A foreign exchange arbitrageur notices that the Japanese yen to U.S. dollar spot

Question

A foreign exchange arbitrageur notices that the Japanese yen to U.S. dollar spot exchange rate is ¥108/$ and the three-month forward exchange rate is ¥107.30/$. The three-month $ interest rate is 5.20 percent per Annum and the three-month ¥ interest rate is 1.20 percent per annum.

A. Is the interest rate parity holding? Also, you need to indicate amount of mispricing, if any.

B. Is there an arbitrage possibility? If yes, what steps would be needed to make an arbitrage profit? Assuming that the arbitrageur is authorized to work with $1,000,000 for this purpose, how much would the arbitrage profit be in dollars???

Explanation / Answer

Answer:A. For three months, i ¥ =0.30% and i $ = 1.30 %. the spot exchange rate is $0.009259/¥ and the forward rate is $0.00931966/¥. Thus, (1+ i $ ) = 1.013 and (F/s) (1 + i ¥ ) = (0.00931966/0.009259) (1.003) = 1.009571

Because the left and right sides of IRP are not equal, IRP is not holding.

Answer:B Because IRP is not holding, there is an arbitrage possibility:

Because 1.013 >1.009571 ,

we can say that ¥ the interest rate quote is less than what it should be as per the quotes for the other three variables. Equivalently, we can also say that the $ interest rate quote is more than what it should be as per the quotes for the other three variables. Therefore, the arbitrage strategy should be based on borrowing in the ¥ market and lending in the $ market.

The steps would be as follows:

1. Borrow ¥ 9259.259 for three months at 0.30%. Need to pay back $9259.259 × (1 + 0.003) = ¥9287.0370 three months later.

2. Convert ¥9259.259 to $ at the spot rate to get $ 1000000.

3. Lend $1000000 for three months at 1.30%. Will get back ¥ 1,000000 × (1 + 0.013) = ¥ three months later.

=1013000

4. Sell $ 1,013000 three months forward. The transaction will be contracted as of the current date but delivery and settlement will only take place three months later. So,three months later, exchange 1,013000 for 1,013000/107.30 =¥ 9440.820.

The arbitrage profit three months later is¥ 9440.820- ¥9287.0370= ¥153.783

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