Optimal-f
As a traders we build systems and methods that give us an edge. A probability advantage. After finding a trading method that is profitable the logical next step is to find a way to maximize profits. One way to do this is to find the optimal amount to risk on each trade to maximize profits. The optimal-f method is one method of doing this. It is used to find the fraction of equity to risk on the next trade. Unfortunately it is often criticized for taking on too much risk.
A seriously problematic assumption is that maximizing the final profit of a group of trades is the most useful criteria for choosing a level of risk. What optimal-f fails to tell us is the likelihood of getting less satisfactory profit, nor does it give any hint of how bad the drawdown might be.
This shortcoming of the optimal-f method has been noted before. It is true that no one is forced to risk the full optimal-f value, but when it suggests a very large risk the question of "how much risk" remains. A smaller amount should be used in most cases, but how much smaller?
For example, using 50 trades from a profitable S&P e-mini day trading method (Commissions deducted. Data.xls ) the optimal-f risk is 60% of equity. At this risk level optimal-f projects a $6,000 account will end with $43,130,000 after 50 trades.
The problem is that at this level of risk a string of losing trades puts you out of the game. The mean drawdown is 88% and there is a 10% chance that drawdown will reach 98%. The lowest equity curve shows a 45% chance of equity falling below $4,000 (the margin for the 2 e-minis being traded), a 12% chance of going below $1,000 and a 0.1% of falling as low as a few dollars. Ouch! Here are the drawdown and lowest equity charts.
Shooting for maximum profit and damn the drawdown should be tempered by the saying 'Little piggies are cute, but hogs get slaughtered.'
The conventional wisdom is that optimal-f can choose too high a risk. Certainly we do not need to take the high risk level, but that begs the question of what is an optimal risk if drawdown is also considered. Finding true optimal risk is the subject of the next topic.
The charts on this page are produced using the TradeSim software.
Copyright 2002, Larry Sanders
Last update 2002.04.12