Final answer:
The profit made via covered interest arbitrage by borrowing 1 million Japanese yen and investing in the US market for one year at the given rates and exchange rates is approximately $194.90.
Step-by-step explanation:
The question relates to covered interest arbitrage, which is a strategy to profit from the difference in interest rates between two countries while hedging against exchange rate risk. In this example, we start by borrowing 1 million Japanese yen (JPY) at an interest rate of 0.5% and converting it to US dollars (USD) at the current spot exchange rate of ¥100 per dollar, resulting in an investment of $10,000 in the US market. This investment would then earn an interest of 4.5% in the US. After a year, the USD amount with interest is converted back into JPY at the one year ahead forward rate of ¥98 per dollar, and the initial loan plus the Japanese interest is paid back. The profit is the leftover amount in USD after converting it back into JPY at the forward rate and accounting for initial borrowing cost.
Here is the calculation step by step:
- Borrow 1 million JPY at a rate of 0.5%, which must be repaid as 1,005,000 JPY after a year.
- Exchange ¥1,000,000 for $10,000 USD at the spot rate of ¥100/USD.
- Invest $10,000 at 4.5% interest rate in the US, which will grow to $10,450 after one year.
- Exchange $10,450 back to JPY at the forward rate of ¥98/USD, resulting in 1,024,100 JPY.
- Repay the borrowed amount of 1,005,000 JPY. The arbitrage profit in JPY is 1,024,100 - 1,005,000 = 19,100 JPY.
- To state the profits in USD, convert 19,100 JPY to USD at the forward rate, which yields approximately $194.90 (¥19,100 / ¥98 per USD).
Therefore, the profit made via covered interest arbitrage, starting by borrowing 1 million yen and investing in the US market, is approximately $194.90.