I am trying to build a monte-carlo simulator for predicting the possible future values of a portfolio. I have daily historical prices for several assets but I don't know how to correctly estimate annual standard deviation of the returns for each specific asset.
Looking on the web there are three different ways to compute it:
- Calculate std on the daily returns and multiply by sqrt(252)
- Calculate std on monthly returns and multiply by sqrt(12)
- Calculate std on annual returns
But each of them return different results with the last one usually being much larger with respect to the first two. For instance if I apply those strategies to the historical daily gold prices I will have the following annual deviations:
I think the most appropriate one is to directly compute std on annual returns but this will lead to a high deviations which is different to the one I usually see on the web for specific assets.