I have hard time understanding the following:
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They’re saying two things:
- Trying to determine the standard deviation of the product of two random variables is complicated.
- Trying to determine the standard deviation of a constant times a random variable is easy.
If we were trying to determine the volatility of returns in the domestic currency of an investment in a stock (or a risky bond) denominated in a foreign currency, we would have a difficult time. Here, however, we’re trying to determine the volatility of returns in the domestic of a risk-free bond denominated in a foreign currency. Because it’s risk-free, its return is known, so we simply take the known factor (constant) 1 + rf and multiply that by the standard deviation of the exchange rate to get the standard deviation of the returns in the domestic currency.
Bob’s your uncle.