1. (Covered Interest Arbitrage) Harry Norman, a foreign exchange trader at UBS’s office in Tokyo has $2,000,000 or its yen equivalent to invest. He faces the following exchange rates and interest rates. Show how can he profit from the covered interest arbitrage?
Spot rate (¥/$) 112.20 180-day forward rate (¥/$) 180-day U.S. dollar interest rate 180-day Japanese yen interest rate 109.80 4.00% 2.00%
To determine whether Harry Norman can profit from covered interest arbitrage, we need to compare the returns from investing in the domestic currency (yen) to returns from investing in the foreign currency (dollar) and hedging the exchange rate risk.
Here's how we can analyze the situation:
1. Calculate the dollar amount Harry can invest in the US with his 2 million yen:
Dollar amount = 2,000,000 yen / 112.20 (spot rate) = $17,821.78
2. Calculate the future value of his investment in yen:
Future value = Dollar amount * (1 + US interest rate) = $17,821.78 * (1 + 4.00%) = $18,531.61
3. Calculate the future value of the investment in yen after converting it back to yen at the forward rate:
Future value (in yen) = $18,531.61 * 109.80 (forward rate) = ¥2,035,357.36
4. Calculate the future value of investing the original amount in yen at the Japanese yen interest rate:
Future value = 2,000,000 yen * (1 + 2.00%) = ¥2,040,000
5. Compare the future values calculated in step 3 and 4. If the future value from investing in yen is higher, there is no profit opportunity from covered interest arbitrage. On the other hand, if the future value from investing in dollars and hedging the exchange rate risk is higher, Harry can profit from covered interest arbitrage.
In this case, the future value of investing in yen is higher (¥2,040,000) compared to the future value of investing in dollars and hedging the exchange rate risk (¥2,035,357.36). Therefore, there is no profit opportunity from covered interest arbitrage.
Note that the example assumes no transaction costs, borrowing and lending rates are equal, and no restrictions on capital mobility. In real-world scenarios, various additional factors and costs may need to be considered.