Optimal Position Size Methods and Other Misconceptions

Optimality usually refers to a solution to a problem derived with respect to some objective function. A solution that is optimal with respect to a given objective function can be non-optimal with respect to another objective function. In trading, for example,  there is the well-known %Kelly method for calculating position size. This method maximizes equity growth without any regard to drawdown.

As I have shown in this paper, the formula for %Kelly is simply the expected gain, or expectation, divided by the average winning trade, a ratio that is known to generate geometric equity growth:

%Kelly = E(T)/AvgW    (1)


E(T) = AvgW × w – AvgL × (1-w)   (2)

where E(T) is the expected gain, AvgW is the average winning trade, AvgL is the average lossing trade and w is the win rate.

However, this method is optimal only with respect to the objective of equity growth. When using such method, the resulting drawdown can be excessive and I would not recommend it to anyone without major modifications.

A better way of dealing with optimal position size determination could be based on an objective function that maximizes equity growth given a constraint on the drawdown. However, future drawdown levels are simply unknown. If one were to know future drawdown levels, then one could size positions using an optimal method so that realized levels never exceed a given percentage of bankroll. This is unrealistic of course given the uncertainty in price moves.

One could use historical drawdown figures to calculate optimal position size that maximizes growth while minimizes drawdown but it is quite unlikely that historical drawdown levels are good estimators of future drawdown levels. Some of those who based position size determination on historical drawdown levels ran into severe problems during the 2008 stock market and commodity sharp decline and even during the recent decline in equities.

So what is a better method for optimal position size determination? Actually I believe there is none and this is the wrong application of optimality. One can talk about optimality when boundary conditions are known, for example a spaceship going from planet A to planet B while minimizing fuel consumption and also minimizing flight time. When the boundary conditions are not know, or worse they are random like it is the case with the markets, it makes no sense to speak about optimal methods. It only makes sense to speak about methods based on proven heuristics. There are such heuristics for all styles of trading, intraday, short-term and trend-following, that old market wizards used to trade very successfully. These specific methods and heuristics will be the subject of another post on position size determination.

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