Gambling is investing simplified. The striking similarities between the two suggested to me that, just as some gambling games could be beaten, it might also be possible to do better than the market averages. Both can be analyzed using mathematics, statistics, and computers. Each requires money management, choosing the proper balance between risk and return. Betting too much, even though each individual bet is in your favor, can be ruinous. When the Nobel Prize winners running the giant hedge fund Long-Term Capital Management made this mistake, its collapse in 1998 almost destabilized the US financial system. On the other hand, playing safe and betting too little means you leave money on the table. The psychological makeup to succeed at investing also has similarities to that for gambling. Great investors are often good at both.
Relishing the intellectual challenge and the fun of exploring the markets, I spent the summer of 1964 educating myself about them. I haunted the big Martindale’s bookstore then in Beverly Hills. I read stock market classics like Graham and Dodd’s Security Analysis, Edwards and Magee’s work on technical analysis, and scores of other books and periodicals ranging from fundamental to technical, theoretical to practical, and simple to abstruse. Much of what I read was dross but, like a baleen whale filtering the tiny nutritious krill from huge volumes of seawater, I came away with a foundation of knowledge. Once again, just as with casino games, I was surprised and encouraged by how little was known by so many. And just as in blackjack, my first investment was a loss that contributed to my education.
A couple of years earlier, when I knew nothing at all about investing, I heard about a company whose stock was allegedly selling at a bargain price. It was Electric Autolite, and among their products were automobile batteries for Ford Motor Company. The story on the business page of my newspaper said we could expect a great future: technological innovations, big new contracts, and a jump in sales. (The same forecasts for battery makers were being made forty years later.)
As I finally had some capital from playing blackjack and from book sales, I decided to let it grow through investing while I focused on family and my academic career. I bought one hundred shares at $40 and watched the stock decline over the next two years to $20 a share, losing half of my $4,000 investment. I had no idea when to sell. I decided to hang on until the stock returned to my original purchase price, so as not to take a loss. This is exactly what gamblers do when they are losing and insist on playing until they get even. It took four years, but I finally got out with my original $4,000. Fifty years later, legions of tech stock investors shared my experience, waiting fifteen years to get even after buying near the top on March 10, 2000.
Years later, discussing my Electric Autolite purchase with Vivian as we drove home from lunch, I asked, “What were my mistakes?”
She almost read my mind as she said, “First, you bought something you didn’t really understand, so it was no better or worse than throwing a dart into the stock market list. Had you bought a low-load mutual fund [no-load funds weren’t available yet] you would have had the same expected gain but less expected risk.” I thought the story about Electric Autolite meant it was a superior investment. That thinking was wrong. As I would learn, most stock-picking stories, advice, and recommendations are completely worthless.
Then Vivian remarked on my second mistake in thinking, my plan for getting out, which was to wait until I was even again. What I had done was focus on a price that was of unique historical significance to me, only me, namely, my purchase price. Behavioral finance theorists, who have in recent decades begun to analyze the psychological errors in thinking that persistently bedevil most investors, call this anchoring (of yourself to a price that has meaning to you but not to the market). Since I really had no predictive power, any exit strategy was as good or bad as any other. Like my first mistake, this error was in the way I thought about the problem of when to sell, choosing an irrelevant criterion—the price I paid—rather than focusing on economic fundamentals like whether cash or alternative investments would serve better.
Anchoring is a subtle and pervasive aberration in investment thinking. For instance, a former neighbor, Mr. Davis (as I shall call him), saw the market value of his house rise from his purchase price of $2,000,000 or so in the mid-1980s to $3,500,000 or so when luxury home prices peaked in 1988–89. Soon afterward, he decided he wanted to sell and anchored himself to the price of $3,500,000. During the next ten years, as the market price of his house fell back to $2,200,000 or so, he kept trying to sell at his now laughable anchor price. At last, in 2000, with a resurgent stock market and a dot-com-driven price rise in expensive homes, he escaped at $3,250,000. In his case, as often happens, the thinking error of anchoring, despite the eventual sale price he achieved, left him with substantially less money than if he had acted otherwise.
Mr. Davis and I used to jog together occasionally and chat about his favorite topics, money and investments. Following my recommendation, he joined a limited partnership that itself allocated money to limited partnerships, so-called hedge funds, which it believed were likely to make superior investments. His expected rate of return after paying his income taxes on the gains was about 10 percent per year, with considerably more stability in the value of the investment than was to be found in residential real estate or the stock market. I advised him to sell his house at current market just after the 1988–89 peak. He would have received perhaps $3,300,000 and then, as was his plan, moved to a $1,000,000 house. After costs and taxes he would have ended up with an additional $1,600,000 to invest. Putting this into the hedge fund he had already joined at my recommendation, the money would have grown at 10 percent per year for eleven years, becoming $4,565,000. Add that to the $1,000,000 house, whose market price would have declined, then recovered, and Mr. Davis would have had $5,565,000 in 2000 instead of the $3,250,000 he ended up with.
I’ve seen my own anchoring mistake repeatedly made by real estate buyers and sellers, as well as in everyday situations. As I was driving home one day in heavy traffic, an SUV forced its way in front of me, giving me a choice of yielding or “maintaining my rights” and having a fender bender. Since I receive these invitations daily, I saw no need to accept this one for fear I would miss out. The SUV was in “my” space (anchoring: I’ve attached myself to an abstract moving location that has a unique historical meaning to me, and am allowing it to dictate my driving behavior). We were now lined up about seventy cars deep in the most notoriously slow left-turn lane in Newport Beach. Ordinarily the road is two lanes wide, but construction had narrowed it to one, and the complex sequence of light changes allowed only about twenty cars through on each two-minute cycle. What if, when we finally got to the signal, the evil SUV was the last one through the yellow? Since it was really “my” space, was I justified in risking an accident by rolling through on the red? Otherwise, the time thief gains two minutes at my expense. The temptation may sound as foolish to you as it does in cold print to me, but I see this kind of behavior regularly.
Having learned the folly of anchoring from my investment experience, I have seen that it can be equally foolish on the road. Being a more rational investor has made me a more rational driver!
Two “expert” longtime insurance investors from Dallas drew me into my next adventure in the market. They claimed to have become rich investing in life insurance companies. According to their figures the A. M. Best AAA index of the average price of such companies had gone up in each of the last twenty-four years, and they had plausible arguments that this would continue. Sure enough, the amazing winning streak they had identified ended just after my purchase, and we all lost money.
Lesson: Do not assume that what investors call momentum, a long streak of either rising or falling prices, will continue unless you can make a sound case that it will.
Thinking about momentum led me to wonder whether past prices could somehow be used to predict future prices. To test this, I looked at charting, the art of using patterns in the graphs of stock (or commodity) prices to forecast their future changes. I was introduced to this by Norman, a Canadian resident living in Las Cruces, while I was teaching at New Mexico State University. After months of examining his data and predictions, I was unable to find anything of value. As Vivian said at the start, “This is going to be a waste of time. Norman’s been doing this for years and you can tell he’s barely getting by. Just look at his worn-out shoes and shabby clothes. And you can tell from the quality of his wife’s old and dated outfits that they were once better off.”
I still owed more tuition to Mr. Market for his introductory course in investment mistakes. Mr. Market is an allegorical character famously introduced by Benjamin Graham to illustrate the excessive market price swings above and below the actual underlying business values of quoted securities. Some days he’s manic and prices are high. Other days he’s gloomy and shares can be bought well below what Graham called their “intrinsic value.” In the early 1960s the demand for silver was exceeding supply and I expected prices to spurt sharply. The value of the silver extracted from melting everyday coins was eventually expected to exceed the face value by enough to pay costs and give a profit. Bill Rickenbacker, who backed my blackjack trip with Mickey MacDougall and Russell Barnhart, had by then purchased US silver dollars and stored them in a vault while he waited for this to happen.
The further price rise of silver would slow somewhat as a new supply came from melting coins. Also some five billion ounces of silver could potentially be extracted from the vast pool of jewelry in India. Once demand absorbed these new supplies, prices would jump even more. When the price of silver actually did pass $1.29 per ounce, those US coins that contained 90 percent silver were worth more as metal than as legal tender. Coins were skimmed from circulation and melted to extract their silver. After the US government banned this, the coins were hoarded and bought and sold in sixty-pound bags via dealers.
Believing this economic supply and demand analysis was correct, I opened a Swiss bank account to buy silver, with the help and encouragement of local promoters who got a commission for making the arrangements. They recommended doing this on 331⁄3 percent collateral. That means that for each dollar’s worth of silver I bought, I had to deposit only 331⁄3 cents in my account. The promoters arranged for my friendly Swiss bank to loan me the rest. Of course, when I borrowed to buy three times as much silver as I could have with cash alone, they got triple the commissions, and the bank was happy to collect interest on the loan and charge me monthly storage fees.
Silver rose as predicted and the promoters recommended using the profits together with more bank loans to buy yet more silver. When the commodity reached $2.40 an ounce my account had a lot more of the metal than when I started, and I had a large profit on all of my purchases. However, as I had reinvested my profits on the way up, $1.60 of that $2.40 an ounce was owed on my loan from the bank. It was like buying a house with one-third down. Then the price of silver dropped. When this happened some people sold to capture their profit. This drove down the price still further until others, who had borrowed to an even greater extent than I had, were sold out by their lenders as their accounts threatened to go underwater—meaning there wouldn’t be enough left to pay off the loan. These sales pushed the price down even more, forcing more sales by the remaining borrowers, causing silver to drop rapidly to a little below $1.60, just enough to wipe me out, after which it resumed its upward path. I learned from this that even though I was right in my economic analysis I hadn’t properly evaluated the risk of too much leverage. For a few thousand dollars I learned from this to make proper risk management a major theme of my life for more than fifty years thereafter. In 2008 almost the entire world financial establishment didn’t understand this lesson and had overleveraged itself.
I also learned from my losing silver investment that when the interests of the salesmen and promoters differ from those of the client, the client had better look out for himself. This is the well-known agency problem in economics, where the interest of the agents or managers don’t coincide with those of the principals, or owners. Shareholders of companies that have been pillaged by self-serving CEOs and boards of directors are painfully familiar with this.
After these lessons from Mr. Market, I was tempted to believe that the academics were right in claiming that any edge in the markets is limited, small, temporary, and quickly captured by the smartest or best-informed investors. Once again, I was invited to accept the consensus opinion at face value, and once again I decided to see for myself.
In June 1965, I began a second summer of self-education in economics, finance, and the markets. The thin pamphlet on common stock purchase warrants that I’d ordered had just come in the mail. I settled into a lawn chair, curious to find out how these securities worked. It was a revelation.
The pamphlet explained that a common stock purchase warrant is a security issued by a company that gives the owner the right to buy stock at a specified price, known as the exercise price, on or before a stated expiration date. For instance, in 1964 a Sperry Rand warrant entitled the holder to purchase one share of common stock for $28 until September 15, 1967. On this final day, if the stock trades above that price, you can use one warrant plus $28 to buy one share of stock. This means the warrant is worth the amount by which the stock price exceeds $28. However, if the stock price is below $28, it is cheaper to buy the stock outright, in which case the warrant is worthless.
A warrant, like a lottery ticket, was always worth something before it expired even if the stock price was very low, if there was any chance the stock price could move above the exercise price and put the warrant “into the money.” The more time left, and the higher the stock price, the more the warrant was likely to be worth. The prices of these two securities followed a simple relationship regardless of the complexities of the balance sheet or business affairs of the underlying company. As I thought about this I formed a rough idea of the rules relating the warrant price to the stock price. Since the prices of the two securities tended to move together, the important idea of “hedging” occurred to me, in which I could use this relationship to exploit any mispricing of the warrant and simultaneously reduce the risk of doing so.
To form a hedge, take two securities whose prices tend to move together, such as a warrant and the common stock it can be used to purchase, but which are comparatively mispriced. Buy the relatively underpriced security and sell short the relatively overpriced security. If the proportions in the position are chosen well, then even though prices fluctuate, the gains and losses on the two sides will approximately offset or hedge each other. If the relative mispricing between the two securities disappears as expected, close the position in both and collect a profit.
A few days after I had the idea of hedging warrants versus common stock, we packed up our possessions and moved from New Mexico State University to Southern California, where I became a founding faculty member of the Mathematics Department of the new Irvine campus of the University of California (UCI). During our four years in Las Cruces, I had learned much more mathematics, directed the PhD dissertations of talented students, and published my research as a series of professional articles in mathematics journals. But we wanted to live in Southern California where our children would see their grandparents and our own siblings and their families, and we would be near old friends. I also liked the fact that UCI purposely was starting out emphasizing collaboration between faculty and students from different subject areas.
On my first day in my new teaching position at UCI, in September 1965, Julian Feldman, the head of the school of information and computer sciences, asked me what I was working on. When I described my ideas about a theory of warrant valuation and hedging, he said that another member of the new faculty, an economist named Sheen Kassouf (1928–2005), had written his PhD thesis on the subject. Feldman introduced us and I learned that Kassouf had discovered the same concepts in 1962 and had already been shorting overpriced warrants and hedging them, doubling his initial $100,000 in just three years.
I realized that if we worked together we could develop both the theory and the techniques for hedged investment more rapidly than by working alone. At the weekly meetings I proposed, we roughly determined the fair price for a warrant, finding quite a few that were substantially overpriced. The way to profit was to sell them short. To sell a security short you borrow the desired quantity through your broker from someone who owns it, sell it in the marketplace, and collect the proceeds. Later you have to repurchase it at whatever price then prevails to meet your contractual obligation to return what you borrowed. If your buy-back price is below your earlier sale price, you win. If it is higher, you lose.
Short selling overpriced warrants was profitable on average but risky. The same was true for buying stocks. The two risks largely canceled each other when we hedged the warrants by purchasing the associated common stock. In a historical simulation our optimized method made 25 percent a year with low risk, even during the great 1929 stock market crash and its aftermath. As we worked on theory, Kassouf and I were investing for ourselves in warrant hedges, which also made 25 percent per year.
We explained our methods for investing and presented the actual results from our hedges in Beat the Market, finished in late 1966 and published by Random House in 1967. There we extended our approach to include the much larger area of convertible bonds. Just as in blackjack, I was willing to share our discoveries with the public for several reasons. Among them was the awareness that sooner or later, others would make the same discoveries, that scientific research ought to be a public good, and that I would continue to have more ideas.
Having somewhat different ideas about how to set up our hedged investments, Kassouf and I ended our collaboration after we finished Beat the Market. As an economist, Sheen felt that he understood the companies well enough to deviate from a neutral hedge. A neutral hedge gives balanced protection against loss whether the market moves up or down. Sheen, however, was willing to modify the long and short proportions in the hedge to favor either a rise in the price of the underlying stock or a fall, depending on his analysis. Given my bad experiences in picking stocks and my lack of background in analyzing companies, I wanted to do hedges that were as protected as possible against changes in the stock price, no matter in which direction. I continued to work on the theory and to invest on my own.
A major theoretical breakthrough came to me in 1967. I used Occam’s razor—the principle that given more than one explanation, you should begin by choosing the simplest one—and plausible reasoning to arrive at a neat formula for determining the “correct” price of a warrant. Armed with this I could tell when they were mispriced and by roughly how much. That same year I began using the formula to trade and hedge over-the-counter warrants and options and, a little later, convertible bonds. An option to buy a stock is similar to a warrant, the principal difference being that warrants are typically issued by the company itself and options are not. Convertible bonds are like ordinary bonds but with the additional feature that they can be exchanged for a fixed number of shares of the issuing company’s stock if the holder so desires.
Having the formula further increased my confidence and returns. This, along with the fact that the available investment opportunities were much larger than I could exploit with my modest capital, led to the next step. I began to manage hedged portfolios for friends and acquaintances.