I´ve been trying to compute a volatility of invesment with currency hedging and I have a question. Let's take this example. We have our money in a fond copying the S&P500 index, which has 16% volatility, we also know that the current volatility of a dollar toward our currency is 5%. We want to know the volatility of the whole invesment.
Can I compute as following? If so, what is the reason for adding the two deviations instead of mulitplying them considering the volalitity of an index and a currency are mutualy independent.