Paired or Independent?

Dear all,
For my thesis I have created 2 portfolios of 250 stocks each (randomly selected). I hypothetically buy them on the 1st of January and sell them back on the last trading day of the year.

I have calculated the returns over the year and collected them in 2 groups of 250 each.

Now I would like to know which test I should use to find out which portfolio performed better based on the returns over 1 year. Should I use an independent samples ttest or a paired samples ttest and why?

Thanks for your help!


Super Moderator
If you're comparing returns then you have two indendent samples of returns - i.e. independent samples t-test. If you wanted to compare one portfolio's value at two different time points that would call for a paired t-test.

However - if each portfolio is genuinely randomly selected from the same sampling frame of companies (?), then you already know that any difference between their returns is due purely to random "chance" (or sampling error, to be more specific). I don't see much value in inferential statistics in that scenario. On the other hand, if the two portfolios were randomly selected from two different sampling frames (e.g. a random sample of small companies vs a random sample of large companies), inferential statistics would make more sense.