Fortune's Formula (18 page)

B
LACKJACK HAD CEASED
to be as profitable or fun as it had once been for Ed Thorp. “I realized that if I pushed it, sooner or later some unpleasant physical things would happen in Nevada,” he said. By 1964 he decided to direct his talents toward the biggest casino of all: the stock market.

Thorp had accumulated about $25,000 in blackjack winnings plus another $15,000 in savings, mainly from book royalties. During the New Mexico summer breaks of 1964 and 1965, he made a systematic effort to educate himself on the market. One of the books he read was Paul Cootner’s
The Random Character of Stock Market Prices
(1964). This was published by the MIT Press and collected key articles on the random-walk model.

Thorp read a news article saying that some people were buying silver. The demand for silver had long been greater than the supply. The difference had been made up by melting down and reclaiming old jewelry and other silverware. Stores of reclaimable silver were running low.

Using his savings, Thorp bought some silver at about $1.30 an ounce. It went up to about $2. He bought more silver on margin (with borrowed money). The price fell. Thorp couldn’t meet the margin calls and lost about $6,000, a crushing sum at the time. “I learned an expensive lesson,” he said. The lesson was: You are unlikely to get an edge out of what you see in the news.

A couple of Texas investors contacted Thorp. They had heard of him through the blackjack publicity. They identified themselves as experts in picking life insurance stocks and wanted to know if Thorp might be able to help them. Thorp met with the investors in Dallas. He studied the life insurance industry and grew confident enough to put some of his own money into companies the pair recommended. The stock “promptly went down the tubes.” All Thorp got out of the experience was a set of defective steak knives the pair sent him as a gift.

Back in Las Cruces, New Mexico, Thorp did what many small investors do. He checked out the “get rich quick” ads in financial magazines. There were hundreds of stock market systems for sale. An ad in
Barron’s
caught his eye. It was for a company called RHM Warrant Service.

The service Paul Samuelson had subscribed to was still in business. It was run by a certain Sidney Fried who claimed it was possible to buy warrants for pennies and sell them for dollars. Thorp sent away for the book.

As he read it, “I got thinking about what it is that determines the price of a warrant,” Thorp said. “In about an hour of thinking and sketching on scratch paper, I realized that there was almost undoubtedly a simple way to price these things.”

Warrants were the only kind of widely traded stock option then. One of the warrants Thorp began following was issued by Sperry Rand, the company that made the first mass-produced digital computer. On March 17, 1958, Sperry Rand issued a warrant that entitled the owner to buy one share of Sperry Rand stock for the price of $25 (the “strike price”). The warrant expired on September 16, 1963, meaning that at the close of business on that date, it became worthless.

What is a fair price for a warrant? The warrant would be immediately valuable if and when Sperry Rand stock traded for more than $25 a share. Should Sperry Rand be selling for $29 a share, the warrant would be worth at least $4, for you could use it to buy a share of Sperry Rand at a $4 discount from the going price.

That does not mean the warrant would be worthless when Sperry Rand was selling for less than $25. You can still sell a warrant to someone who thinks that stock will rise above the strike price before the expiration date.

The newspaper listings quoted prices for warrants, just as they listed handicapper’s odds for horse races. The people pricing warrants factored in a lot of gut instinct. When you say that a warrant is worth such and such, you are essentially quoting odds that the stock will rise above the strike price before the expiration. You are further guessing by how much it might rise above that price. This is a complex judgment call. The warrant price must reflect such scenarios as the failure of a new product launch, the resolution of a lawsuit, or an executive selling a big block of stock to pay for a Matisse. The butterfly whose flapping causes a hurricane could lead to the sinking of a yacht full of Sperry executives, pummeling the stock’s price. How can anyone predict such contingencies systematically?

Then Thorp thought of the random walk model. Assume that there is no possible way of predicting the events that move stock prices. Then buying a stock option is placing a bet on a random walk. Thorp knew that there were already precise methods for calculating the probability distributions of random walks. They depend on the average size of the random motions—in this case, how much a stock’s price changes, up or down, per day.

Thorp did some computations. He found that most warrants were priced like carnival games. They cost too much, given what you can win and your chance of winning it. This was especially true of warrants that were within a couple of years of expiring. Traders were too optimistic about the prospect of stock prices rising in that time.

There is nothing you can do about a carnival game that costs too much except to refuse to wager. But should you find a warrant that costs too much, you can sell it short. This flips the unfavorable odds in your favor.

A trader who sells short is selling a security he doesn’t yet own. The trader borrows the security from a third party and sells it at today’s price. He agrees to deliver the same security to the third party at a future date. The trader is hoping that the price of the security will fall in the meantime. He will then be able to buy the security for less money than he received in the sale.

Selling short carries an unpleasant risk. When the price of a company’s stock shoots up, the value of its warrants goes up, too. Theoretically, there is no limit to how much a stock’s (or warrant’s) price might rise. That means that there is no limit to how much a short-seller might lose.

Compare this to the more usual situation of buying a stock or warrant (“buying long”). You cannot lose more than you paid for the securities. That is a painful enough prospect, but at least the losses are capped. The short-seller is liable, potentially, for infinite losses.

There is a time-honored way of reducing this risk. It is to buy and sell short nearly the same thing simultaneously. Jay Gould bought “underpriced” gold and sold it where it was “overpriced.” Gould did not have to know which price was “correct” or even whether such words have meaning. He did not have to predict whether the price of gold was going to go up or down. By buying
and
selling, Gould eliminated practically all the risk of owning gold. He locked in the “irrational” price difference as a sure profit.

Most forms of arbitrage loosely follow Gould’s design. An arbitrageur buys an underpriced security
and
simultaneously sells short a closely related security that is overpriced. Here “closely related” means a security whose price has to rise or fall apace with the original security. In the case of warrants or options, the “closely related” security is the company’s stock itself.

This scheme may sound confusing on first hearing. It is much like Kelly’s “bet your beliefs” horse race system. In a race with just two horses, one horse has to win and the other has to lose. Because of this obvious correlation, it is possible to eliminate the usual risk of betting on horses. By betting on both horses, you can’t lose.

The value of an option or warrant goes up as the price of the underlying stock does. By buying the stock and selling the option, you create a “horse race” where one side of the trade has to win and the other side has to lose. And if you know the “true” odds better than everyone else and use your beliefs to adjust your bets, you can expect a profit.

It can be shown that these long-short trades are Kelly-optimal. They were in use in the stock market long before Kelly, though. Thorp’s innovation was to calculate exactly how much of the stock he had to buy to offset the risk of short-selling the warrant. This technique is now called “delta hedging,” after the Greek letter used to symbolize change in a quantity.

In delta hedging, the paper profit (or loss) of any small change in the price of the stock is offset by the change in the price of the warrant. You make money when the “irrational” price of the warrant moves into line with the price of the stock.

John Maynard Keynes is famous for remarking that the market can remain irrational longer than you can remain solvent. It does little good to buy something at an irrational price unless you are sure you can sell it for profit at the “reasonable” price. You have to know when all those other “irrational” people will come to their senses and agree with you.

That was the beauty of Thorp’s scheme. The market can’t persist in its irrational valuations of warrants. On the expiration date, the warrant goes
poof!
—and with it, any irrational notion of its value.

Someone who holds a warrant to the bitter end winds up with either (a) nothing at all, if the stock is selling for less than the warrant’s strike price; or (b) an immediate profit, if the stock is selling for more. Any irrational sentiment about the warrant’s worth is a memory. (The stock itself may be “irrationally” priced—who knows?—but that’s beside the point.)

S
UMMER
1964
BROUGHT CHANGES
in Thorp’s life. The grant supporting his appointment at New Mexico State had run out. It looked like the math department would fall into the hands of a “clique of group theorists.” Thorp began a job search. The University of California was starting a new campus at Irvine in Orange County. Both Ed and Vivian had fond memories of Southern California, so Thorp interviewed there. He got an offer and took it.

On Thorp’s first day at UC Irvine, he happened to mention his interest in warrants to Julian Feldman, the head of the computer sciences department. Oh, Feldman said, we’ve got a guy who’s doing the same thing.

He was talking about an economist named Sheen Kassouf. Kassouf had written his Columbia University Ph.D. thesis on how to determine a fair price for warrants. Kassouf had not come up with a rigorous answer, but he had a good practical sense of the problem. He was already trading warrants.

Feldman introduced Thorp to Kassouf. They resolved to do a weekly research seminar on the subject. There were no students; Thorp and Kassouf simply met weekly to figure out how to get rich.

Thorp began trading warrants too. His hedging system worked as he’d hoped. By 1967 Thorp had parlayed his original $40,000 into $100,000.

The system was not bulletproof. There were relatively few warrants out there, so the market was illiquid. Someone who sells short too many warrants may find it difficult to buy them when needed. The “artificial” demand created by the deal itself can drive up the prices of these warrants. That is bad because Thorp was betting the warrants would get cheaper.

The delta hedging scheme protects against only small movements in the stock’s price. Should the stock’s price change greatly, it is necessary to readjust by buying or selling more stock or warrants. This means the trader must watch stock and warrant prices closely.

Sometimes a company would change the terms of a warrant, and this could be disastrous for the trade. For these and other reasons, not every warrant deal turned a profit. Unlike many young traders, Thorp understood the concept of gambler’s ruin. He was able to estimate the chances of profit and use the Kelly formula to make sure he was not committing too much money to any one deal.

By the end of 1965, Thorp was up for a full professorship at UC Irvine. He wrote Shannon for a letter of recommendation. In his request, Thorp reported that

While the 33 percent figure was optimistic, Thorp was beating market returns. In the margin of this letter, he drew an arrow pointing to the phrase “the stock market” and added the question “Have you continued attacking it? And how have you made out?”

Paul Samuelson coined the term “PQ,” or performance quotient. Like IQ, this supposedly measures a portfolio manager’s ability. A PQ of 100 is average. The question is, does anyone have a PQ of over 100?

Samuelson theorized that
if
such people existed, they would be all but invisible. You would not find them working for investment banks or the Ford Foundation. “They have too high an I.Q. for that,” Samuelson wrote. “Like any race track tout, they will share [their talents] for a price with those well-heeled people who can most benefit from it.”

Samuelson concluded that the high-PQs would operate by stealth, investing their own money or that of friends. They would keep their “systems” to themselves. Otherwise, the efficient market would copy what they were doing, nullifying the system’s advantage.

For a few years, Thorp was the model of a high-PQ trader. He operated his warrant system quietly, investing his own money and that of a few relatives who had bugged him to invest for them. Soon he was investing over a million dollars of friends’ money.

Then Thorp did what Samuelson said wouldn’t happen. He told Kassouf they should reveal their system to the world. Thorp was looking two calculated moves ahead. He was thinking of managing money professionally. By writing a book on the warrant hedge system, “we’d get a certain cachet,” Thorp recalled, “which would make it a lot easier to raise investment money.” Thorp felt that he had such a steady stream of profitable ideas that he could afford to give away the warrant hedges, much as he had the blackjack system.

Kassouf consented. They got a $50,000 advance for the book. To Kassouf that was “staggering.” The advance was about five times his annual salary.

The book was called
Beat the Market
(1967). It described a simplified version of the warrant hedge system for small investors. No one had home computers then. Overpriced warrants had to be identified by drawing charts on graph paper.

The book seems to have been the first discussion in print of delta hedging. Yet as one of the hundreds of books of advice for the small investor that come out every year, the book received little notice from most academics.

One exception was the prolific Paul Samuelson. He reviewed the book for the
Journal of the American Statistical Association
. “Just as astronomers loathe astrology,” Samuelson began unpromisingly, “scientists rightly resent vulgarization of their craft and false claims on its behalf.” Though Samuelson allowed that a minority of readers might make some money from the system, he feared that it would require too much work and mathematical sophistication to satisfy the majority of readers, who were doubtless looking for a get-rich-quick scheme. “The Pure Food and Drugs Administration should enjoin the authors from making such misleading claims,” Samuelson carped, “or at least require them to take out of the fine print, so to speak, the warning showing they know better.”

Thorp and Kassouf kicked around the idea of starting an investment partnership. Kassouf proposed an arrangement where the principals would be Thorp, Kassouf, and Kassouf’s brother. Thorp worried that that would shift the balance of power too much toward the Kassoufs. There was a philosophical difference, too. Kassouf believed that he could sometimes predict in which direction certain stocks were going to move. Kassouf was willing to buy stocks he thought were going up and sell short stocks he thought were going to go down. Thorp wasn’t. He was unconvinced that Kassouf, or anyone, could predict the market that way. As Thorp told me, “We had a different degree of daring about what we wanted to do in the marketplace. I was
not
daring.”

Thorp wanted to start a “market neutral” investment partnership, meaning that its returns would be independent of what the stock market did. A bad year for the stock market could be a good year for the partnership—that was the idea, anyway. This would itself be a great selling point. The big investors Thorp hoped to attract would be placing just part of their money in the partnership. If he could show that the partnership’s performance was not correlated with the stock market’s, people who already had large stock holdings could reduce their overall risk by investing in the partnership.

Thorp asked an attorney about starting an investment partnership. The attorney told him the idea was impractical. Thorp objected that Warren Buffett had a partnership. The attorney replied that Buffett hadn’t been incorporated in California. The state had too many regulations to permit the type of freewheeling operation Thorp had in mind.

The attorney billed Thorp for 20 hours’ work. That came to $2,000, a good fraction of Thorp’s salary. Thorp negotiated the fee down, but the experience left him disillusioned and poorer.