is that returns of the fund are entirely typical, which we can represent by the linear regression parameter set H₀:(α,β) = (0,1). From our analysis we see that Astenbeck does indeed have an alpha of (58 ± 92) bp/month. This is large, but for our small data set not sufficiently large to rule out the null. We find the beta of 0.90 ± 0.32 consistent with the null. In this case our precision is significant enough to rule out excessive leverage, as we can say with 99% confidence that β < 1.6. Compare this to the levels in the region of 3 and 4 we found for Goldman Sachs and Morgan Stanley.

In summary, based on the small dataset available, we conclude that Astenbeck's returns may exhibit an alpha, but that this is not proven from this dataset alone, and that the fund does not use use excessive leverage.

I will finished off by pointing out that I have no connection to either Mr. Hall or his company and that I am currently a shareholder in Citigroup. This analysis was performed purely because it is a topic of current interest and because it is interesting.

The early estimate of the return of the Dynamic Trading Risk Factor is now available; the data can be downloaded from the blog.

In the prior post we presented evidence that the forecasting skill of our AR(1) model of the returns due to the dynamic trading risk factor was +18% relative to the null hypothesis forecast based on the sample mean return. However, we did not give a statement of the significance of this excess skill based on the sample data recorded.

The principal reason for this omission was that I don't know the sampling distribution of the skill statistic, and so cannot easily assess it's sample variance. In this post we will use the Jackknife, which is a statistical resampling technique, to estimate the bias and variance of the skill statistic.

For N data points, the basic technique is to compute the statistic we are interested in over the N subsets of the data that may be selected by leaving one of the data points out in each group. Unlike bootstrapping, we do not select subsets at random — we consider every possible subset that may be formed with just one datum left out. We may then use the sample distribution of these leave-one-out estimators of the skill to estimate the bias and variance of our whole sample statistic. 

Our data has a null forecast of 0.46% per month and a relative skill of 18%. From the data below, we compute a Jackknife bias of −2% in skill, leading to a Jackknife estimator of 20% skill with a Jackknife variance estimator of 0.0207 (std.err. of 14% in skill). 

For a while now I've made forecasts of the future returns of the Dynamic Trading Risk Factor and therefore, by proxy, the monthly returns of a typical hedge fund, based on a classic Box-Jenkin's style AR(1) model for the factor.

The purpose of this post is to analyse the relative skill exhibited by this forecast relative to two appropriate nulls. Those are:

1. The Law of Large Numbers Forecast — i.e. the mean of all the previous returns in the in-sample period, which is the data on which the AR(1) model was developed; and,
2. The Markov Process Forecast — i.e. the forecast based on the assumption that best estimate of the future returns is the return that just occurred.

For the purposes of comparing these forecasts we will use the commonly defined Forecasting Skill, being one minus the ratio of the mean square error of the proposed forecast to that of the null or “business as usual” forecast — which in our case will be the Law of Large Numbers forecast. This is based on the idea that, in the limit, the sample mean is an efficient and unbiased estimator of the population mean (for distributions for which the second moment exists).

Using these metrics we find that (entirely out-of-sample) the relative skill of a classic Box-Jenkins AR(1) model is 18% and the relative skill of the Markov Process model is −9%. A satisfying confirmation of the (well known) validity of the Box-Jenkins approach. For completeness, the skill of the AR(1) forecast relative to the Markov Process forecast is 25%.