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 how Harry Norman can profit from covered interest arbitrage, we need to compare the returns he would earn from investing in Japanese yen and converting it to U.S. dollars using the forward exchange rate, with the returns he would earn from investing in U.S. dollars directly.
Here are the steps to calculate the potential profit:
1. Calculate the amount of U.S. dollars Harry Norman can invest with $2,000,000:
Amount in US dollars = $2,000,000 / Spot rate (¥/$)
= $2,000,000 / 112.20
= $17,822.17 (rounded)
2. Calculate the future value of the investment in U.S. dollars using the forward exchange rate:
Future value in U.S. dollars = Amount in U.S. dollars * 180-day forward rate (¥/$)
= $17,822.17 * 109.80
= $1,956,583.01 (rounded)
3. Calculate the return from investing in U.S. dollars directly:
Return in U.S. dollars = Future value in U.S. dollars - Initial investment
= $1,956,583.01 - $2,000,000
= -$43,416.99 (rounded)
4. Calculate the return from investing in Japanese yen and converting it to U.S. dollars:
Amount in yen = $2,000,000 * Spot rate (¥/$)
= $2,000,000 * 112.20
= ¥224,400,000
Future value in yen = Amount in yen * (1 + 180-day Japanese yen interest rate / 100)
= ¥224,400,000 * (1 + 2.00% / 100)
= ¥228,888,000
Future value in U.S. dollars = Future value in yen / 180-day forward rate (¥/$)
= ¥228,888,000 / 109.80
= $2,084,036.67 (rounded)
Return in U.S. dollars = Future value in U.S. dollars - Initial investment
= $2,084,036.67 - $2,000,000
= $84,036.67 (rounded)
5. Calculate the profit from covered interest arbitrage:
Profit from arbitrage = Return from investing in Japanese yen - Return from investing in U.S. dollars
= $84,036.67 - (-$43,416.99)
= $127,453.66 (rounded)
Therefore, Harry Norman can profit from covered interest arbitrage by investing in Japanese yen and converting it to U.S. dollars, which would yield a profit of approximately $127,453.66.