This might be a rather basic question that might be closed... but I can't for the life of me understand why in many Google search results the annualization of daily returns is done like this:
r_yearly = (1+r_daily)^252 - 1
However, this is not the correct way to annualize returns in a portfolio optimization context. Meaning, if I were to annualize the daily returns and daily volatility of a stock to generate an annualized Sharpe ratio, it should be like:
r_yearly = r_daily * 252
vol_yearly = vol_daily * 252^0.5
Sharpe_yearly = r_yearly / vol_yearly
The reason why I am posting this is because I have wasted so much time searching about daily returns annualization and I have realized that there is a difference between annualizing and compounding. Most of the Google search results that stated annualization actually mean compounding. Can anyone confirm this and give some useful insights to understand/remember this well?