Posts to Statistical Trader have slowed down a lot — I've been busy working for a hedge-fund startup that I joined in August.  To manage this new responsibility, I've cut back from some of my activity in writing articles for this blog, and am no longer publishing my trade record to Twitter. I am still compiling data on the Dynamic Trading Risk Factor, and will publish articles relating to that analysis from time-to-time…

I've been having a lot of fun with the hedge fund factor analysis; so, for a limited time, if anybody out there would like to provide me with data on a particular fund, I'll do the regression for them. Just email it to blog@gillerinvestments.com and I'll see what I can do.

I'd also be happy to share the data I have with any of the folks at the funds we've analyzed here or maybe you could fill in some of the data holes and we can get a complete picture out there (I know you're reading this stuff, thanks to Google Analytics).

Recent turmoil in the financial markets has been accompanied by daily volatility reaching unprecedented levels. (The chart DJIA Volatility illustrates the daily point volatility for the DJIA estimated from a simple GARCH model. n.b. This chart was prepared during the day, so the "current" levels indicated numerically do not represent the "end of day" levels.)

The level of volatility enters into our trading strategy in several places. Firstly, if we are risk averse, then our asset price change forecasts must be weighed against a risk metric when we decide whether or not to trade. Most likely this risk metric will scale in some way with the level of volatility. If we do not dynamically alter our risk metric to take account of the current levels of volatility then we will fail to maintain the same risk/reward ratio (or signal-to-noise ratio) in volatilite times that we have in quiescent times. This will act to deteriorate the Sharpe Ratio of the trading strategy. To pick a guady metaphore, when one hears the noise of the waterfall ahead one should start to paddle less swiftly.

Secondly, if our forecasting procedure involves variables in lagged returns; or, cross-sectional dispersive measures; or, implied volatilities; or such like factors; then, our alpha itself will scale in some way with the level of volatility and so it itself will become larger in magnitude during volatile times.

Canonical "Modern Portfolio Theory" explicitly specifies that the ideal portfolio should be linear in the product of the inverse of the covariance matrix into the vector of forecasts. This quantity, whether expressed in price change space or return space or some other manner, is not dimensionless (it has the dimension of quantity/forecast e.g. contracts/dollar) and will therefore scale inversely with the level of volatility.

So theory often tells risk averse traders to take some account of volatility when making their trade decision. However, in practice I've often found it difficult to show the actual benefit of such considerations as an empirical reality. But one problem with econometric analysis of financial markets is that the data does not do a good job of exploring the available ranges of empirically important variables. Interest rates, for example, can stay in a similar range for years. This, as we see from the DJIA chart referenced above, is also true for volatility.

Now, in stark contrast, volatility has broken into a wholly new region of phase space. Now we can actually compare decisions made in times of radically high volatility with those made in more quiet times. Of course, this analysis still has a temporal bias --- for we only have one such region of high volatility and during that time the markets fell dramatically --- so we must maintain caution as to what we do with this dataset but, nevertheless, we have a new volatility laboratory to work in.

When re-reading the first post I saw that I'd used the term "trading strategy" and so feel a need to define this as I am using it.

Quantitative trading generally means using quantitatively derived information to trade. This can be thought of a three stage system. The first is using quantitative methods to forecast alphas, or asset specific (i.e. idiosyncratic) returns. I view most alphas as stochastic (i.e. random) with a zero mean longitudenally, but that does not mean that they cannot be conditionally forecast.

Once one has a set of forecasts one has to decide when to trade. This is what I mean by trading strategy: given private or semi-private forecasts of asset returns, knowledge of trading costs, and forecasts of risk, how do you combine this information to produce a decision to trade.

The third element is how much capital to commit to a given trade. This, you would call risk management.

The nice thing about making this devision is that it makes it easier to work and easier to evaluate one's work. One could call a trading system "separable" if it's analysis can be cleanly divided in this way (sort of in the way in which a partial differential equation is separable if f(x,y,z) is written X(x)Y(y)Z(z), for example).

The job of forecasting, or alpha generation, is a cleanly defined piece of statistical analysis: viz, to construct a forecasting system that is consistently reliable out-of-sample, meaning when used on data not used to develop it. This is unambiguously a piece of science.

The job of trading strategy is a cleanly defined piece of mathematical logic. Given a forecast set, when should one trade? This is applied mathematics, nothing more nor less. We have no need of backtesting if our forecasts are good and our logic is correct.

The job of risk management is more fuzzy, as this is the point at which economic theory enters the picture. Given a trade decision and a risk estimate, how much should I invest relative to capital.

Note how the paradigm described above differs from what one would call a "technical trading" system. Which is a black box system that takes in market data and outputs trades, based on parameters which are optimized through backtesting. Of course, this method can also work.

I am a quantitative trader. I sometimes call myself a statistician, although I have no formal statistical training. However, I have a considerable informal statistical training which was acquired while completing my doctorate in experimental elementary particle physics at Oxford. For my professional career I have applied this empirical knowledge, and some theoretical skills, to the financial markets.

I used to work in the Process Driving Trading Group (PDT) at Morgan Stanley. One of the things I did there was develop a formal mathematical description of the trading strategy used as part of their "Stat. Arb." quantitative trading system. I also managed futures trading which, overall, was not successful. PDT were great at relative value trading, but futures require a different focus, on outright risk taking, and I feel the two didn't mesh very well.

In 1999 I got married, and in 2000 I left PDT. I set up a commodity trading advisory (CTA) firm and, later, a registered exempt commodity pool operator (CPO). I abandoned my futures trading style from Morgan Stanley and created an entirely new business, albeit trading the same contracts -- three month eurodollar futures. This was a much more successful business generating returns, for its partners, of approximately 30% per annum from 2000 to 2003. I closed that business for personal reasons, and have been managing a private family investment fund since then.


I learned a lot working at Morgan Stanley, but I learned much much more investing my own capital. I have always tried to think carefully, and more importantly analytically, about my activities in the markets. Over the years I have developed some interesting models for financial data, and it is my intention to use this forum to publish some of this information.

I don't believe markets are efficient, but I do believe they are nearly so. I will publish some information on methods, some on particular forecasting systems, and some on general items of interest. I do hold positions in the markets and will always disclose them.

I am going to start with something concrete: a stock selection strategy I call the Compact Model Portfolio.