Question

# Suppose the spot \$/Yen exchange rate is 0.008, the 1-year continuously compounded dollar- denominated rate is...

Suppose the spot \$/Yen exchange rate is 0.008, the 1-year continuously compounded dollar-
denominated rate is 5% and the 1-year continuously compounded yen-denominated rate is 1%. Suppose

the 1-year forward exchange rate is 0.0084. Explain precisely the transactions you could use (being
careful about currency of denomination) to make money with zero initial investment and no risk. What
is such a strategy being referred to in the markets?

The strategy is the interest rate arbitrage.

Let's work with \$100. You can execute the following transactions.

1. Borrow \$100 for 1 year at 5%. Total principal + interest to be returned after 1 year = 100e^0.05 = \$105.13

2. Convert 100 USD to Yen at \$0.008 /yen. Total Yen = 12500

3. Invest 12500 Yen for one year at 1%. Total principal + interest to be received after 1 year = 12500e^0.01 = 12625.63 Yen

4. Enter into futures contract to sell 12625.63 Yen at \$0.0084 per Yen.

After one year

2. Sell yen to receive USD, USD received = 12625.63*.0084 = \$106.06

3. Pay USD loan with interest

Total profit = \$106.06 - \$105.13 = \$0.93

This is interest rate arbitrage