Question

Why is the R-squared of the portfolio not the same as the average of all stock R-squares?

Answer 1

R-squared of the portfolio is not same as the average of all the stocks because it is reflective of the correlation of overall variance of various stocks in respect to the overall market index and when we are comparing to the overall portfolio then the overall variation of different stocks in respect to the market index will be different from the stock portfolio and even if we are going to average it, we are not going to get the equal result.

This is related to the theory that is standard deviation cannot be found out of the average of all the stocks in the portfolio and standard deviation will always be specific in nature, and variance will be the measure of the square of standard deviation so it will also be not equal to the average of all the stock.

Hence it can be summarised that R squared of the portfolio is not same as the average of all Stock R square