All the major market indices had massive spikes in volatility at the end of last year. I use a common paradigm to model all of them. A simple GARCH model to forecast daily price volatility. These models were all developed on prior data and are running out of sample.

We looked at the volatility of the DJIA relative to its history in a recent post. Presented here is the same chart built for the S&P 500 Index, which is popular with institutional fund managers but has an inbuilt large-cap bias and does not represent a mimumum variance portfolio. Although the member selection method is less arbitary than that for the Dow, it is still not 100% mechanical.

We see the S&P volatility has also reduced and is at the upper end of the "normal" range. Like the Dow analysis, the volatility model is presented in terms of daily point move (for clarity of exposition) and is fitted with driving innovations that are intrinsically leptokurtotic — i.e. we model the fat tails as an intrinsic property of the driving process and not solely attributable to the composite nature of GARCH type process. The
generalized error distribution is used to model the i.i.d. innovations.

When I started this blog, I mentioned a system I call Compact Model Portfolio.

This is a portfolio selection system in which econometric methods are applied to the time series of daily dollar volume for stocks traded on U.S. exchanges. The goal is to answer the question: which stocks are market participants most interested in, using dollar value traded as a metric of interest. Using this data we select a small portfolio which represents the stocks voted by the market as those most likely to outperform.

I call this a "semi-efficient markets" approach because we accept the hypothesis that the market is a voting method which possesses the ability to efficiently select the best stocks; however, we do not accept the hypothesis that all information about these companies is fully and efficiently incorporated into their current prices.

I select these stocks daily, although the turnover is low, and a
representative portfolio is available from my website. Historical regression analysis shows that this portfolios' next day returns are well correlated with the NASDAQ-100 index, but that it outperforms this benchmark over the long run.

I did this analysis before the current work on dynamic trading risk factors; however, since this is a dynamically selected portfolio, it is interesting to ask whether there is a covariance between this system and what, we have found to be, is a common factor behind the returns of many large hedge funds.

If this system is well characterized by the null hypothesis (α,β)=(0,1), then we have a discovered a simple procedure that replicates what we have discovered to be an explanatory factor for the returns of several large hedge funds — this is a very interesting outcome!

The chart shows a comparison of the monthly returns accruing to the Compact Model Portfolio when hedged by allocating one third of the assets to a long position in the ProShares UltraShort QQQ ETF (AMEX:QID).

The results of this regression shows an insignificant but positive alpha of (1.04±0.73)%/month and a beta onto the dynamic trading risk factor of 0.84±0.32, which is not significantly different from unity. Overall, the R² is 20%.

This analysis is restricted to the period for which QID traded. For a longer period we have to look at hedging with a short position in QQQQ.

I thought that now would be a suitable time to take an aside and look at the long term volatility of major market indices. Many market participants use the term "volatility" to mean "large losses" and so, in current times, we are hearing the term frequently.

I use a simple GARCH model to forecast volatility for the Dow Jones Industrial Average. Although many professional money managers dismiss the Dow, I like to look at it because: a, it is what the media and public talk about when they talk about "the market;" and b, it is equal weighted rather than "cap. weighted" so it represents a more efficient variance reduction than cap. weighting (which over emphasizes the largest companies and so represents the economy and not the market).

The chart above shows the level, and volatility of the Dow, since 1995. The volatility model was fitted on data from 2000 to 2003 and is out-of-sample prior to 2000 and from 2003 to date. (For clarity of exposition, I'm presenting the volatility as a daily point volatility.) We see that the volatility has fallen precipitously from the extreme levels at the end of the prior year.

The innovations are well described by the generalized error distribution, and no severe shocks seem to have occurred since the beginning of 2007 (which was associated by the Jerome Kervial panic liquidation by Societe Generale).

In the post discussing Warren Buffett's Berkshire Hathaway vehicle, I omitted to forecast returns for February, 2009 (which was done for all the other funds and companies studied here).

So, briefly, based on the whole data sample linear regression we forcast a return of 0.75% for BRK A shares. The prior number is for the least squares estimator, which is equivalent to assuming that the innovations are i.i.d. Normal. In the prior post, we raised the issue as to whether a robust regression might provide a more accurate result. I repeated the regression using least absolute deviations, which is equivalent to assuming that the innovations are i.i.d. Laplacian (i.e. of the form exp -|x|). This tempered the forecast to 0.27%.

UPDATE: This forecast is based on January data and regressions up to the end of January. February is 2/3 over at this point, and BRK A is down 15% on the month (from $90,000 to $76,900 per share). At this point, it seems unlikely that the return for the rest of the month will be sufficient to put BRK into the black, as the model predicts.

I was listening to Dylan Ratigan's Fast Money TV show in my car this evening and was interested by the panel discussing the fact that Warren Buffett sold half of his position in JNJ. A memorable comment was "Maybe Warren's finally become a trader?"

I recalled that there was much discussion several months ago around the fact that Berkshire Hathaway had sold $40 billion in at the money index puts, receiving $5 billion in premium income. Of course, these puts were now heavily in the money, leaving Berkshire with a substantial liability on it's books.

This is an odd strategy for one who called derivative securities "weapons of financial mass destruction." Selling index puts is a hedge fund/investment bank strategy, not that of a long term value investor.

So this brings us to the question: is Berkshire Hathaway a hedge fund?

We can answer this question, as far as the equity investor is concerned, as before by comparing the monthly returns of Berkshire Hathaway to the returns accruing to dynamic trading. For this regression we have a strong prior, which differs to that for pure play investment banks such as Morgan Stanley or Goldman Sachs. We expect a significant positive alpha and zero beta, indicating that Berkshire makes money in a way entirely independant of trading risk premia.

The charts above show the Value Added Monthly Index for both Berkshire and the dynamic trading risk factor and a longitudenal regression of the monthly returns. This is for the entire dataset, from 2001 to date.

The regression shows that, over almost the entire previous decade, the monthly returns of Berkshire Hathaway common stock have a beta of 0.70±0.24 onto the dynamic trading risk factor, with a significance level (p-Value) of 0.005. The alpha is positive, but not significant, at 0.10±0.46.

Again we can break down the analysis into the pro articulum and per articulum parts; and, from this division, we see that this result is not driven by the current financial crisis.

As a final note, the appearance of the scatter plot suggests that a larger beta might be a more suitable estimate, which could be established with a robust regression procedure.

When I compile my original list of "banking" stocks, for the analysis presented in a prior post regressing common stock returns onto the dynamic trading risk factor, I omitted to include Wells Fargo. This is my fault, and probably represents an East Coast Bias of my own. The list was not compiled via a rigorous procedure --- it was entirely ad hoc.

That notwithstanding, the regressions for WFC are actually very interesting when compared to those for other banks.

Wells shows no significant covariance with the factor and no significant alpha with respect to it either.

On this basis, Wells Fargo is quite a different animal to the other banks studied previously.