Quant foundations · Foundations
Statistical analysis in trading
Also called: trading statistics, statistical testing of strategies
Statistical analysis in trading tests whether an observed pattern in returns is distinguishable from chance, and how large and stable it is.
Definition
Statistical analysis in trading applies inference methods, such as estimation, hypothesis testing, confidence intervals and resampling, to market data and strategy results. Its goal is to separate effects that are likely real from those that chance alone could produce.
It underpins strategy evaluation, risk estimation and the comparison of competing models.
Intuition
Returns are noisy enough that random strategies regularly look skilful over months or even years. Statistics quantifies how surprising a result is under a no-effect baseline, and how much the estimate would vary with a different sample.
Two questions matter more than any single test: is the effect large relative to its uncertainty, and does it persist on data that played no part in finding it?
How it's calculated
For a strategy with n independent period returns, sample mean r̄ and standard deviation s, a basic test of whether the mean return differs from zero is
t = r̄ / (s / √n)
which under the null approximately follows a Student-t distribution with parameter n − 1. For autocorrelated or overlapping returns, use Newey–West standard errors or a block bootstrap instead.
When m variants have been tested, the chance that at least one passes at level α by luck alone is about 1 − (1 − α)m. Corrections such as Bonferroni (α / m) or false-discovery-rate control keep the overall error rate in check.
Confidence intervals, for example from bootstrapping the return series, describe the range of plausible effect sizes, which is often more useful than a p-value.
Example: a strategy with a mean monthly return of 0.5% and a monthly standard deviation of 4% over 60 months has t = 0.5 / (4 / √60) ≈ 0.97, well within what chance produces. The same mean and volatility over 240 months gives t ≈ 1.94, still borderline.
How to read it
A t-statistic of 2 on a single pre-specified test is modest evidence; after searching through many variants it is weak. Prefer results that hold across sub-periods, assets and reasonable parameter changes.
Report effect size, uncertainty and sample size together, and compare against a simple baseline such as holding the asset.
Common mistakes
- Running many tests and reporting only the significant ones.
- Treating overlapping returns as independent, which overstates significance.
- Ignoring regime changes that make the sample unrepresentative.
- Reading a non-significant result as proof of no effect when the sample is small.
- Quoting a p-value without the effect size, which hides whether a result matters in practice.
In Saqrid
In SV you can test strategies built on formula signals and keep a log of runs to compare.
Open SV.
Go deeper
Saqrid Institute lesson: Hypothesis Testing: Significance, Errors & Power. Lesson text is open to read without an account.