Question

The South African Rand is trading at USD/ZAR 14.34. The 1-year USD OIS rate is trading at 2.59%, and the comparable one year ZAR rate is trading at 8.40%. You call up a broker and get a quote for a 1-year forward FX rate of 14.75.

Is there an arbitrage opportunity with the broker-dealer that you called? If so, structure a US$ 100 mil (or equivalent) trade that would earn an arbitrage profit. What would the profit be (enter this in millions, so $100,500,000 would be 100.500)?

If there is no arbitrage profit opportunity, enter a "0" in the answer box.

Answer 1

The Expected exchange rate after One year in USD/ZAR can be calculated as

Expected One year Exchange rate = Spot Exchange Rate * (1+ Interest rate of ZAR) / (1+Interest rate of USD)  

=  14.34 * (1+0.084) / (1+0.0259)

= USD/ZAR 15.15212

As this expected rate is different rate from the rate quoted by the Broker, There is an Arbitrage Opportunity

If we have a USD 100 million , we can contract for purchase of USD from the broker after one year and simultaneously convert USD 100 million to ZAR and invest the same in South Africa for one year

Today :

Step 1 :   Borrow USD 100 million @ 2.59%. Convert USD 100 million to ZAR at today's rate,  get ZAR 1434 million , invest this amount @ 8.4% for One year.

Maturity amount is ZAR 1434 * (1+0.084) million =ZAR 1554.456 million

Step 2: Contract with the Broker to purchase USD by selling ZAR 1554.456 million after one year @ USD/ZAR 14.75

After One year

Step 3: Get ZAR 1554.456 million , sell the same to broker @ USD/ZAR 14.75 and get USD 1554.456/14.75 million = USD 105.3868 million

Step 4 : Repay Borrowed USD 100 million @2.59% , we would have to pay USD 100 * (1+0.0259) after one year i.e USD 102.59 million

So, the arbitrage profit in this case is USD (105.3868-102.59) million = USD 2.7968 million

(The amount to enter is 2.7968)