# The R-squared of the four factor model.

Why does papers such as Fama and French (2010) and Barras et al. (2010) construct equal weighted portfolio of all funds when they analyse the aggregate performance of mutual funds?

They both report an R-squared of 0.98 by weighting funds equally.

When I do 2000 time series regression for all funds, and calculate the average R-squared obtained from all 2000 regressions, I get an average of 0.81.

But, when I construct an equally weighted portfolio of all 2000 funds (similar to the papers mentioned above), I obtain an R-squared of 0.97.

My main question is why does R-squared increase significantly when I construct an equally weighted portfolio of funds compared to taking the average R-squared of 2000 time series regressions.

2. Run each of the S&P500 stock returns of the S&P500 on the market and you get what? Probably an $R^2$ around 0.2-0.5 for each stock? Take the average of those and you get a similar figure;
3. Now, value-weight those stocks and run them on the market factor. Which $R^2$ you get? You get 100%.