Question

1. With the information provided you should be able to (1) determine if there are arbitrage opportunities and (2) explain how those arbitrage opportunities can be exploited.
2. The answers should be laid out clearly in numbered steps with simple sentences indicating:
   1. When the trade is happening
   2. If you are buying/selling
   3. If the action is taking place in the spot/forward market
   4. When will the action mature
   5. Show all cashflows and indicate the level of profits.
   6. If the steps are not clearly explained they will not be considered

Suppose you are a speculator who lives in a world where there are two islands: Island A and Island B. These two islands produce and trade rice. Today, the spot price for rice in both islands is trading at 320 cts/bushell and the storage costs in either island is 40 cts/bushell for a period of two weeks. Additionally, since these two islands trade, you can buy shipping to take from one island to the other one. The cost of shipping is 30 cts/bushell from one island to the other and it takes two weeks from the time it leaves one port to reach the final destination. Shipping is a complex process since it requires the grain to be loaded into containers, then stacked and secured inside the vessel along with everyone else’s cargo. Today, the 2-week forward with delivery in Island A is trading at 360 cts/bushell and the 2-week forward with delivery in Island B is trading at 340 cts/bushell. Can you arbitrage this market and how much do you stand to earn for every unit traded? (Suppose you don’t have an initial cash position, but that the interest rate is zero percent).

Answer 1

Yes, we canu arbitrage this market and we stand to earn cts 10 for every unit traded.

1. Buy in the spot market @ island B

2. Enter into a forward contract to sell @ island A in 2 weeks times

3. Ship the goods bought in the spot market @ island B to island A

4. Handover the physical delivery in 2 weeks times @ island A

In order to execute trade at step 1, buy 320 cts. Incur cost of shipping as 30 cts. Interest = 0

Total cost = 320 + 30 = 350

Proceeds from forward sale after two weeks = 360

Hence, arbitrage gain = cts 360 - 350 = cts 10 / bushell