For better understanding of currency hedging and its impact on volatility, we outline some basic formulas of hedged and unhedged returns. The value of the unhedged asset in the investor's base currency is given by
where is the value of the foreign asset at time t in foreign currency and St is the exchange rate at time t, measured in units of investor's home currency per one unit of foreign currency.
The log return of the unhedged asset is the sum of the asset log return in local currency and the log return on holding foreign currency:
where is the log of the value of the unhedged foreign asset exposure in domestic currency at time t, is the log of the foreign asset value in foreign currency at time t, and st is the log of the exchange rate, measured in units of investor's home currency per unit ...