In his recent post The Curious Incident of Hedge Funds During the Financial Crisis, Tadas Viskanta, mentions our analysis of the returns of Goldman Sachs and that they are well explained by the Dynamic Trading Risk Factor. Our conclusion was that Goldman generates it's returns by engaging in typical hedge fund trading activity, albeit with three times more leverage.

In view of this link, it seemed apropos to update the published charts with the most up to date data I have. In the prior post, I also stated that I personally held no investment position in Goldman Sachs. This is no longer correct. Largely as a result of the analysis referred to here, I now have a long position in Goldman (and other hedge fund like stocks).

With an extra month's data for the Dynamic Trading Risk Factor, we can look to see whether there has been any re-ordering of the members of the XLF that are selected for membership of the Poor Man's Hedge Fund.

The above data shows no change to our prior computation, and the membership is still:

1. Invesco plc IVZ
2. Goldman Sachs Group Inc. GS
3. Morgan Stanley MS
4. T Rowe Price Group Inc. TROW
5. Janus Capital Group Inc. JNS
6. Ameriprise Financial Services Inc. AMP
7. Franklin Resources, Inc. BEN
8. Lincoln National Corp. Inc. LNC

Note that Ameriprise is no longer in the top five, having been replaced by Janus.

This post describes the first draft of the Poor Man's Hedge Fund portfolio. (This is noted as a first draft because there are several XLF members which exhibited very poor regressions and probably need data cleaning.) As I noted in the prior post, I took all eighty current members for the S&P Select Sector SPDR for the Financials and regressed the adjusted monthly returns of each stock onto the series of monthly returns of the dynamic trading risk factor. Using the R² for the regressions as a ranking factor, we then picked the top five stocks to build an equal rated portfolio.

These stocks are:

1. Invesco IVZ
2. Goldman Sachs GS
3. T. Rowe Price TROW
4. Morgan Stanley MS
5. Ameriprise Financial AMP.

As noted above, we are seeking to choose a portfolio that comprises the five stocks with the highest R²s for regression of the adjusted monthly returns onto the dynamic trading risk factor. We find a equal weighted portfolio has a regression R² of 69%; an α of (−1.13 ± 0.48) %/month; and, a β of 3.54 ± 0.24 onto the same risk factor. Therefore, the final portfolio is chosen to weight each stock's dollar value by 5.6% and the residual 72% of the assets are put in treasury bills. In sample, this combination will deliver a portfolio with an effective α of (−11 ± 14) bp/month and a β of 1 ± 0.07. The expected mean return due to the dynamic trading risk factor is 50 bp/month, so we expect this portfolio to deliver an average return of 5% per annum when held entirely passively.

In an earlier post we asked Is Berkshire Hathway a Hedge Fund?. Since that work was done, in mid. February, Berkshire has rebounded sharply off its low. Hedge funds have also been making money again, so I decided to revisit the data and see how Berkshires regression significance has changed. Has the recent months reinforced or weakened our prior conclusion that there was a significant element of the monthly returns that can be simply attributed to the risk premium arising from dynamic trading?

The prior regression showed that, over almost the entire previous decade, the monthly returns of Berkshire Hathaway common stock have a β of 0.70 ± 0.24 onto the dynamic trading risk factor, with a significance level (p-Value) of 0.005. The α is positive, but not significant, at 0.10 ± 0.46. The R² was 8%, which corresponds to a correlation coefficient of 28%.

In this regression we find a correlation of the monthly returns (to shareholders) with the dynamic trading risk factor, which should correspond to the returns of a typical hedge fund, has strengthened slightly. The β is now 0.83 ± 0.26, which is statistically indistinct from unity (t-Statistic is 0.63 referenced to the β = 1 hypothesis). The t-Statistic for the β is 3.15 for the null hypothsis of β = 0, which is equivalent to a p-Value of 0.002. The α is now estimated at (−0.01 ±0.50) % per month, which is statistically indistict from zero. The R² for the OLS regression (in the left hand panel of the chart) is 9%, which corresponds to a correlation coefficient of 31%.

In the prior article we chose not to draw a bold conclusion from the data, but I think the conclusion has to be stated more firmly. The data suggests that Berkshire Hathaway, Inc., as far as the returns available to the ordinary shareholders are concerned, is making money solely by following hedge fund trading strategies. One caveat to this, as compared to our regressions for Goldman Sachs and Morgan Stanley, is that the R² is much smaller. However, this could be attributed to skill. i.e. We could conclude that Morgan and Goldman are just better at executing hedge fund style trading strategies, with less zero expectation noise trading getting in the way, and this is why their returns are better explained by the factor (remember that the factor has a non-negative mean).

In the previous post we exhibited regressions of the returns of various banking companies onto the dynamic trading risk factor. Two distinct regression periods we used, and we made general comments about how the parameter estimates had changed.

In this post we're going to try to delve a little more into those changes. We're going to assume that the changes represent an actual change of behaviour on behalf of the institution concerned rather than that they represent statistical fluctuations about a common "true" value. With such a small sample, and such large errors relative to the estimates, this is a dubious exercise, but we will press on as it is entertaining.

These changes are represented by the vector flows on the "tadpole" chart below. The vector is from the "thin end" to the "head" (and is represented as such because Excel can't draw arrows).

So, overinterpreting to the best of our abilities, we see that: MS and GS have moved towards eachother - adopting similar behavioural profiles; JPM has essentially abandoned its hedge fund like trading business; MER (which were "rescued" by BAC), BAC, and C have started winding down their trading businesses at considerable expense; and LEH and BSC traded more desperately as they failed.

The above is, of course, entirely unrigourous and barely supported by the data. Don't place too much faith in it.

The table below shows the estimated parameters, alpha and beta, for a linear regression of the monthly adjusted returns of the common stock of a well known group of companies onto the dynamic trading risk factor series. These regressions are done separately for the pro articulus (01/2001 until 12/2006) and per articulus (01/2007 to date) periods. If the company still exists as an independent entity, a forecast is given for the return for 02/2009 (i.e. this month) based on a "whole dataset" regression (01/2001 to date). The companies studied are: Goldman Sachs; Morgan Stanley; Citigroup; Bank of America; Merrill Lynch; Lehman Brothers; JP Morgan; and, Bear Stearns. (Of course MER, LEH, and BSC terminated at some point within the latter period. For these companies, the regression used data upto the "end" of the company and not for the later trading of "stub" equity in the remnants of the company, if any.)

What is there to conclude from this? Starting with the innocent days of the pro articulus period, we see that all of these firms, with the exception of BAC, have an alpha estimated to be of order -1%/month to -2%/month and a beta of approximately 3 to 4 onto the risk factor. An plausible explanation is that, with the exeption of BAC, these firms all were in the business of trading and the negative alpha represents the high costs of financing this activity. Interestingly, the damage done due to the fiscal crisis, at least as far as the parameter estimates for the per articulus period go, was done idiosyncratically (i.e. it is expressed through the alpha) and not as a result of highly leveraged exposure to dynamic trading.