Exercise Solution 1.9
It is always necessary to specify a base currency for a PMMR because risk depends upon the base currency. Suppose an investor holds a cash position of EUR 5MM. The position’s standard deviation of one-day EUR return is 0 because the position’s value today is EUR 5MM and its value tomorrow will also be EUR 5MM. On the other hand, its standard deviation of one-day USD return is positive due to uncertainty in the USD/EUR exchange rate. We may know the USD/EUR exchange rate today, but we don’t know what it will be tomorrow. It will impact the USD value of our position.