A Man for All Markets: From Las Vegas to Wall Street, How I Beat the Dealer and the Market

by Edward O. Thorp

We didn’t ask, Is the market efficient? but rather, In what ways and to what extent is the market inefficient? and How can we exploit this?

Among the scores of fundamental and technical measures we considered were the ratio of earnings per share to price per share, known as the earnings yield, the liquidation or “book” value of the company compared with its market price, and the total market value of the company (its “size”).

To control risk further, I replaced Bamberger’s segregation into industry groups by a statistical procedure called factor analysis. Factors are common tendencies shared by several, many, or all companies. The most important is called the market factor, which measures the tendency of each stock price to move up and down with the market. The daily returns on any stock can be expressed as a part that follows the market plus what’s left over, the so-called residual. Financial theorists and practitioners have identified a large number of such factors that help explain changes in securities prices. Some, like participation in a specified industry group or sector (say, oil or finance) mainly affect subgroups of stocks. Other factors, such as the market itself, the levels of short-term and long-term interest rates, and inflation, affect nearly all stocks.

The beauty of a statistical arbitrage product is that it can be designed to offset the effects of as many of these factors as you desire. The portfolio is already market-neutral by constraining the relation between the long and short portfolios so that the tendency of the long side to follow the market is offset by an equal but opposite effect on the short side. The portfolio becomes inflation-neutral, oil-price-neutral, and so on, by doing the same thing individually with each of those factors. Of course, there is a trade-off: The reduction in risk is accompanied by limiting the choice of possible portfolios. Only those that are market-neutral, inflation-neutral, oil-price-neutral, et cetera, are now allowed, and so the attempt to reduce risk also tends to reduce return.

Unlike some hedge fund managers who also had a waiting list, we could have increased our fees by raising our share of the profits or adding more capital, thereby driving down the return to limited partners. Such tactics by the general partner to capture nearly all the excess risk-adjusted return, or “alpha,” rather than share it with the other investors are what economic theory predicts. Instead, I preferred to treat limited partners as I would wish to be treated in their place.

We decided to close down in the fall of 2002. Returns, although respectable, had declined in 2001 and 2002. I believed this was due to the huge growth in hedge fund assets, with a corresponding expansion of statistical arbitrage programs. I had seen this happen before in 1988 when Morgan Stanley’s expansion of statistical arbitrage seemed to have a negative effect on our returns. The declining rate of return in statistical arbitrage seemed to be confirmed by the experience

Here’s how it is done. Imagine a hypothetical mutual savings and loan, which we’ll call Magic Wand S&L, or MW, with $10 million in liquidation or book value, and net income of $1 million per year. If MW were a stock bank with one million shares outstanding, each share would have a book value of $10 and earn $1 per share, which is 10 percent of book value. Suppose that if there were such a thing as MW stock, it would, as is typical, trade at one times book value, or $10 per share.

Management decides to “convert” MW to a stock savings and loan and issue for the first time one million shares of stock at $10 per share, for proceeds of $10 million. After this initial public offering, or IPO, MW has $10 million in new cash plus the $10 million in equity previously owned by the depositors, for a new total of $20 million in equity. Each share now has a book value of $10 cash plus $10 in contributed equity, for a total of $20. What will the new shares sell for in the marketplace? The contributed equity ought to be worth $10 based on the current market price of comparable stock S&Ls and the $10 in cash ought to be worth another $10, so once the public understands this, we expect the new stock to trade at about $20.

With Princeton Newport, growth from new capital came slowly and was earned by performance. Over forty years this battle for funding changed dramatically. So-called alternative investments became the hottest new frontier for what to do with your money. Beginning in the late 1990s, you could, in effect, just put up a sign saying HEDGE FUND OPENING HERE, and a line of investors would quickly extend around the block. A modest-sized $100 million hedge fund earning a gross return of 10 percent per year ($10 million) may pay the manager or general partner a management fee of 1 percent of $100 million—$1 million. In addition, the manager gets 20 percent of the remaining $9 million in profit, or another $1.8 million, as a performance fee, for a total of $2.8 million per year. Some of this, perhaps $1 million, pays expenses, leaving a net of $1.8 million a year in pretax income. The investors, or limited partners, get the remaining $7.2 million for a 7.2 percent annual return. The general partners in a similar billion-dollar hedge fund—and there are scores of them—might share ten times as much, or $28 million a year. Even a little $10 million hedge fund would, with proportionate fees, expenses, and returns, provide a single general partner with $280,000 a year. It’s clear from this that you can get very rich running a hedge fund. With these rewards, we shouldn’t be surprised to find many of the (believed to be) best investors in the business running hedge funds.

Should you invest in hedge funds? First you need to determine if you’re economically qualified. Though such funds typically require a minimum investment of $250,000 or more, some start-ups will relax this to $50,000 or $100,000 when they first raise money. The original reason to require a substantial minimum investment was historical. In order to qualify for certain exemptions from securities regulations, and thereby gain the freedom to make a wide range of investments, hedge funds had to limit themselves to fewer than one hundred partners. But then, in order to have a pool of tens or hundreds of millions of dollars, the fund had to avoid filling their quota of partners with small investors.

Another issue is taxes. US domestic hedge funds, like most active investment programs, are tax-inefficient. Their high turnover tends to produce short-term capital gains and losses taxed at a higher rate than securities owned for more than one year.

For tax-exempt investors, US hedge funds that borrow money (but not their clones based outside the United States) trigger taxes for the otherwise tax-exempt entity to the extent the realized gains, losses, and income are generated by the loans. This is called unrelated business taxable income (UBTI).

One method that leads to this has also been used to launch new mutual funds. Fund managers sometimes start a new fund with a small amount of capital. They then stuff it with hot IPOs (initial public offerings) that brokers give them as a reward for the large volume of business they have been doing through their established funds. During this process of “salting the mine,” the fund is closed to the public. When it establishes a stellar track record, it is opened to everyone. Attracted by the amazing track record, the public rushes in, giving the fund managers a huge capital base from which they reap large fees. The brokers who supplied the hot IPOs are rewarded by a flood of additional business from the triumphant managers of the new fund. The available volume of hot IPOs is too small to help returns much once the fund gets big, so the track record declines to mediocrity. However, the fund promoters can use more hot IPOs to incubate yet another spectacularly performing new fund; and so it goes on.

It’s that increase in net worth from year to year that takes you up the ladder of wealth. To measure your increase in wealth from one year to the next, compare the yearly balance sheets. Divide the difference by the beginning wealth to get your percentage change for the year. This gives you an idea of how fast you are compounding. If you also construct an income statement for the period, the net income after expenses should match your change in net worth. Balance sheets are snapshots that tell you where you are at a particular time. The income statement tells you what happens between two balance sheets. To appreciate the income statement without bothering to look anything up, jot down a list of all the sources that added to, or subtracted from, your wealth during the last twelve months. Do this “rough and dirty”; focus on the ideas rather than details and precision. Here are some categories to check: A. Income, taxable and nontaxable: 1. Earned income such as wages and salaries. 2. Unearned income such as interest and dividends. 3. Realized capital gains and losses. 4. Royalties, honoraria, all other taxable receipts. 5. Tax-free interest, such as municipal bonds. B. Nontaxable gains and losses: 1. Appreciation or depreciation of property such as real estate, art, and autos. 2. Unrealized capital gains or losses in securities. C. Expenses (all money paid out for “costs”—that is, not saved): 1. Living expenses, consumption. 2. Income taxes. 3. Gifts. 4. Any other money earn...

Our portrait of real markets tells us what it takes to beat the market. Any of these can do it: 1. Get good information early. How do you know if your information is good enough or early enough? If you are not sure, then it probably isn’t. 2. Be a disciplined rational investor. Follow logic and analysis rather than sales pitches, whims, or emotion. Assume you may have an edge only when you can make a rational affirmative case that withstands your attempts to tear it down. Don’t gamble unless you are highly confident you have the edge. As Buffett says, “Only swing at the fat pitches.” 3. Find a superior method of analysis. Ones that you have seen pay off for me include statistical arbitrage, convertible hedging, the Black-Scholes formula, and card counting at blackjack. Other winning strategies include superior security analysis by the gifted few and the methods of the better hedge funds. 4. When securities are known to be mispriced and people take advantage of this, their trading tends to eliminate the mispricing. This means the earliest traders gain the most and their continued trading tends to reduce or eliminate the mispricing. When you have identified an opportunity, invest ahead of the crowd.

The tables in appendix B show that stocks and commercial real estate have provided the best long-run results for investors. Interest rate investments have been roughly break-even after taxes and inflation, and only modestly positive for nontaxable investors. However, though equities have performed best in the long run, they have had extended periods when they have been in drawdown, meaning that they were below their previous all-time high. Real estate fell sharply in the financial crisis of 2008–09. Assuming that the risks and returns for asset classes in the twenty-first century will be similar to what they were in the twentieth, long-term passive investors are likely to do best in common stocks and income-producing commercial real estate, though the data is sketchier for the latter. Diversifying between the two may reduce risk and increase overall return.

The investor who is willing to do a little thinking, along with the investing work that follows, has many ideas to check. For instance, there has been a strong inverse relationship between the last few years’ average price/earnings ratio of the stock indexes like the S&P 500 and the total return on the index over the next few years. Put simply, a high P/E ratio suggests stocks are overpriced and are likely to underperform, whereas a low P/E indicates the opposite. An investor who is diversified among asset classes might exploit this by decreasing his allocation to stocks when P/Es have been historically higher and shifting more into stocks when the P/Es have been lower.

prefer to think in terms of the inverse of P/E, or earnings divided by price, sometimes known as E/P but perhaps better described as earnings yield. When the P/E is 20, for example, the earnings yield is 1/20, or 5 percent. An investor who owns the S&P 500 Index could think of it as a low-grade long-term bond, comparing the earnings yield of this “bond” to the total return from some benchmark for actual bonds, such as long-term Treasuries or corporates of a particular quality grade. When the earnings yield on the stock index is historically high relative to the bond benchmark, the investor sells some of his bonds and buys stocks. When bond yields are high compared with stocks, he shifts money from stocks back to bonds. Stories

Although stories like this abound, my uncle was lucky. According to economist Robert Shiller, average US home prices after inflation increased from 1890 to 2004 by about 0.4 percent a year, with the rate being about 0.7 percent in the later 1940–2004 period. It follows from this that making a profit should not be a primary reason for owning your home. You can rent instead and do about as well financially. However, you may want, as I do, the non-quantified benefits of homeownership: You are your own boss, able to make changes and improvements at will without prior approval from a landlord. If you have a fixed-rate loan or have paid for your house in full, you have the security of knowing that your future monthly costs are controlled.

its simplest form, investors sell losing stocks before the end of the current year, realizing losses that reduce the year’s income taxes. This behavior contributes to the so-called January effect where selling pressure in December further depresses the stock prices of the year’s losers, followed by a rebound and excessive performance in January. The impact is greater for smaller companies. Investors used to realize a tax loss by selling a loser and buying it back immediately, with little risk of economic loss (or gain). To inhibit this loss of tax revenue by making it risky, the US government introduced the “wash sale rule,” which says that anyone who sells a stock at a loss and buys it back within thirty-one days may not recognize the loss for tax purposes. The rule is worded also to thwart savvy investors inclined to swap into an “equivalent” stock to get around this.

To cut taxes, start with a tracking basket and, each time a stock drops, say, 10 percent, sell the loser and reinvest the proceeds in another stock or stocks chosen so the new basket continues to track well. If you want only short-term losses, which is usually best, sell within a year of purchase. I advise anyone considering doing this in a serious way to study it first with simulations using historical databases. When making an investment, it is important to understand how easy it might be to sell later, a feature known as liquidity. The lack of liquidity in hedge funds and in real estate would prove costly for investors in the 2008–09 recession.

In his fascinating history of the topic, Fortune’s Formula, William Poundstone points out that for a favorable bet that pays odds of $A for a bet of $1, the optimal Kelly bet is the percent of your capital equal to your edge, divided by the odds, A. In blackjack, the typical favorable edge was usually between 1 and 5 percent and the odds, or payoff per dollar bet, averaged a little more than 1. So, following the criterion when the card count was good, I bet a percentage of my bankroll that was a little less than my percent advantage. Kelly’s criterion is not limited to two-value payoffs but applies generally to any gambling or investing situation in which the probabilities are known or can be estimated.

Some key features of the Kelly Criterion are: (1) The investor or bettor generally avoids total loss; (2) the bigger the edge, the larger the bet; (3) the smaller the risk, the larger the bet.

Three caveats: (1) The Kelly Criterion may lead to wide swings in the total wealth, so most users choose to bet some lesser fraction, typically one-half Kelly or less; (2) for investors with short time horizons or who are averse to risk, other approaches may be better; (3) an exact application of Kelly requires exact probabilities of payoffs such as those in most casino games; to the extent these are uncertain, which is generally the case in the investment world, the Kelly bet should be based on a conservative estimate of the outcome.