Motivations for Establishing a Short Box Spread

Whether paid on borrowed funds or earned on funds invested, interest is an essential component of arbitrage strategies.Option market makers who trade in several stocks frequently will find that they have conversion positions in one stock and reverse-conversion positions in another. As a result, they might borrow from or lend to themselves.After all, a borrower who pays 5 percent to borrow funds from a bank and receives 4 percent on funds invested with the bank would save 1 percent by using the invested funds directly instead of borrowing.

Consider a market maker who prices conversions and long box spreads assuming a borrowing rate of 5 percent and who prices reverse conversions and short box spreads assuming a lending rate of 4 percent.Further assume that this market maker has accumulated a conversion position in stock 1 that requires $1 million in borrowings.In theory, one might think that the lending rate on net credit positions could be dropped to zero because the borrowed funds on net debit positions cost 5 percent, but there is a complicating factor—the market maker’s capital requirement.

Every position involves risk, and therefore, every position requires a supporting equity requirement to cover that risk. Stock purchased on margin or sold short, for example, requires an equity deposit of 50 percent.While option arbitrage positions involve significantly less risk than long or short stock positions, they still require some equity. Therefore,the decision of how low to lower the lending rate when pricing a net credit arbitrage to fund a net debit arbitrage depends partly on the availability of equity.

When the size of trading positions expands to the limit of available equity, it may not be possible to create additional positions,let alone positions at lower-than-normal interest rates. At other times,when equity is plentiful because positions are small, pricing short box spreads and reverse conversion positions at near-zero lending rates may be practical. This decision will depend on a market maker’s individual circumstances.

Summary:Arbitrage, conceptually, involves trading in two different markets with the goal of profiting from small price differences. Options arbitrage involves buying real stock and selling synthetic stock or, vice versa,
buying synthetic stock and selling real stock.A strategy known as the conversion consists of buying stock, buying
puts, and selling calls on a share-for-share basis.

The call and put have the same strike price and the same expiration date. All options arbitrage strategies are based on the conversion concept. A conversion makes a profit if the time value of the call exceeds the time value of the put by an amount sufficient to cover transaction costs, including borrowing costs.The reverse conversion, as its name implies, is the opposite of a conversion.

It consists of short stock, short puts, and long calls on a share-for-share basis and is established for a net credit. A reverse conversionwill make profit if the interest earned exceeds transaction costs plus the difference of call time value minus put time value.Box spreads are four-part options-only arbitrage strategies. They consist of a long synthetic stock position at one strike price and a short synthetic stock position at another strike price.

A long box spread is established for a net cost, or net debit, and a short box spread is established for a net credit.Although market makers can price arbitrage strategies with a target profit in mind, competition in the marketplace often influences whether the target profit can be achieved. Frequently, market makers must choose between accepting a lower profit and not making a trade.

Deciding whether or not to accept a lower profit is part of the art of trading as a market maker.Knowledge of arbitrage strategies and synthetic pricing relationships helps all traders to evaluate trading strategies and make trading decisions.Knowing that puts are in line with calls or that the options are in line with the stock gives a trader confidence that prices are fair in the current market environment.