A box spread, commonly called a long box strategy, is an options arbitrage strategy that combines buying a bull call spread with a matching bear put spread. Box spread can be thought of as a vertical spread, but one that must have have the same strike prices and expiration dates.

### Key Takeaways

- A box spread is an options arbitrage strategy that combines buying a bull call spread with a matching bear put spread.
- A box spread’s payoff is always going to be the difference between the two strike prices.
- The cost to implement a box spread, specifically the commissions charged, can be a significant factor in its potential profitability.

## Understanding Box Spread

A box spread (long box) is optimally used when the spreads themselves are underpriced with respect to their expiration values. When the trader believes the spreads are overpriced, they may employ a short box, which uses the opposite options pairs. The concept of a box comes to light when one considers the purpose of the two vertical, bull call and bear put, spreads involved.

A bullish vertical spread maximizes its profit when the underlying asset closes at the higher strike price at expiration. The bearish vertical spread maximizes its profit when the underlying asset closes at the lower strike price at expiration. By combining both a bull call spread and a bear put spread, the trader eliminates the unknown, namely where the underlying asset closes at expiration. This is so because the payoff is always going to be the difference between the two strike prices at expiration.

If the cost of the spread, after commissions, is less than the difference between the two strike prices, then the trader locks in a riskless profit, making it a delta-neutral strategy. Otherwise, the trader has realized a loss comprised solely of the cost to execute this strategy.

BVE= HSP − LSPMP= BVE − (NPP+ Commissions)ML = NPP + Commissionswhere:BVE= Box value at expirationHSP= Higher strike priceLSP= Lower strike priceMP= Max profitNPP= Net premium paidML= Max Loss\begin{aligned} &\text{BVE}=\text{ HSP }-\text{ LSP}\\ &\text{MP}=\text{ BVE }-\text{ (NPP} + \text{ Commissions)}\\ &\text{ML }= \text{ NPP }+ \text{ Commissions}\\ &\textbf{where:}\\ &\text{BVE}=\text{ Box value at expiration}\\ &\text{HSP}=\text{ Higher strike price}\\ &\text{LSP}=\text{ Lower strike price}\\ &\text{MP}=\text{ Max profit}\\ &\text{NPP}=\text{ Net premium paid}\\ &\text{ML}=\text{ Max Loss} \end{aligned}BVE= HSP − LSPMP= BVE − (NPP+ Commissions)ML = NPP + Commissionswhere:BVE= Box value at expirationHSP= Higher strike priceLSP= Lower strike priceMP= Max profitNPP= Net premium paidML= Max Loss

## Box Spread Construction

To construct a box spread, a trader buys an in-the-money (ITM) call, sells an out-of-the-money (OTM) call, buys an ITM put and sells an OTM put. In other words, buy an ITM call and put and then sell an OTM call and put.

Given that there are four options in this combination, the cost to implement this strategy, specifically the commissions charged, can be a significant factor in its potential profitability. Complex option strategies, such as these, are sometimes referred to as alligator spreads.

## Box Spread Example

Intel stock trades for $51.00. Each options contract in the four legs of the box controls 100 shares of stock. The plan is to:

- Buy the 49 call for 3.29 (ITM) for $329 debit per options contract
- Sell the 53 call for 1.23 (OTM) for $123 credit
- Buy the 53 put for 2.69 (ITM) for $269 debit
- Sell the 49 put for 0.97 (OTM) for $97 credit

The total cost of the trade before commissions would be $329 – $123 + $269 – $97 = $378. The spread between the strike prices is 53 – 49 = 4. Multiply by 100 shares per contract = $400 for the box spread.

In this case, the trade can lock in a profit of $22 before commissions. The commission cost for all four legs of the deal must be less than $22 to make this profitable. That is a razor-thin margin, and this is only when the net cost of the box is less than the expiration value of the spreads, or the difference between the strikes.

There will be times when the box costs more than the spread between the strikes so the long box would not work. However, a short box might. This strategy reverses the plan and sells the ITM options and buys the OTM options.

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