Feb

4

Under the central limit theorem, the distribution of sample means approximates a normal distribution as the sample size gets larger, regardless of the population's distribution. For a Gaussian distribution a sample size of 30 is fine. For Student T distribution with 3 degrees of freedom, which many of us use, with fatter tails, convergence under CLT requires a sample of at least 130! This would leave only some very broad trade criteria for a robust confidence level.

William Huggins responds:

that sample size is only required is you want to make confidence intervals based on the normal distribution (which requires convergence) but you can make confidence interval from almost any sample size and certainly with any distribution. the difference is that smaller sample T's produce large standard errors (due to fatter tails).

Theodosis Athanasiadis comments:

i believe one should approach testing and risk management differently. for back-testing you care more about the mean of the distribution so you should use either a bootstrap (as William mentioned) or even shrink the outliers using some robust statistic. for risk management/stops you should definitely use fatter tails.


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