True or False?
E=exchange rate
Suppose E$/euro = 3/2 and E$/pound = 2 and there is no trade friction, the no arbitrage condition implies that E pound/euro = 2
To determine if the statement "E pound/euro = 2" is true or false, we need to understand the concept of arbitrage and how exchange rates are related.
Arbitrage is the practice of taking advantage of price differences in different markets to make risk-free profits. In the context of exchange rates, the no arbitrage condition states that there should be no risk-free profit opportunity by exchanging currency through different routes.
In this case, we will use the given exchange rates to determine if there is an arbitrage opportunity. Let's calculate the cross-rate E pound/euro using the given exchange rates:
E pound/euro = (E$/pound) / (E$/euro)
Substituting the given values:
E pound/euro = 2 / (3/2)
E pound/euro = 2 * (2/3)
E pound/euro = 4/3
Therefore, the cross-rate E pound/euro is 4/3, not 2. Hence, the statement "E pound/euro = 2" is false.
Explaining the calculation:
To calculate the cross-rate between pound and euro, we divide the exchange rate of pound to dollars (E$/pound) by the exchange rate of euro to dollars (E$/euro). This gives us the rate at which pounds can be exchanged for euros directly without using dollars as an intermediate currency. In this case, dividing 2 by 3/2 gives us 4/3 as the cross-rate between pound and euro.
Note: The no arbitrage condition ensures that if there were a risk-free profit opportunity through exchange rate discrepancies, market participants would exploit it until the rates align. In the given scenario, the calculated cross-rate is different from 2, indicating that there is no arbitrage opportunity.