About the Model Portfolios

I've posted three model portfolios. Two of these (the eurodollar portfolio and the long-short version of the CMP) represent actual positions I hold. The last (long-only CMP) represents the equivalent portfolio when positions in QQQQ are replaced with QID. This data is updated every day and is valid as of the timestamps embedded in the file.

Profit Maximizers, Risk Averse Traders and Separable Models

In trying to predict a market, there are essentially three classes of forecasting model we can attempt to build: directional models, which forecast only the future direction of the market; point models, which forecast a conditional mean of the future distribution of returns for some horizon from any given decision point; and, distributional models that attempt to describe the entire conditional probability density function (or maybe the lower moments of it) from which the next period(s) realized return will be drawn.

(Note, in the following we asume that the forecasting models are all actually valid out-of-sample.)

In the first circumstance, we do not have much sophistication. The actual return that occurs on any given day can be modelled as an i.i.d. random number plus a constant times our directional forecast. That constant is the mean return conditioned on our forcast indicator (+1, 0, -1).

Now, if that mean return is less than the costs of trading (slippage, brokerage fees, etc.) then a rational profit maximizer would not ever trade. If it exceeded the costs of trading then a rational profit maximizer would always trade in the direction of the forecast.

With the second style of forecast, a point forecast which changes dynamically, then a rational profit maximizer could compare the forecast on any given day with his knowledge of transaction costs (slippage as a function of position size, fixed trading fees etc.) and decide dynamically whether to trade on any given forecast. Since this makes a conditional decision, which should take the trader out of the market on some occasions when the first scenario would have us in the market, we expect that this strategy would perform better than the first (it may fail to for a particular realization). With a point forecast a profit maximizer would trade only on a forecast with a net positive expectation (i.e. forecast return exceeds all trading costs) and they will trade on every forecast with a net positive expectation.

However, we are not pure profit maximizers. Most of us are risk averse to some extent, and few of us would go any buy 10,000 S&P futures contracts if our net expected profit was just $1 on the whole trade (to give a cartoon example). A risk averse trader, which describes anybody who seeks to maximize a risk adjusted returns metric such as the Sharpe Ratio, does not do every trade that has a net positive expectation. They choose to veto the set of trades in which the expected profit does not pay them sufficiently for the risk they are taking in entering the trade.
This is equivalent to adding an additional cost to the trade: I will trade when my point forecast exceeds my trading costs and my risk penalty.

Thus a risk averse trader will outperform a profit maximizing trader in expectation on a risk adjusted basis. This is because they will not do some of the trades that the profit maximizer would enter.

Perhaps suprisingly, we should take this all into account when choosing our basic modelling paradigm. The reason is the Law of Large Numbers, which tells us that when we make a measurement with a large sample size we get a more accurate estimate of the true value of a parameter than when we make a measurement with a small sample size.

When we build a trading system which is optimized by examing a backtest of the trades, we are dealing with a sub-sample of the data available --- the data for the trades actually entered. When we build a forecasting system which is optimized by following a statistical estimation procedure on the returns data, we are dealing with the full dataset available. Thus the accuracy of our parameter estimates, by the Law of Large Numbers, is as high as possible. Furthermore, we are not embedding assumptions about our risk aversion or transaction costs etc. into our estimation procedure.

Defining Some Terms

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.

Identity and Agenda

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.