Interest Rate Arbitrage

You observe that the NZD/USD spot exchange rate (i.e., the price of 1 New Zealand Dollar in terms of U.S. Dollars) is 0.7234 and the 3-month NZD/USD forward exchange rate is quoted at 0.7212.

Does an arbitrage opportunity exist given that the 3-month deposit rates in New Zealand and the U.S. are 0.35% and 0.08% per annum, respectively? If so, outline an arbitrage strategy and explain step-by-step why your strategy yields risk-free profits.

Answer:

An arbitrage opportunity exists in the 2 given markets (forex and money markets) since risk-free profit can be made.

The strategy is given below:

1. Convert NZD100 into USD at the spot exchange rate NZD/USD 0.7234

We will receive 100 x 0.7234 = USD 72.34 (since 1 NZD = 0.7234, we multiply NZD 100 by 0.7234 to find how much USD would be received on conversion)

There is no risk in the conversion since it is at spot rate.

2. Now invest USD 72.34 in a 3 month deposit at 0.08% per annum.

At the end of 3 months the deposit will give us USD 72.34 + (USD 72.34 x 0.08/100 x 3/12) = USD 72.34+ (USD 0.057872 x 3/12) = USD 72.34 + USD 0.014468 = 72.354468 or USD 72.35

There is no risk in the deposit since we are assured the principal and interest at the end of the 3 month term.

3. Now convert this amount at the forward exchange rate of NZD/USD 0.7212 since this would now be the (3 months later) current spot rate. We will receive NZD 72.35 / 0.7212 = 100.3189 or NZD 100.32

There is no risk in the conversion as we have avoided the forex rate risk by our deposit and its conversion at the (3 month later) spot rate.

4. So we have made a riskless profit of NZD (100.32 - 100) = NZD 0.32 out of our initial amount of NZD 100