Q: Could you please explain more on "locked" option trades such as box spreads?

A: 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.

Q: I have a trading question that nobody could answer for me. My question is about the collar (ATM Collar). Here is an example. Today, 2/28/07, the DIA is trading at exactly 123. If I buy 100 shares of DIA and buy May 123 put for 2.70 and sell May 123 call for 3.40, do I automatically lock in a profit of .70 at expiration no matter what the price of the DIA will be? I really appreciate your answer. Thank you.

A: Yes, you are correct that you would lock in the guaranteed 70-cent profit by purchasing the stock, selling the call, and buying the put. However, before you get too excited about risk-free money, you must measure that return against other risk-free alternatives.

The May options expire on 5/18/07, which is 79 days away from the 2/28/07 posting date of your question. Let’s find out what interest rate is necessary to match the 70-cent return and then compare that rate to current market rates. If you invest $123 for 79 days, it would take an interest rate of about 2.6% to yield 70 cents interest. We can find that by solving for i (interest rate) in the following equation: $123 * i * 79/360 = 0.70. If you solve for i, you’ll find that it is 2.59%.

Rather than buy the DIA collar, the above equation shows that you could, instead, take your $123 and place it in a money market for 79 days and get the same guaranteed 70-cent return if your broker pays an interest rate of 2.6%. With the Fed funds rate at 5.25%. I suspect that most brokerage firms are paying far more than 2.6%. However, even if they are, we must account for commissions. There is no cost for putting money in the money market but there are THREE commissions for the collar trade you referred to.

If your broker charged you $1 for each of the three trades, you will have effectively invested $126 to gain the 70 cents interest. If you solve the earlier equation by substituting $126 for $123, you’ll find that the required interest rate is now 0.25%, or one quarter of one percent. Because most brokers would definitely charge more than $3 for the above trades, it’s safe to say that you are better off in the money market.

Many new traders think that risk-free trades in the options market are a source of “free money” but you must remember that the market prices all assets according to risk. If the trade is risk-free, you’re going to earn the risk-free rate. However, to accomplish this using the collar, you must pay three commissions and three bid-ask spreads and that’s why the resulting interest rate is so low thus making the money market alternative more attractive.

For those who may be wondering why the collar is risk-free, it’s easy to see if you break it down into the resulting rights and obligations created by the options. To create a collar, the trader buys the shares, sells the call (has the obligation to sell shares), and buys the put with the same strike (has the right to sell shares). In this example, if DIA is above $123 at expiration, the investor will be assigned on the short call and receive $123 cash. If DIA is below $123 at expiration, the trader will exercise the put and receive $123 cash. No matter what happens to the price of DIA, the trader is guaranteed to receive $123 at expiration. Alternatively, the trader could place an amount of money into the money market and also be guaranteed to receive $123 at expiration. In this example, the trader receives a net credit of 70 cents for the collar so has effectively deposited $123 – 0.70 = $122.30 and will receive $123 at expiration, which is synonymous with an interest rate of 2.6%.