Question

Suppose you observe the following 1-year discrete interest rates, r_USD = 4%, r_EUR = 3%, spot exchange rates S_USD/EUR = USD 1.45/EUR, and futures prices F_USD/EUR = USD 1.48/EUR. Futures contracts are available on €10,000. How much risk-free arbitrage profit could you make on 1 contract at maturity from this mispricing?

Select one:

a. $130.55

b. $153.33

c. $159.22

d. $142.44

Answer 1

Solution:-

Current exchange rate= USD 1.45/EUR

The interest rates in US are 4% and in Europe are 3% per annum. Taking into account the impact of interest rate parity, the exhcnage rate expected after one year should be as follows:

Exchange rate after one year (interest rate parity)= Current exchange rate*(1+r_usd)/(1+r^EUR)= (1+ 1.45*(1+4%)/(1+3%) = USD1.464078/EUR

Therefore, as per interest rate parity, the exchange rate expected after one year will be USD 1.464078/EUR

The forward exchange rate available in the futures market is USD 1.48/EUR. This means that the EUR is overvalued in the forward market and the arbitrager can make profit by selling Euros in futures market. The amount of profit is calculated as the euros invested multiplied by difference of exchange rate in futures contract and exchange rate expected after one year, In other words, the arbitrager is trying to take advantage of the mispricing or overvaluation of euro as the value of euro in forward market is more than the fundamental value of euro based on interest rate parity. the calculations are as follows:

Dollar profit on arbitrage trade= Euros per contract*(USD exchange rate in futures contract - USD exchange rate after one year) = 10,000*(1.48-1.464078) = $159.22

Therefore, the correct option is option c.