Evaluating Trading Systems with Expectancy, Risk Sizing, and Monte Carlo
Summary
This article presents a quantitative framework for judging a trading system through win rate, reward-to-risk ratio, and the fraction of capital risked per trade. It derives the basic expectancy condition and tabulates the minimum win rate associated with several reward-to-risk ratios, as well as the reverse thresholds. Its examples emphasize that a high win rate alone does not establish an edge, and that a positive expectancy can still be undermined by excessive risk or an unrepresentative sample of trades.
The proposed evaluation process uses backtest statistics as inputs to Monte Carlo simulations of randomized trade sequences. These simulations are intended to show how outcomes, losing streaks, drawdowns, and account survival can vary despite identical headline statistics. The article gives numerical illustrations of risk needed to pursue specified growth targets, but those calculations depend on assumed win rates, payoff ratios, and trade counts. The excerpts do not establish that simulated outcomes will match live trading; costs, changing market conditions, and uncertainty in estimated inputs limit the conclusions.
Key ideas
- Expectancy depends on both win probability and the reward-to-risk ratio.
- A minimum win rate can be calculated for a given reward-to-risk ratio, and vice versa.
- Position sizing affects drawdowns and survival even when a strategy has positive expectancy.
- Monte Carlo simulations can illustrate the range of paths consistent with assumed backtest statistics.
- Win-rate estimates become more representative when based on a larger trade sample, though they remain uncertain.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.