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 if Harry Norman can profit from covered interest arbitrage, we need to compare the returns from investing in yen and investing in dollars.
Step 1: Calculate the forward premium/discount:
Forward Premium/Discount = (Forward Exchange Rate - Spot Exchange Rate) / Spot Exchange Rate
Forward Premium/Discount = (109.80 - 112.20) / 112.20
Forward Premium/Discount = -0.0213 or -2.13% (approximately)
Since the forward premium is negative (-2.13%), it represents a discount on the forward exchange rate.
Step 2: Calculate the expected future value of the investment in yen:
Expected Future Value in Yen = Investment Amount * (1 + Japanese Yen Interest Rate) * (1 + Forward Premium/Discount)
Expected Future Value in Yen = $2,000,000 * (1 + 0.02) * (1 - 0.0213)
Expected Future Value in Yen = $2,000,000 * 1.02 * 0.9787
Expected Future Value in Yen = $1,998,800 (approximately)
Step 3: Convert the expected future value from yen to dollars:
Expected Future Value in Dollars = Expected Future Value in Yen / Forward Exchange Rate
Expected Future Value in Dollars = $1,998,800 / 109.80
Expected Future Value in Dollars = $18,173.03 (approximately)
Step 4: Compare the expected future value in dollars with the initial investment:
Profit/Loss = Expected Future Value in Dollars - Initial Investment
Profit/Loss = $18,173.03 - $2,000,000
Profit/Loss = -$1,981,826.97 (approximately)
As the "Profit/Loss" value is negative, it indicates a loss. Therefore, Harry Norman cannot profit from covered interest arbitrage in this scenario.
To determine if Harry Norman can profit from covered interest arbitrage, we need to compare the returns from investing in Japan and investing in the United States.
1. Calculate the return from investing in Japan:
- Convert the $2,000,000 to yen using the spot rate: $2,000,000 * 112.20 = ¥224,400,000
- Determine the future value of the investment after 180 days using the Japanese yen interest rate: ¥224,400,000 * (1 + 2.00% / 2) = ¥228,888,000
2. Calculate the return from investing in the United States:
- Determine the future value of the investment after 180 days using the forward rate: ¥224,400,000 / 109.80 = $2,042,781.46
- Convert the future value back to yen at the spot rate: $2,042,781.46 * 112.20 = ¥229,364,769.91
3. Compare the returns:
- The return from investing in Japan is ¥228,888,000
- The return from investing in the United States and converting back to yen is ¥229,364,769.91
Since the return from investing in the United States and converting back to yen is higher than the return from investing in Japan, Harry Norman can profit from covered interest arbitrage.
Here’s how the profit is made:
- Harry Norman borrows ¥224,400,000 in Japan at a 2.00% interest rate.
- He converts the yen to dollars and invests the $2,000,000 in the United States.
- After 180 days, he repays the yen loan plus interest, which amounts to ¥228,888,000.
- He converts the dollar investment back to yen at the forward rate and gets ¥229,364,769.91.
- By repaying the yen loan and converting the dollar investment back to yen, he gains ¥229,364,769.91 - ¥228,888,000 = ¥476,769.91 in profit.