Volatility of investment (/w currency hedging)

[egikm]

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.

$$\sigma=\sqrt{(16^2)+(5^2)}$$

Thank you.

 

[mfb]

How would multiplying them make sense? If one gets fixed, do you lose all volatility?

What you can multiply are the actual courses, e.g. for deviations like (1+0.16)*(1+0.05) = 1+0.16+0.05+0.16*0.05. Neglect the last term, and you see that the deviations add.
If the deviations become large, neglecting the last term does not work any more.

 

[egikm]

Oh I see, I thought if it does´t follow the principles of variances (https://en.wikipedia.org/wiki/Variance#Product_of_independent_variables), but this is something different