Fortune’s Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street, 2005, $27.00
By William Poundstone
Hill and Wang
Several years ago, one of the popular investment magazines presented a list of the most important books for speculators. At least one of Ralph Vince’s books on fractional f trading was on the list. The article noted, however, that while a number of people in the industry greatly admire Vince and his work, a great many—how shall I put this—do not. A lot of people in the industry have told me that they think Ralph is crazy and so is fractional f trading.
Which means I’m crazy too, I suppose. Vince got the basic idea from me. I got the idea from money manager Edward Thorp. Thorp got the idea from Claude Shannon, who got the idea from John Kelly. Although Poundstone’s new book doesn’t mention Vince and me, it is essentially the history of that idea.
Put baldly, Kelly and his followers argue that for certain people all of the time and for most people most of the time, the proper criterion for evaluating risky investments is the geometric mean, known in some investment circles as the Kelly criterion and in others as the compound rate of return. Fractional f trading is a derivative of that idea.
Words of one syllable.
Investment professionals are likely to be surprised there is any argument at all over the importance of maximizing the geometric mean. But the economics profession has almost completely rejected this approach. Nobel Prize winner Paul Samuelson, for example, has written several papers arguing against using the geometric mean criterion—including one, published in the Journal of Banking and Finance, written in words of one syllable.
I haven’t done enough research to say this definitively, but I suspect that few people whose vocabulary is limited to words of one syllable read the Journal of Banking and Finance on a regular basis. I also suspect that Samuelson decided that those who accept the geometric mean criterion are too stupid to be able to understand arguments containing polysyllabic words.
Samuelson has a point or part of a point. While trying to maximize geometric mean return will produce the highest possible return on average and will, by definition, reduce the risk of ruin to zero, it is not too hard to find situations where it is the wrong thing to do. For example, some trading approaches involve accepting a small risk of going bankrupt for relatively large returns.
Maximizing the geometric mean return means never accepting such risks. (For a review of alternative techniques and when to use them—shameless plug coming—see my book Quantitative Trading and Money Management.) More, maximizing the geometric return can produce terrifying drawdowns. Remember, kids: Hedge fund managers are trained professionals! Don’t try these tricks at home!
The default strategy.
Nevertheless, maximizing the geometric mean should be the hedge fund manager’s default strategy. If a manager chooses to do something else, he should still know what the geometric mean criterion suggests and know exactly why he is not following this path. (Hint for investors and fund-of-funds managers: another question to add to your due diligence list.)
If the distribution of profits and losses is known, the amount to commit to the market to maximize the growth of assets can be calculated. Consider a series of bets where the wins and losses are the same and P is the probability of a win on any given bet. In this case, the optimal strategy is to commit nothing if P is smaller than 50% and to commit P-(1-P) of your trading capital to the bet if P is larger.
If you win such bets 60% of the time, you should commit 0.6-(1-0.6) = 0.2 or 20% of your assets to that bet at any given time. If you lose that bet, you bet 20% of your remaining capital. If you win the bet, the same. In this case, betting more than 20% is over betting. Betting less than 20% is under betting.
For most systems traders, the probabilities do not change from trade to trade; so the proportion of trading capital committed to the market at any one time should not change either. This is where the fractional f that Vince advocates comes from. The math for more realistic examples is more complicated, of course. Much more important, for the math to work exactly, you have to know what the distributions of profits and losses will be.
In the real world, this is never the case. In the real world, hedge fund managers estimate distributions of profits and losses and in the main, their estimates are overly optimistic—which means they overbet and, perhaps, eventually lose all their money. Worse, the most irresponsible and self-destructive hedge fund managers, those most inclined to overbet, seem most attracted to this technique.
Does this mean the technique should never be used? No, and a good example of its proper use is Ed Thorp’s Princeton-Newport Partners, a convertible arbitrage hedge fund. Princeton-Newport Partners is no longer in business. Its demise was a side effect of the government’s attacks on Mike Milken. But during its run from 1969 to 1988, it produced a compound rate of return of 15.1% with very little volatility. During the same time, the S&P 500 produced 8.8%.
In contrast, Long-Term Capital Management’s demise seems to have been caused by over betting. An analysis by William Ziemba alluded to in Poundstone’s book calculates that LTCM was taking twice the optimal risk. There were lots of reasons why LTCM overbet, but one of them, surely, was that many of the heavy hitters at LTCM were economists. Indeed, LTCM’s Robert Merton was second only to Samuelson as a critic of the geometric mean criterion.
Investment ideas.
Poundstone writes well. He understands the investment issues and knows how to tell a story. On the downside, he uses the most bizarre and annoying citation system I have ever seen. You noticed I was a little vague in my reference to Ziemba? Not my fault. Information that should have been in Poundstone’s citations isn’t there. Worse, he doesn’t seem to know how to structure a long work. It wasn’t until the eighth sentence of this review that you knew where I was going. You won’t know where Poundstone is going for dozens of pages. Finally, this book doesn’t read like an investment book. Poundstone spends tens of pages on subjects most investment professionals will consider side issues. But these are quibbles. I got a half dozen really good investment ideas from this book, which is more than I got from the last half dozen investment books I read.
An earlier version of this review was published in MARHedge.
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