Futures ArbitrageFutures Arbitrage

Program TradingProgram TradingProgram TradingProgram Trading

► Essentially a cash and carry, or reverse Essentially a cash and carry, or reverse cash and carry, arbitrage between an cash and carry, arbitrage between an index and a basket of stocks related to the index and a basket of stocks related to the index.index.

► One of the confusing factors about One of the confusing factors about program trading is that if the basket pays program trading is that if the basket pays income (ie dividends) during the arbitrage income (ie dividends) during the arbitrage period, then there will be a payment period, then there will be a payment necessary if the underlying is “shorted” necessary if the underlying is “shorted” and a receipt if the underlying is bought.and a receipt if the underlying is bought.

Program Trading cont’dProgram Trading cont’dProgram Trading cont’dProgram Trading cont’d

►Assume you have $10 million in credit Assume you have $10 million in credit to play with. The index is at 405, but to play with. The index is at 405, but the 3 month futures is trading for 420, the 3 month futures is trading for 420, while a 5% riskless rate is available.while a 5% riskless rate is available.

Your expectation should be:

F = 405 * (1.05) (3/12)

= 409.97Thus, futures are too high, so sell futures, buy stocks, and borrow.

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► Difficulty is that futures is on an index with Difficulty is that futures is on an index with 500 stocks, and trading in 500 stocks at once 500 stocks, and trading in 500 stocks at once is near impossible. So, use a proxy basket of is near impossible. So, use a proxy basket of 15 or so stocks and measure relation of 15 or so stocks and measure relation of basket with index (Beta).basket with index (Beta).

► Also, stocks are expected to pay a dividend, Also, stocks are expected to pay a dividend, in total, of $12,000, across the next 3 months. in total, of $12,000, across the next 3 months. As you will buy stocks, you will get the As you will buy stocks, you will get the dividends.dividends.

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► If the basket beta with the index is .90, If the basket beta with the index is .90, you will need:you will need:

to cover the $10,000,000 in funds to cover the $10,000,000 in funds available. Further, you will pay:available. Further, you will pay:

Value portfolio $10,000,000-------------- * contracts, or, -------------- * .90 = 42.86 contractsValue futures

$210,000

$10,000,000 * (1.05)(3/12) - $10,000,000 = $122,722.34in interest on the borrowings.

Program Trading ResultsProgram Trading ResultsProgram Trading ResultsProgram Trading Results

Spot at Maturity -10% 10%Spot/Futures Value 364.5 445.5

Buy Stock Portfolio -900000 900000(1+(0.90*Chg))*value - Initial

Dividends 12000 12000

Short Futures 1189286 -546429-42.86 * ((1+Chg)*Index*$500 - 420*$500)

Borrowing 5.00% -122722 -122722

Position Value 178563 242849