T-test of stock data

Question

I have a dataset which contains of 4(4 different portfolios) * 120 rows monthly return data of stocks in the US-market (over ten years).

I want to compare the means of the different portfolios and want to tell if they are significantly different from eachother.

Should I use the monthly stock data or the cumulative data (over the 120 months) for an unpaired two-sided t-test?

When I use the monthly data I have no significance, when I use cumulative data i have some significant p-values between some portfolios. At this point I don't know which data I have to use for this sort of t-test in order to obtain meaningful results

Answer 1

You may try to use ANOVA instead of a t-test since you have more than two groups. Before using ANOVA, you need to run the Homogeneity of Variance (HOV) test. With this, you measure if there is a variational difference between the groups. As HOV, you can use Bartlett test or Fligner-Killeen test. Bartlett test gives more accurate results if the data is normal. If the data is not normal, Fligner test is a better choice. Only in the case that the null hypothesis (no variational difference) is accepted, ANOVA can be used. If the null hypothesis is rejected, then multiple t-tests can be used in place of ANOVA as you have done already.

As far as which dataset to use is concerned, monthly stock data sounds more plausible. An alternative solution could be to use correlations between portfolio returns and to carry out a significance test of those correlations.