Consider a 1-day standard deviation of simple return JPY VaR metric. A portfolio’s return is a unitless quantity; so is its conditional standard deviation of return. Must we specify a base currency (JPY) for this VaR metric? Couldn’t we just call it a 1-day standard deviation of simple return VaR metric?

It is always necessary to specify a base currency because risk depends upon the base currency. Suppose an investor holds a cash position of EUR 5MM. The position’s one-day standard deviation of return EUR VaR is 0, but its one-day standard deviation of return USD VaR is positive due to uncertainty in the USD/EUR exchange rate.