Futures Arbitrage

1. Futures Arbitrage

2. Program Trading • Essentially a cash and carry, or reverse cash and carry, arbitrage between an index and a basket of stocks related to the index. • One of the confusing factors about program trading is that if the basket pays income (ie dividends) during the arbitrage period, then there will be a payment necessary if the underlying is “shorted” and a receipt if the underlying is bought.

3. Your expectation should be: (3/12) F = 405 * (1.05) = 409.97 Program Trading cont’d • Assume you have $10 million in credit to play with. The index is at 405, but the 3 month futures is trading for 420, while a 5% riskless rate is available. Thus, futures are too high, so sell futures, buy stocks, and borrow.

4. Program Trading cont’d • Difficulty is that futures is on an index with 500 stocks, and trading in 500 stocks at once is near impossible. So, use a proxy basket of 15 or so stocks and measure relation of basket with index (Beta). • Also, stocks are expected to pay a dividend, in total, of $12,000, across the next 3 months. As you will buy stocks, you will get the dividends.

5. Value $10,000,000 portfolio contracts b -------------- * contracts, or, -------------- * .90 = 42.86 Value $210,000 futures Program Trading cont’d • If the basket beta with the index is .90, you will need: to cover the $10,000,000 in funds available. Further, you will pay: $10,000,000 * (1.05)(3/12) - $10,000,000 = $122,722.34 in interest on the borrowings.

6. Program Trading Results