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I have a sample of 92 monthly observations (n=92) returns of an asset in %. I calculate the variance of these 92 returns. Now, I divide this sample into positive (n=85) and non-positive (n=7) returns. I calculate the variance of both of these subsamples. If I add the variance of the subsamples, they do not add up the the variance of the entire sample. Why?

RJ63
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    Notice that you have two sample means in the case where you split it up, and only one in the overall variance calculation. This is the root of the issue. Without looking at your data, I can thus tell that the sum of the two variances is less than the overall variance. – John Madden Oct 12 '22 at 02:00
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    Piggybacking off what coach @JohnMadden said, note that variance is additive if and only if your two variables are independent. – Sean Roberson Oct 12 '22 at 02:52
  • Thank you John and thank you Sean. – RJ63 Oct 12 '22 at 04:17
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    @Sean Variance is additive iff the variables are uncorrelated. They needn't be independent. RJ63: the fact that a suitably weighted combination of these variances does not equal the overall variance is mathematically related to a difference in mean values in the groups. However, adding the variances isn't relevant to anything in this situation. – whuber Oct 12 '22 at 12:23

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