The Box Spread, or long box, is a common arbitrage strategy that involves buying a Bull Call Spread together with the corresponding Bear Put Spread, with both vertical spreads having the same strike prices and expiration dates. The long box is used when the spreads are underpriced in relation to their expiration values.
Buy 1 call at the lower strike price; Sell 1 call at the higher strike price; Sell 1 put at the lower strike price; Buy 1 put at the higher strike price. Use the same expiration date.
Loss potential
Loss is finite under the stated assumptions, but can be substantial. A stock or nonnegative index cannot fall below zero.
Lower strike price plus net opening cost minus higher strike price.
Example
Suppose XYZ stock is trading at $45 in June and the following prices are available:
- JUL 40 put - $1.50
- JUL 50 put - $6
- JUL 40 call - $6
- JUL 50 call - $1
Buying the Bull Call Spread involves purchasing the JUL 40 call for $600 and selling the JUL 50 call for $100. The Bull Call Spread costs: $600 - $100 = $500
Buying the Bear Put Spread involves purchasing the JUL 50 put for $600 and selling the JUL 40 put for $150. The Bear Put Spread costs: $600 - $150 = $450
The total cost of the Box Spread is: $500 + $450 = $950
The expiration value of the box is computed to be: ($50 - $40) x 100 = $1000.
The combined expiration payoff can be fixed under matched contract assumptions. That is not a guarantee of risk-free profit: financing, stock borrow, dividends, early assignment, execution and settlement must also be considered. American-style Box Spreads can be disrupted by early exercise. A price difference alone does not establish an executable arbitrage.
If XYZ remain unchanged at $45, then the JUL 40 put and the JUL 50 call expire worthless while both the JUL 40 call and the JUL 50 put expires in-the-money with $500 intrinsic value each. So the total value of the box at expiration is: $500 + $500 = $1000.
Suppose, on expiration in July, XYZ stock rallies to $50, then only the JUL 40 call expires in-the-money with $1000 in intrinsic value. So the box is still worth $1000 at expiration.
What happens when XYZ stock plummets to $40? A similar situation happens but this time it is the JUL 50 put that expires in-the-money with $1000 in intrinsic value while all the other options expire worthless. Still, the box is worth $1000.
As the trader had paid only $950 for the entire box, their profit comes to $50.
Commissions
These examples exclude commissions and fees. Include all transaction costs when evaluating the profit or loss of a position.
Short Box
The Box Spread is profitable when the component spreads are underpriced. Conversely, when the box is overpriced, you can sell the box for a profit. This strategy is known as a Short Box.
Payoff summary
Maximum profit: Higher strike price minus lower strike price minus net opening cost.
Breakeven
The position breaks even at every stock price only when the net opening cost equals higher strike price minus lower strike price. Otherwise, there is no breakeven stock price.
Net opening cost means everything paid to open the position, less everything received. Include the shares as well as the options. If opening the position brings in money overall, treat that cost as a negative amount.
Amounts are per share before fees. Multiply by the shares covered by the position; standard equity options usually cover 100 shares per contract. If a maximum profit or loss calculation gives a negative amount, use zero. These figures assume matching contracts held to expiration and do not include financing or early assignment.
Compare This Strategy
Optional further reading to help you compare the tradeoffs.
- Box Spread vs Jelly Roll — First identify what is closed or settled at each date.
Advanced Strategy Variations
Build on the core strategies with these less common structures. Match the option legs and expirations when comparing names.
