Quantitative Trading Systems

Position sizing is an important aspect of trading. For a given trading system, proper position sizing makes the difference between slow growth, optimal growth, and bankruptcy.

While I understand and appreciate the work and writing of others, such as Ralph Vince, their methods omit a very important aspect of trading — system health.

If a system remains healthy, and if the characteristics of the trades remain constant, then the formulas that describe position size are applicable. But systems change, as I describe in my earlier post, Trading Systems — Logic, Data and Synchronization, and almost always for the worse.

This post is an outline of the technique I describe in detail in my book, Modeling Trading System Performance, that extends computation of position size beyond the static formula to include:
• The distribution of trading results — rather than single values such as mean, standard deviation, and largest losing trade.
• The time horizon of the forecast.
• The distribution of final account equity.
• The distribution of drawdown.
• The personal risk tolerance of the individual trader.
• The health of the system.

The result is both:
• A value for position size that maximizes account growth while keeping drawdown to a limit.
• A measure of health of the system.

Outline of the procedure

1. Begin with any set of trades — trades actually taken, out-of-sample trades from validation runs, or hypothetical trades. These can come from any system or source — mechanical or discretionary — and are independent of the trading system development platform.
2. Analyze the distribution of those trades, normalized so that each trade is a fixed size — either a fixed dollar amount or a fixed number of futures contracts.
3. Define a time horizon for the simulation, say four years.
4. Generate a sequence of trades, each drawn at random from the distribution or normalized trades, that cover the time horizon.
5. Analyze the sequence, keeping track of the metrics or variables that are of interest, such as final equity, maximum drawdown, percentage of winning trades, etc.
6. Using the modeling and simulation technique known as sampling with replacement, generate many, say 1000, of those sequences.
7. Form and analyze the distribution of drawdowns.
8. Decide on your own personal tolerance for risk. For example, if you would stop trading a system that had a drawdown of more than 20%, your tolerance is 20%.
9. Decide how certain you want to be to avoid exceeding your level of risk. For example, if you are willing to take a 1 in 20 chance that the drawdown will exceed 20%, you want to be 95% certain.
10. Using a fraction of the account balance for each trade, vary the fraction and make several more sets of simulation runs. Analyze the drawdowns after each set. Determine the highest fraction that still limits your risk of a 20% drawdown to less than 5% or 1 in 20. That is your personal position size fraction.
11. Make another set of simulation runs using your personal position size fraction. Keep track of the account growth and other metrics.
12. Analyze the distribution of final equity and determine the annual compound rate of return that your system will achieve most of the time, say 19 times out of 20 or 95%.
13. Decide whether the annual return is worth the risk, and decide to trade the system or not.

As time goes on and the system is traded, periodically rerun the simulations using the most recent results. Update your personal position size fraction. If it decreases, that may be a sign that the system is losing its edge.