Lessons from the Pros

Options

# Breaking Even and Crossing Over

When a stock stands still, its options don’t.

This is because, unlike the stock it’s based on, every option has a fixed date when it will cease to exist. For each minute of its life that ticks by, an option has a minute less to gain intrinsic value. Intrinsic value accrues when the price of the underlying asset (the stock) moves in that option’s favor (up for calls, down for puts). Because of this, the idea of a break-even price for an option is a bit different than it is for anything else.

If we buy a stock at \$100, then \$100 is our break-even price. But if we buy a call option on that same stock, then our break-even price is different. The stock can not just stay at \$100 for us to break even on the call. It must go up. For example, we might pay \$2.00 for a one-month call option at the \$100 strike price. Since that \$100 call is not in the money, it has no intrinsic value. The entire \$2.00 purchase price consists of time value. If the stock is still at \$100 when the call expires in a month, the call will be worth nothing. When all of the time is gone, so is the time value. For the option to have any value at that time, the stock must have moved up, by enough so that all of the \$2.00 of lost time value is replaced by intrinsic value. In this case, the stock must move to at least \$102.00. That would be our break-even price on the call option.

Note that \$102.00 would also be the break-even price for the person who sold us the call option. They sold it expecting that the stock would not go up that far. We paid them the \$2.00 when we bought the call because we thought it would. If in fact it does go up by exactly \$2.00, then both of us break even.

To see how, let’s change places and imagine that instead of the buyer, we were the call seller. We took in \$2.00 for the call. If the stock is at \$102 when the call expires, we’ll have to buy the stock in the market for \$102, and then sell it to the call buyer for \$100, losing \$2.00. That consumes the \$2.00 we originally got for the call, so we break even on the whole transaction. Alternatively, we could have just bought the call back for \$2.00, which would result in the same \$0.00 profit/loss.

Now let’s combine that call sale with a long stock position. Say that we bought that stock for \$100 at the same time we sold the \$100 call for \$2.00. This is a covered call position. Our obligation to sell the stock is covered, because we have the stock and can deliver it. From our point of view we are looking to make \$2.00 or 2% on our \$100 stock investment in a month. We are just looking to generate income on our \$100 investment, and we would be satisfied with 2% in a month.

Now once again at expiration the stock is at \$102, so that the call is worth \$2.00. If we want to keep the stock, we’ll have to buy back that call for \$2.00, breaking even on it. But we do have the \$2.00 profit on the stock. So our profit overall is still \$2.00.

Now imagine that the stock goes higher than \$102. Say that at the option’s expiration the stock is at \$103. As the call seller, how did we do?

Well, since that \$100 call is \$3.00 in the money, it’s now worth \$3.00. If we want to avoid losing the stock, we’d have to pay that \$3.00 to buy it back, for a loss of \$1.00. So we made \$3.00 on the stock and lost \$1.00 on the call, for a net profit of \$2.00. Alternatively, we could allow the stock to be taken from us. In that case we receive the \$100 strike price for the stock, for no gain or loss. Adding in the \$2.00 we got for the call, we still have the same \$2.00 profit. That’s what we were looking for, so our plan has worked.

Going a step further, imagine that instead of the covered call position, we had bought a vertical spread. We did not buy any stock. Instead we bought a \$95 strike call for \$6; and simultaneously sold the \$100 call for \$2.00. Our net debit (cash paid out) is \$4.00. What is our break-even price now?

We have to recover our \$4.00 debit in order to break even. At expiration each option will be worth only its intrinsic value. If the \$95 call that we own is worth \$4.00 more than the \$100 call that we are short, that will be the case. For the \$95 call to be worth \$4.00, the stock would have to be at \$95 + \$4 or \$99. At that price, the \$100 call would be out of the money and worthless – we would not have to buy it back. So the spread in total would be worth \$4.00. \$99.00 would be our break-even price on this position.

Our object in the vertical spread, of course, is not to break even but to make money. We’d like the stock to end up above the \$100 strike price of the call we sold. If that happened, then the \$95 call would be worth \$5 more than the \$100 call. We could sell the spread (sell the long call and buy back the short one) for a net of \$5.00. After subtracting the debit of \$4.00, that would represent a \$1.00 profit on a \$4.00 investment, or 25% in a month.

In this scenario, in addition to the break-even price, there is also a crossover price. This is the price at which it would have been more profitable to buy the \$95 call alone, rather than turning it into a spread by selling the \$100 call. This is a useful idea when we are comparing bullish trade ideas. In this case, the best-case profit on the spread is 25% as calculated above. To make 25% on the 95 call alone, that call would have to have been worth 25% more than the \$6.00 we paid for it, or \$7.50. That means a stock price of \$95 + \$7.50, or \$102.50. At any price below this, the spread is more profitable, in percentage terms, than the \$95 call alone. If we believe that the stock will go up, but not beyond \$102.50, then the spread will be a better trade than the call alone.

We’ll explore this idea of the crossover price further in future articles. It can help us to decide between different trade possibilities, tailoring our trades to our market outlook.