Category Archives: Edward Thorp

Edward Thorp

[U]sing the mathematical theory of probability, it was proven that if all roulette numbers were equally likely to come up, and they appeared in random order, it was impossible for any betting system to succeed. Despite this, hope flared briefly at the end of the nineteenth century when the great statistician Karl Pearson (1857–1936) discovered that the roulette numbers being reported daily in a French newspaper showed exploitable patterns. The mystery was resolved when it was discovered that rather than spend hours watching the wheels, the people recording the numbers simply made them up at the end of each day. The statistical patterns Pearson detected simply reflected the failure of the reporters to invent perfectly random numbers.

Edward Thorp, A Man for All Markets: From Las Vegas to Wall Street, How I Beat the Dealer and the Market, New York, 2017, p. 123

Edward Thorp

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 me 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!

Edward Thorp, A Man for All Markets: From Las Vegas to Wall Street, How I Beat the Dealer and the Market, New York, 2017, pp. 146-148