Generally speaking, any time you hear the term “locked trade” in options, it is referring to a trade that has no risk. However, to be thorough in our answer, we really need to divide locked trades into two groups. One group contains true locked trades that have no risk. The other group has no “theoretical” risk and should really be considered “risk arbitrage” or “pseudo arbitrage. So you must be careful of your interpretation of any strategy that is lumped into the nonspecific category of “locked” trades because they may not be locked in the truest sense of the word.
The box spread belongs in the first group and is a true locked trade. The box spread is made up of a long call + short put at one strike and a long put + short call at another strike. All options have the same expiration date. For example, if you buy a $50 call and sell a $50 put and then buy a $55 put and sell a $55 call you have entered a box spread.
To understand why it is a locked trade, it’s best to break the trades down into synthetic parts. The long $50 call + short $50 put is a synthetic long stock position. A synthetic position is one that behaves exactly like another in terms of the profit and loss profile. So if one trader buys the underlying stock for $50 while another buys the $50 call and sell the $50 put then both have effectively done the same thing. On the flip side, if a trader buys the $55 put and sells the $55 call then he has entered a synthetic short stock position.
The box spread, synthetically, is nothing more than a long stock position matched with a short stock position. If you are long and short the same stock, your account value will not change in any way regardless of the price of the underlying stock. Every dollar the stock rises for the long position will be exactly offset by a dollar loss in the short position and vice versa. Prior to computers, brokers had to manually calculate risks in customers’ accounts. To make it easier, they would draw a “box” around any long and short position of the same underlying since there was no risk. This was a way of eliminating the unnecessary components of risk in the account. For the same reason, the “box” spread has no risk.
What is the above box spread worth? If you have synthetically purchased stock for $50 and effectively sold it for $55 then the box spread is guaranteed to be worth $5. If it is guaranteed, its value today must be the present value of $5. To make the calculation easy, if interest rates are 5% and you have a one-year box, it is worth $5/1.05 = $4.76 today. If you pay $4.76 for the box, it is guaranteed to grow to a value of $5 and you have earned exactly the risk free rate which is what you should earn for a position that has no risk. It is possible for the trader to earn more than $5 if he is assigned early on one of the short positions but he will never earn less.
On the other hand, we can enter another “locked” trade called a reversal. A reversal consists of short stock + long call + short put with the options having the same strike prices. Synthetically, the options make up a long stock position so, again, this appears to be a short stock position matched with a long stock position so should have no risk as well. However, during unusual circumstances, the trader may have to exit his short stock position during early thus exposing him to risk. So while this locked trade has no risk on paper, it certainly does have risk in the real world and is therefore a risk-arbitrage (or pseudo-arbitrage).
Locked trades are ways for the market makers to borrow or lend money to the market. They are one of the many ways to show that, despite their risky assumed nature, options can create risk-free positions. It all depends on how they are used.