结构推理
The euro is quoted at “€0.008300/￥ Bid and €0.008200/￥ Ask” in Tokyo. The yen is quoted at “￥121.20/€ Bid and ￥121.10/€ Ask” in Paris. Convert the Tokyo quote into a ￥/€ quote and then answer these questions.
A、Calculate the bid/ask spread on the euro (in the denominator) as a percentage of the bid price from the Japanese and from the French perspectives.
B、Is there an opportunity for profitable arbitrage? If so, describe the necessary transactions using a €1 million starting amount.
【正确答案】In the Tokyo quote of “€0.008300/￥ Bid and €0.008200/￥ Ask,” the bid price is higher than the ask price. Consequently, the currency being quoted must be the euro (in the numerator of the quotes). Converting the Tokyo quote yields a direct quote for the euro of “￥121.21/€ Bid and ￥121.36/€ Ask.” Similarly, the Paris quote of “￥121.20/€ Bid and ￥121.10/€ Ask” indicates that euros can be purchased at ￥121.10/€ and sold at ￥121.20/€.
A、Percentage bid-ask spreads on the euro are as follows:
Tokyo quote for the euro: (￥121.36/€ - ￥121.21/€)/(￥121.21/€) = 0.121/%
Paris quote for the euro: (￥121.20/€ - ￥121.10/€)/(￥121.10/€) = 0.083/%
B、The winning strategy is to buy euros from the Paris bank at the ￥121.20/€ euro ask price and sell euros to the Tokyo bank at the ￥121.21/€ bid price. Buying €1 million in Paris yields (€1 million)/(￥121.20/€) = €121.20 million. Selling €1 million in Tokyo yields (€1 million)/(￥121.21/€) = €121.21 million. Your arbitrage profit is €0.01 million, or €10,000