Expectancy measures a trading strategy’s profit potential. It considers both the reliability or win rate as well as the amount gained by each win. That way, it can compare trading strategies that often win small gains with strategies that rarely win but win big when they do.
Expectancy = (win_rate * avg_win) – (loss_rate * avg_loss)
Van Tharp defines expectancy in terms of risk here, as the average of the R-multiples returned by trading or backtesting the system.
Extra Insight:
Over a large number of trades, the expectancy is the expected gain of the trading strategy. Higher expectancy is generally better. Always avoid trading strategies with negative expectancy.
Scaling the expectancy by risk is indeed useful, especially when it comes time to compare different systems. I use the R-multiples as suggested by Van Tharp for ease of calculation.
Expectancy is also known as the Kelly Criterion for the Bell Labs researcher who proved the equation as an upper bound on the amount to risk. A common language way to say it is to risk an amount proportional to the expected gain. So if the expectancy is 45%, Kelly advocated risking 45% of the account value. This may be mathematically optimal over a large number of trades but it can have a very vicious drawdown! Imagine trading a high expectancy system, say 80% and the first trade is a loss. For a $100k account, that would leave only $20k in the account and a long road to make a 4x gain to break even.
Expectancy is not the be-all and end-all of a trading system. The standard deviation or variance of the results is important. The win rate is too. Both give insight into how psychologically difficult it is to stick to the trading strategy.
Updated: 11/12/08.
Tags: backtesting, expectancy, Kelly criterion, long, R-Multiple, risk, strategy, system, trading, Van Tharp