thanks for looking into this question.
I am comparing an investment strategy against the S&P 500 for a financial article I'm writing.
I compute volatility of the Portfolio in this way, as the square root from the variance computed like this:
[This is for 4 stocks, but it can of course be extended to an amount of i stocks]
So for that I take volatility of all individual stocks and correlation between these stocks, that constitute the portfolio, into account.
However, when I calculate the volatility of the index, I just compute the standard deviation from the logreturns on the index. So no correlation of constituents is taken into account for the index.
What I am wondering: is comparison of the volatility of a portfolio against the volatility of an index valid? Or should you also treat the portfolio as an index when you want to perform this comparison?
Thanks in advance!