Suppose I have developed two versions ($A$ and $B$) of a factor model for ranking stocks. Both versions of the model use the same scoring system: stocks are percentile ranked within a given universe of stocks from 0-100% based on a weighted sum of standardized factor scores.
The difference between model $A$ and model $B$ is that $B$ includes several new factors (but overall, mostly the same factors), and also uses drastically different weights for the factors.
Now, suppose I construct two portfolios (one for $A$, and one for $B$) using an identical strategy: I select the Top $N$ stocks based on their model ranking, equal-weighted, and rebalance monthly.
I construct the portfolio returns for each month by taking the cross-sectional mean of returns, giving me two vectors (time-series) of monthly returns, $R_A$ and $R_B$. I have a good sample size, with the time-series starting around 1995.
What I am interested in is comparing the statistics of $R_A$ and $R_B$. To start, I am wondering how I can determine whether the mean of $R_B$ is significantly different from that of $R_A$. A t-test would seem like a reasonable tool to use, but then I'm not sure if it's more appropriate to use a paired t-test vs. unpaired, given the similarity between the two models.
Furthermore, suppose I wanted to compare the standard deviations of returns $\sigma_A$ and $\sigma_B$. How could I assess whether these two statistics differ significantly?
