Thinking About Stock Options

I was thinking of writing here something about the now-concluded college basketball season. But since Great Britain's former Prime Minister Margaret Thatcher passed away recently I've changed my mind. I think the best tribute I can do Thatcher is to continue my recent discussions of some considerations pertaining to market economies. I'm told that was something of an interest of hers.

Besides, I didn't have anything especially incisive to say about basketball.

Today's question, then: First: what IS a stock option?

It is either an option to buy (call) a stock or an option to sell (put) a stock. An option to buy a stock is a contract by which the buyer acquires the right (without incurring any obligation) to purchase shares of a stock at a specific price on a specified date.  An option to sell is much the same, except as you might already have inferred, the buyer of an option to sell acquires the right (again, without obligation) to sell shares of a stock at a specified price on a specified date.

I say “on the specified date” because I will be referring in all that follows to European options, which must in fact be exercised, if at all, on that date. There are other styles of option. The most important alternative is the American option, which may be exercised at any time on or before that date. The valuation mathematics is a good deal simpler for European options, and that is a good-enough reason to stick with them here.

To get a quick sense of the mechanics of it, consider that John has a call that enables him to buy stock in XYZ Corp. on this coming August 1 at $45 a share. Of course, if the stock of XYZ company is actually selling for $45 a share or less than that on that date, then the option will expire unexercised. After all, if John wants XYZ stock at the time of the expiration and he can get it on the open market for $40 he’ll do so, rather than exercise his option of spending an extra $5.

If it is August 1 and the price is above $45 a share, then we know exactly how valuable the option is. If the market price is $55, my option to buy at $45 is on that day worth $10.

Conversely if it is August 1 and the price is $45 a share, my put option with a strike price of $40 is worthless. I can sell for five dollars more on the market than I have a right to sell at by exercising that option. If it is August 1, the price on the market is $30 a share, my put with a strike price of $40 is worth $10.

Complicate Things

Suppose, to complicate things just a bit, that it is now July 15, the exercise date is August 1, and the price of XYZ stock is $40 a share, what can we say about the value today of a call with a strike price of $45?

The phrase to know in this context is under water. The option is not worthless. After all, the share’s market price could rise over the next few days, and end up above my call’s strike price by the exercise date. The possibility that it will have some value then surely gives it some value now. But for now, at any rate, it is under water and hopes for its value on that day amount to the hope that it will break the surface.

Under water options are unsurprisingly cheaper than in-the-money options because they are more likely to expire worthless.

I’ve just accessed an online calculator for stock option value, made some reasonable-sounding assumptions about the volatility and dividend payments of our fictional XYZ stock, and entered them. The calculator tells me that the call option for this underwater stock with a strike price of $45 and a present market value of $40 is worth about $0.14 a share. [Later in this chapter we’ll address the mathematics behind any such calculator. For now, please just take it as the outcome of a black box.]  

We can specify three distinct ways in which an investor or asset manager might express optimism about the value of XYZ stock in the days and weeks to come, along with two distinct ways in which he might express pessimism. The optimist, someone who believes that the price will increase, might put his money where his mouth is by (a) buying the stock, (b) buying a call, that is, an option to buy the stock at its present value in the future, or (c) writing a put. 

Why not stick with actually buying the stock about which I’m optimistic? For one thing, because buying the option to buy is a lot less expensive than actually buying the stock. As a consequence, by buying the call I express my optimism more cheaply. If I buy a call option, I don’t risk $40 on my hypothesis that XYZ stock will soon head upward and get above $45 within a specified period. I only risk 14 cents.

This isn’t just penny pinching. It is risk management. If I’m wrong, the worst that can happen is that my option may expire worthless. The best that can happen? – Well, some high-rollers may decide to buy out XYZ because they admire its smart engineers and want them on its own payroll. They may offer $80 a share to get this deal done and over with quickly. My $0.14 expenditure then gives me the right to buy a share for $40 and immediately sell it for $80, for a profit of $39.86.

As noted, I might also express my optimism by writing a put. If I’m confident XYZ’s price is heading up, I can write and sell to you a contract promising to buy your shares on a date certain at a strike price of $45.  Since the market price is now below that strike price, this option is “in the money,” and would fetch a price in the neighborhood, again given reasonable made-up assumptions, of $5.50.

So … you pay me $5.50. If I’m right and the stock is worth more than $45 a month from now you obviously won’t want to sell me any at that price, and your option expires worthless. I pocket your $5.50. Thanks.

If I’m wrong and the stock is at, say, $35 on the exercise date, I’m obliged to buy your stock on that date for $10 more than its market value. Even though my pain is somewhat lessened by the $5.50 you paid me, I’m still out $4.50 net.  Notice that the writer/seller of the put or call option is incurring an obligation, whereas the buyer in either case is buying a right, without obligation.

For the Pessimist

Let’s turn it around and suppose I’m pessimistic about the future of XYZ stock. I have the same three ways to express that view as an investor that I have to express optimism on the other side. I can sell (and if I don’t have any of this stock to sell, I can borrow some for that purpose); I can write/sell call options. And I can buy puts.

Let’s focus for now on the pessimist who writes call options. That is, he creates and sells a contract in which he promises to sell the holder of the contract a share of XYZ stock at $45 on a date certain. Again, he gets a certain amount of money upfront and, if he is right about his directional speculation, he’ll get to keep that money.

The pessimist option-writer is not in a position exactly symmetrical with that of his optimistic counterpart, though, because the optimistic option writer knows the limits of his possible losses. The pessimist does not. If the optimist writes a put, thereby betting on an increase in the value of XYZ stock, he can be wrong. The worst case is that XYZ stock can go to zero. At any moment, the distance to zero is finite and known. On the other hand, if the pessimist writes a call betting the stock will go down, and it goes up … what is the limit of the loss? How far up can it go?

If I write a call promising to sell you shares at $45, and the stock goes to $65, I lose $20 (minus whatever I got from you up front of course). If the stock goes to $165 during that period, I lose $120. Heck, if it goes to $1165, I lose $1,120. There is in principle no limit.

So, although as we’ve seen above options can be a risk management tool, they can also be a directional speculation that creates the risk that has to be managed.