Estimating Trading-System Results with Statistical Measures
Summary
This article outlines statistical tools for evaluating a sequence of trade results. It uses the central limit theorem to explain why averages of samples can approach a normal distribution, while cautioning that financial returns and their derivatives can have heavier tails than a Gaussian model. It also argues that a small trade sample offers weak grounds for conclusions about a strategy.
The worked example calculates mean trade result and sample standard deviation from a set of trade outcomes, interpreting the mean as average expectancy and dispersion as a measure of variability and risk. The article then introduces Z-score as a way to examine whether wins and losses occur in a pattern consistent with random ordering, and discusses using multiple performance characteristics to scrutinize positive results. Its broader lesson is that no single statistic establishes a system’s quality: these measures help identify weaknesses and guide further assessment. The methods remain estimates; normality assumptions can understate rare losses, and the article does not establish that its sample or measures predict future performance.
Key ideas
- Mean trade result estimates the average outcome per trade, while standard deviation describes variability around that average.
- A small sample of trades provides limited evidence about a strategy’s performance.
- Financial returns may have heavier tails than a normal distribution, making Gaussian risk estimates incomplete.
- Z-score can be used to examine whether a sequence of wins and losses appears randomly ordered.
- Several evaluation measures should be considered together because each one reveals only part of a system’s strengths and weaknesses.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.