# October 2009 Data for the Dynamic Trading Risk Factor

November 10, 2009 16:01

As of this afternoon, a total of 1149 of approximately 2,500 hedge funds have reported data for October, 2009; so it's now time to update our data and forecasts for the dynamic trading risk factor. This gives us an early estimate of a number that is not much likely to change during the rest of the month.

Out-of-sample, our final forecast of the return for September, 2009, was 1.10% (our early forecast was 1.11%), and the realization was a substantial 3.25%. Our final forecast for October, 2009, was 1.61%, yet our current estimate of the performance for the most recent month is a loss of −0.20%. As a result we are forcasting a 0.30% return for November, 2009. These forecasts represent an a priori expected monthly return for any fund or firm that makes it's living by trading.

# Do Outperforming Funds Report Early?

September 27, 2009 22:05

In my prior post, describing the August, 2009, performance of the Dynamic Trading Risk Factor, I alluded to the fact that the source data, the Barclay Hedge hedge fund indices, does not accrue atomically — in fact it is gradually updated during the course of each month.

In prior posts, I pointed out that the final month's factor return is mostly little changed from that computed from earlier, incomplete, data. As it should be, if the Law of Large Numbers is working it's usual magic. However, nature is often a little more subtle than that, and mankind often deliberately so. It therefore falls to us to ask whether there is any bias between the latency of a given fund's publication of its performance numbers and that same fund's performance relative to the mean of all reporting funds? Our strong prior is that human frailty would lead the bearers of good news to rush it out as soon as possible; and, in contrast, the bearers of bad news to wait a little longer than they should before revealing their shame.

The above chart illustrates my attempt to quantify this effect on the September, 2009, data, which represents the aggregated reported August, 2009, returns of around 2,500 funds as reported during the month. Not possessing an inside track at the data vendor, I had to resort to archiving and timestamping sampled copies of the cumulatively reported data. Thus, it was tedious to collect. Exhibited above is the mean relationship between the relative error in the Hedge Fund Index's reported average return and the relative proportion of the total number of funds that had reported at that time. (In both cases, relative means relative to the final sample value I have for that month's datum.) From this sample there does appear to be a very strong negative correlation, confirming our cynical prior from the earlier paragraph. Unfortunately, the serial correlation of the errors complicates a statistical analysis of the goodness of fit — but by eye it appears excellent.

# August 2009 Data for the Dynamic Trading Risk Factor

September 21, 2009 10:10

As of this morning, a total of 2,077 of approximately 2,500 hedge funds have reported data for August, 2009; a little later than previously, it's now time to update our data and forecasts for the dynamic trading risk factor. This gives us an estimate of a number that is not much likely to change during the rest of the month.

Out-of-sample, our final forecast of the return for August, 2009, was 1.68% (our early forecast was 1.97%), and the realization was a 1.87%. Hedge funds are continuing to grow out of their catastrophic drawdown, and we expect this to continue, so we are forcasting a 1.11% final return for September, 2009. These forecasts represent an a priori expected monthly return for any fund or firm that makes it's living by trading.

# Hedge Funds and Mutual Funds: Analysis of Franklin Mutual Shares

August 14, 2009 09:53

In 1949, one of the oldest mutual funds, the company now known as Franklin Mutual Shares was established under the name Mutual Shares Corporation by Heine Securities Corporation. This fund recently celebrated its 50th. anniversary with the appearence of it's fund manager on the floor of the New York Stock Exchange, where he espoused the fund's philosophy as a long term large cap. value oriented stock picker.

I noticed this event, although in general I don't pay much attention to mutual funds as a class, because the fund's parent company, Franklin Resources, Inc. is a member of the Poor Man's Hedge Fund portfolio. That membership indicates that the fund manager's monthly returns regress strongly onto the Dynamic Trading Risk Factor. As the fund manager's revenues arise from the fund itself, albeit mostly from the assets under management rather than from incentive fees, as would be the case for a pure hedge fund, it is naturally interesting to ask whether the fund's monthly returns are also explained by the factor. The regression above indicates that this is indeed the case, and strongly so with an of 75%; α = (−0.7 ± 0.2) %/month; and, β =1.7 ± 0.1. This is a stronger regression than that we observed for Goldman Sachs, although with less leverage onto the factor and higher (relative) funding costs.

# July 2009 Data for the Dynamic Trading Risk Factor

August 10, 2009 22:40

As of this morning, a total of 985 of approximately 2,500 hedge funds have reported data for July, 2009; so it's now time to update our data and forecasts for the dynamic trading risk factor. This gives us an early estimate of a number that is not much likely to change during the rest of the month.

Out-of-sample, our final forecast of the return for July, 2009, was 0.65% (our early forecast was 0.75%), and the realization was a substantial 3.87%. Hedge funds have done well, and we expect this to continue, so we are forcasting a 1.97% final return for July, 2009. These forecasts represent an a priori expected monthly return for any fund or firm that makes it's living by trading.

# Kernel Density Estimation with Error Bands

August 07, 2009 12:42

As I mentioned in my post discusssing Kernel Density Estimators for the Dynamic Trading Risk Factor, one nice property of histogramming is that the sampling errors for the kernel density estimate that the histogram represents and well understood and straightforward to compute. Computing the sampling distribution for the estimator is considerably more complicated for kernel density estimators.

The above chart was prepared in Mathematica. On the laptop I have Mathematica 6 installed on, the k.d.e. chart takes about 30 seconds to run (Mathematica is a symbolic computation system and, as such, will always execute on the slower side), but the computation of the error bands took several hours — I set the job up at midnight and looked at the results over breakfast — and the resulting data is not particularly profound!

The expression for the mean square error of the point estimator is

$\frac{(K_h^2*f)(x)-(K_h*f)^2(x)}{n}+\left\{(K_h*f)(x)-f(x)\right\}^2$.

However, this expression is written in terms of the true population density and, since the entire premise of kernel density estimation is to estimate the density, we clearly do not know that. As the procedure is relatively efficient, when compared to histogramming, and an unbiased estimator, we can assume that the density estimate converges in expectation to the true population density. This justifies the step of replacing f(x) with its estimator in the above expression, which was what I did to compute the error bands.

I started this analysis to look at whether there was evidence for clustering of factor returns in the region of 2%, but am not seeing that in these procedures with a standard choice of bandwidth. The book I've been working from, Ward and Jones's Kernel Smoothing (Monographs on Statistics and Applied Probability) is silent on the sampling distributions for the estimators. Although I drew error bands on the plot, I don't actually know the probability that the true density estimate lies within those bands at a given point. We can reach for the Central Limit Theorem, and suggest that it is in the region of 68% of the probability mass — but that is truthfully just a guess. I think I have to go back to histogramming, with an arbitary bin-width, to assess whether the clustering is statistically significant.

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GRAHAM GILLER
Dr. Giller holds a doctorate from Oxford University in experimental elementary particle physics. His field of research was statistical astronomy using high energy cosmic rays. After leaving Oxford, he worked in the Process Driven Trading Group at Morgan Stanley, as a strategy researcher and portfolio manager. He then ran a CTA/CPO firm which concentrated on trading eurodollar futures using statistical models. From 2004, he has managed a private family investment office. In 2009, he joined a California based hedge fund startup, concentrating on high frequency alpha and volatility forecasting. My updated resume is on LinkedIn.

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