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Beating the Market Is a No-Brainer - High Average Return Takes Skill

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By taking sufficiently irresponsible risk, you can generate extraordinary track records over very long periods of time. In analyzing a track record, dig deeply.

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MINYANVILLE ORIGINAL Last week in Why Correlations Are Unreliable Risk Indicators, I mentioned reading Maneet Ahuja's The Alpha Masters: Unlocking the Genius of the World's Top Hedge Funds. Oddly enough, another book of interviews with top hedge fund traders came at almost exactly the same time. This was the fourth book in Jack Schwager's incomparable Wizards series: Hedge Fund Market Wizards: How Winning Traders Win. Anyone interested in trading should read both books, as well as the other three Wizards books: Market Wizards, The New Market Wizards and Stock Market Wizards.

I'm not going to review the book here. Instead, with apologies to the author, I am going to discuss what in my opinion, is the one glaring error.

In the interview with Ed Thorp, Schwager writes:

Princeton Newport partners compiled a track record of 227 winning months and only 3 losing months. . . . To calculate the probability of this achievement if markets were efficient, we make the simplifying assumption that the average win and average loss were equal. . . . [The probability] is equivalent to probability of getting 227 or more heads in 230 coin tosses, which is approximately equal to an infinitesimally small 1 out of 1063. . . . Track records such as Thorp's prove conclusively that it is possible to beat the market and that the large group of economists who insist otherwise are choosing to believe theory over evidence.

I have no doubt that it's possible to beat the market, and also that Thorp has beaten the market more conclusively than anyone. But his track record on its own does not prove that, and the 1063 figure is sheer math abuse -- the same math abuse that leads half-numerate people to claim some recent market event was so unlikely that it should never have happened in the history of the universe.

It doesn't take a genius like Thorp to make money in all 230 of the months from November 1969 to December 1988, all you would have to do is buy one-month Treasury bills and collect a 7% annualized return -- 9% if you chose to use LIBOR bank accounts instead. You can't pronounce the market beaten just because someone failed to lose money in 227 out of 230, or even 230 out of 230 months.

Schwager would have a stronger argument if he looked at Thorp's average return, nearly 20% per year over the life of the fund from 1969 to 1988, versus a standard deviation around 4%. That is far better than the stock market delivered over the same period-10% annual return at a 17% standard deviation.

It is, however, possible to manufacture a track record as good as Thorp's without skill.

Of course, Thorp didn't do anything like this, but other people have. Suppose you had a $10 million fund and followed the following strategy: Every month, you put $2,500 in the S&P 500 at the open (actually, S&P 500 futures were not available until 1982, but this is just an illustrative example). Every day, you check to see if liquidating your position at the close would generate at least $25 profit for the month. If not, you double your position on the next day's open. If so, you put in a limit sell order for your entire position at that level at the next day's open. If that order gets executed at any time during the day, you stay in cash for the rest of the month.

This strategy produces an average annualized return on the $10 million of 20%, actually a little higher than Thorp's, and it has no losing months. On average, you have $1.3 million of your $10 million invested in the market.

You do have a little bit of risk. In April 1970, the S&P 500 fell 9% and worse, fell 18 of 22 days. Three of the gain days were small, but on April 29, one day before the end of the month, the market rose 1.9%. That was fortunate for the strategy because all the doubling had led to a notional position of $2.4 billion. The 1.9% day allowed you to get out of your gigantic position at a profit. There were similar months like September 1972 when you were saved two days before the end of the month, and October 1977 with the saving day three days before the end. If this strategy loses, it doesn't just lose money, it "blows up," causing losses massively greater than its capital.

You might object that no broker would have allowed the 240 to 1 leverage this strategy held at its maximum point. Even Long-Term Capital Management couldn't get much above 100 to 1. Rogue traders like Nick Leeson get much higher leverage, but they have to commit fraud to do it. There are other examples where the brokerage loans got so large that the firm allowed leverage to skyrocket rather than take a loss; that is arguable fraud. Another problem is that your gigantic positions would move the market, and Thorp's record is real with mistakes, transaction costs, and other drags while this is only a theoretical construction.

However the point is that by taking sufficiently irresponsible risk, you can generate extraordinary track records over very long periods of time. And we haven't even covered tricks like manipulating month-end prices, mismarking illiquid securities, parking positions, merging track records, and out-and-out Madoff-type fraud. If you have to choose between a 1 in 1063 probability event or a dodgy manager, bet on the latter every time.

The reason we know Thorp can beat the market is that he tells us how he does it. The reasons make sense, and the strategies have been tested by others. His records are honest, and he controlled his risk expertly. That plus a track record (and Thorp's record continues beyond 1988) is convincing evidence. The track record alone as a black box result proves nothing.
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