How the Law of Large Numbers Affects Trading Results
Summary
The article explains how sample averages tend to approach their underlying population averages as observations accumulate. A restaurant-rating simulation illustrates that small samples can vary widely, while larger groups of reviews give a more stable estimate. The same idea applies to estimating a strategy’s performance from its returns.
A second simulation draws returns from a strategy assumed to have a Sharpe ratio of 1.5, then compares estimated Sharpes across short and longer samples. The exercise shows why a strategy’s realized Sharpe can look very different from its assumed long-run value over a limited period. The article recommends either using strategies with unusually strong Sharpe ratios, which may reveal their performance sooner, or accepting uncertainty and finding other ways to manage it. These are illustrative simulations rather than evidence from live trading. Their conclusions depend on the assumed return distribution and strategy characteristics; the article does not address how non-normal returns, changing market conditions, or estimation choices could affect the results.
Key ideas
- A sample average can differ substantially from the population average when the sample is small.
- Larger samples tend to make estimates of average performance more stable.
- Short return histories can produce Sharpe estimates far from a strategy’s assumed long-run Sharpe.
- Simulation can illustrate sampling uncertainty, but its conclusions depend on the assumptions used.
- Traders must account for statistical uncertainty, especially when evaluating strategies with limited histories.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.