# Volatility of investment (/w currency hedging)

• I
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.

## Answers and Replies

mfb
Mentor
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.