I have two set of optimized returns over a period of time and called this portfolio 1 and 2 and two benchmark portfolio (a value-weighted and equally-weighted benchmark). I want to see the difference in performance between portfolio 1 and 2.
In order to gauge the performance (alpha) of the Portfolio 1&2& I have regressed the two (EW & VW) benchmark upon the returns of portfolio 1 & 2. This results in an alpha. However, I could have also regressed (OLS) returns 1 & 2 upon eachother and examine the alpha. However, and this is the problem, the returns of both portfolio 1 and 2 are highly (positively) skewed and have positive kurtosis. How will this affect the alpha?
The bottom line is: how to compare their performance using OLS?
1) Show the alpha of both portfolio (1 & 2) over the benchmark portfolio? So that at least the bencmark portfolio is somewhat normally distributed? And compare those. 2) Or regress both (skewed) portfolio upon eachother?
I know that OLS does not assume normality of variables (only error terms) however I believe the alpha will somehow be biased, but not sure why.