Suppose now the rate of EUR/USD is 1. and in half-year, maybe become 1.25EUR/USD, or 0.8 EUR/USD, the probability of each case is 0.5.
what's the Expectation of EUR/USD in half-year? And, what's the Expectation of USD/EUR in half-year?
E(EUR/USD) = 0.5*1.25 + 0.5*0.8 = 1.025 EUR/USD。
answer 2: since 1.25EUR/USD is equivalent to 0.8 USD/EUR , and 0.8EUR/USD is equivalent to 1.25 USD/EUR, so
E(USD/EUR) = 0.5*1.25 + 0.5*0.8 = 1.025 USD/EUR。
Both USD and EUR ate expected to be appreciated. It's confusing me.