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You Can't Become Rich In Your Pocket Until You Become Rich In Your Mind | ||||
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Many people think of stock options as slot machines, roulette wheels, or dark horse long shotsOptions, Risk, and Volatility Consider a rather ugly mathematical physicist who goes to the same bar every evening, always takes the second to the last seat, and seems to speak toward the empty seat next to his as if someone were there. The bartender notes this, and on Valentines Day when the physicist seems to be especially fervent in his conversation, he asks why he is talking into the air. The physicist scoffs that the bartender doesnt know anything about quantum mechanics. There is no such thing as a vacuum. Virtual particles flit in and out of existence, and there is a non-zero probability that a beautiful woman will materialize and, when she does, I want to be here to ask her out. The bartender is baffled and asks why the physicist doesnt just ask one of the real women who are in the bar. You never know. One of them might say yes. The physicist sneers, Do you know how unlikely that is? Being able to estimate probabilities, especially minuscule ones, is essential when dealing with stock options. Ill soon describe the language of puts and calls, and well see why the January 2003 calls on WCOM at 15 have as much chance of ending up in the money as Britney Spears has of suddenly materializing before the ugly physicist. Options and the Calls of the Wild Heres a thought experiment: Two people (or the same person in parallel universes) have roughly similar lives until each undertakes some significant endeavor. The endeavors are equally worthy and equally likely to result in success, but one endeavor ultimately leads to good things for X and his family and friends, and the other leads to bad things for Y and his family and friends. It seems that X and Y should receive roughly comparable evaluations for their decision, but generally they wont. Unwarranted though it may be, X will be judged kindly and Y harshly. I tell this in part because Id like to exonerate myself for my investing behavior by claiming status as a faultless Mr. Y, but I dont qualify. By late January 2002, WCOM had sunk to about $10 per share, and I was feeling not only dispirited but guilty about losing so much money on it. Losing money in the stock market often induces guilt in those who have lost it, whether theyve done anything culpable or not. Whatever your views on the randomness of the market, its indisputable that chance plays a huge role, so it makes no sense to feel guilty about having called heads when a tails comes up. If this was what Id done, I could claim to be a Mr. Y. It wouldnt have been my fault. Alas, as I mentioned, it does make sense to blame yourself for betting recklessly on a particular stock (or on options for it). There is a term used on Wall Street to describe traders and others who blow up (that is, lose a fortune) and as a result become hollow, sepulchral figures. The term is ghost and I have developed more empathy for ghosts than I wanted to have. Often they achieve their funereal status by taking unnecessary risks, risks that they could and should have diversified away. One perhaps counterintuitive way in which to reduce risk is to buy and sell stock options. Many people think of stock options as slot machines, roulette wheels, or dark horse long shots; that is, as pure gambles. Others think of them as absurdly large inducements for people to stay with a company or as rewards for taking a company public. I have no argument with these characterizations, but much of the time an option is more akin to a boring old insurance policy. Just as one buys an insurance policy in case ones washing machine breaks down, one often buys options in case ones stock breaks down. They lessen risk, which is the bete noire, bugbear, and bane of investors lives and the topic of this chapter. How options work is best explained with a few numerical examples. (How theyre misused is reserved for the next section.) Assume that you have 1,000 shares of AOL (just to give WCOM a rest), and it is selling at $20 per share. Although you think its likely to rise in the long term, you realize theres a chance that it may fall significantly in the next six months. You could insure against this by buying 1,000 put options at an appropriate price. These would give you the right to sell 1,000 shares of AOL for, say, $17.50 for the next six months. If the stock rises or falls less than $2.50, the puts become worthless in six months (just as your washing machine warranty becomes worthless on its expiration if your machine has not broken down by then). Your right to sell shares at $17.50 is not attractive if the price of the stock is more than that. However, if the stock plunges to, say, $10 per share within the six-month period, your right to sell shares at $17.50 is worth at least $7.50 per share. Buying put options is a hedge against a precipitous decline in the price of the underlying stock. As I was first writing this, only a few paragraphs and a few days after WCOM had fallen to $10, it fell to under $8 per share, and I wished I had bought a boatload of puts on it months before when they were dirt cheap. In addition to put options, there are call options. Buying them gives you the right to buy a stock at a certain price within a specified period of time. You might be tempted to buy calls when you strongly believe that a stock, say Intel this time (abbreviated INTC), selling at $25 per share, will rise substantially during the next year. Maybe you cant afford to buy many shares of IlNrTC, but you can afford to buy calls giving you the right to buy shares at, say, $30 during the next year. If the stock falls or rises less than $5 during the next year, the calls become worthless. Your right to buy shares at $30 is not attractive if the price of the stock is less than that. But if the stock rises to, say, $40 per share within the year, each call is worth at least $10. Buying call options is a bet on a substantial rise in the price of the stock. It is also a way to insure that you are not left out when a stock, too expensive to buy outright, begins to take off. (The figures $17.50 and $30 in the AOL and INTC examples above are the strike prices of the respective options; this is the price of the stock that determines the point at which the option has intrinsic value or is in the money.) One of the most alluring aspects of buying puts and calls is that your losses are limited to what you have paid for them, but the potential gains are unlimited in the case of calls and very substantial in the case of puts. Because of these huge potential gains, options probably induce a comparably huge amount of fantasy-countless investors thinking something like the option for INTC with a $30 strike price costs around a dollar, so if the stock goes to $45 in the next year, Ill make 15 times my investment. And if it goes to $65, Ill make 35 times my investment. The attraction for some speculators is not much different from that of a lottery. Although Ive often quoted approvingly Voltaires quip that lotteries are a tax on stupidity (or at least on innumeracy), yes, I did buy a boatload of now valueless WCOM calls. In fact, over the two years of my involvement with the stock, I bought many thousands of January 2003 calls on WCOM at $15. I thought that whatever problems the company had were temporary and that by 2003 it would right itself and, in the process, me as well. Call me an ugly physicist. There is, of course, a market in puts and calls, which means that people sell them as well as buy them. Not surprisingly, the payoffs are reversed for sellers of options. If you sell calls for INTC with a strike price of $30 that expires in a year, then you keep your proceeds from the sale of the calls and pay nothing unless the stock moves above $30. If, however, the stock moves to, say, $35, you must supply the buyer of the calls with shares of INTC at $30. Selling calls is thus a bet that the stock will either decline or rise only slightly in a given time period. Likewise, selling puts is a bet that the stock will either rise or decline only slightly. One common investment strategy is to buy shares of a stock and simultaneously sell calls on them. Say, for example, you buy some shares of INTC stock at $25 per share and sell six-month calls on them with a strike price of $30. If the stock price doesnt rise to $30, you keep the proceeds from the sale of the calls, but if the stock price does exceed $30, you can sell your own shares to the buyer of the calls, thus limiting the considerable risk in selling calls. This selling of covered calls (covered because you own the stock and dont have to buy it at a high price to satisfy the buyer of the call) is one of many hedges investors can employ to maximize their returns and minimize their risks. More generally, you can buy and sell the underlying stock and mix and match calls and puts with different expiration dates and strike prices to create a large variety of potential profit and loss outcomes. These combinations go by names like straddles, strangles, condors, and butterflies, but whatever strange and contorted animal theyre named for, like all insurance policies, they cost money. A surprisingly difficult question in finance has been How does one place a value on a put or a call? If youre insuring your house, some of the determinants of the policy premium are the replacement cost of the house, the length of time the policy is in effect, and the amount of the deductible. The considerations for a stock include these plus others having to do with the rise and fall of stock prices. Although the practice and theory of insurance have a long history (Lloyds of London dates from the late seventeenth century), it wasnt until 1973 that a way was found to rationally assign costs to options. In that year Fischer Black and Myron Scholes published a formula that, although much ref i ned since, is still the basic valuation tool for options of all sorts. Their work and that of Robert Merton won the Nobel prize for economics in 1997. Louis Bachelier, whom I mentioned in chapter 4, also devised a formula for options more than one hundred years ago. Bacheliers formula was developed in connection with his famous 1900 doctoral dissertation in which he was the first to conceive of the stock market as a chance process in which price movements up and down were normally distributed. His work, which utilized the mathematical theory of Brownian motion, was way ahead of its time and hence was largely ignored. His options formula was also prescient, but ultimately misleading. (One reason for its failure is that Bachelier didnt take account of the effect of compounding on stock returns. Over time this leads to what is called a lognormal distribution rather than a normal one.) The Black-Scholes options formula depends on five parameters: the present price of the stock, the length of time until the option expires, the interest rate, the strike price of the option, and the volatility of the underlying stock. Without getting into the mechanics of the formula, we can see that certain general relations among these parameters are commonsensical. For example, a call that expires two years from now has to cost more than one that expires in three months since the later expiration date gives the stock more time to exceed the strike price. Likewise, a call with a strike price a point or two above the present stock price will cost more than one five points above the stock price. And options on a stock whose volatility is high will cost more than options on stocks that barely move from quarter to quarter (just as a short man on a pogo stick is more likely to be able to peek over a nine-foot fence than a tall man who cant jump). Less intuitive is the fact that the cost of an option also rises with the interest rate, assuming all other parameters remain unchanged. Although there are any number of books and websites on the Black-Scholes formula, it and its variants are more likely to be used by professional traders than by gamblers, who rely on commonsense considerations and gut feel. Viewing options as pure bets, gamblers are generally as interested in carefully pricing them as casino-goers are in the payoff ratios of slot machines. |
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