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I'm in a situation where I need to compute a p-value relating to the hypothesis that the mean daily return from a strategy applied to a group of stocks is different from zero. The usual way to do this would be a t-test, but since there will be correlations between the return time series from each stock and dates of the daily returns will appear in more that stock for most dates the sample size will be inflated.

An example would be taking the return series for one stock and computing the p-value and then doing the same for two types of the same stock (which will have a correlation of 1) and then computing the p-value. The mean and standard deviation will be the same for each case but in the second case there will be twice as many data points. I can think of two ways to approach this.

For each date contained in the total sample compute the mean/sum of all returns for that date and use the resulting sample to compute the p-value from a t-test or using the bootstrap method. Unless the return time series for stock all contain the same dates there will be a difference between using the sum or the mean. Are there any reasons to use one or the other?

The other way of doing it would be to use a monte carlo simulation and resample the returns while preserving the correlation between the stocks. This would very computationally intensive and might be a bit tricky to code up.

Any other ways of doing it?

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The most frequent solution to this problem I have seen is to look at the stocks' "alpha," which we define as the residual return after removing correlating factors. I.e., if there's no correlation between the stock returns you are testing then it sounds like your problem goes away.

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  • $\begingroup$ Yes, but there is a lot of correlation between individual stocks on a daily basis and I'm not sure how to remove it. $\endgroup$ – Freelunch Jan 6 '15 at 21:36
  • $\begingroup$ See "factor models" -- you can use a method like Principal Component Analysis if you want to eliminate all significant correlation, or a popular named factor model for stocks like Fama-French. $\endgroup$ – feetwet Jan 6 '15 at 21:50

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