Fortune’s Formula on The Kelly Criterion

"Because of this complex lineage, the Kelly criterion has gone by a welter of names. Not surprisingly, Henry Latané never used 'Kelly criterion.' He favored 'geometric mean principle.' He occasionally abbreviated that to the catchier 'G policy' or even, simply, to 'G.' Breiman used 'capital growth criterion,' and the innocuous-sounding 'capital growth theory' is also heard. Markowitz used MEL, for 'maximize expected logarithm' of wealth. In one article, Thorp called it the 'Kelly[-Breiman-Bernoulli-Latané or capital growth] criterion.' This is not counting the yet-more-numerous discussions of logarithmic utility. This confusion of names had made it relatively difficult for the uninitiated to follow the idea in the economic literature."

Daniel Bernoulli's Contribution

"The person most shortchanged by this nomenclature is probably Daniel Bernoulli. He had a 218-year priority over Kelly. The unique and unprecedented part of Kelly's article is the connection between inside information and capital growth. This is a connection that could not have been made before Shannon rendered information measurable. Bernoulli considers a world where the cards are on the table, so to speak, and all the probabilities are public knowledge. There is no hidden information.”

The Law of Large Numbers and Investment Outcomes

"None of these figures are 'guaranteed.' The law of larger numbers doesn't work that way. A few more or less lucky spins, and the benefitscould be much different. That said, it is close to certain that the first wheel will yield vastly more than the third, and anyone se foolish as to make parlaying bets on the second will be broke."

Mean-Variance Analysis and Its Limitations

"Standard mean-variance analysis does not treat the compounding of investments. It is, you might say, a theory for Kelly's dollar-a-week gambler. But as the wealth to be amassed by compounding is so fantastically greater than can be achieved otherwise, a practical theory of investment must largely be a theory of reinvestment."

Ed Thorp's Critique and Advocacy for the Kelly Criterion

"When you try to apply Markowitz theory to compounding, the results can be absurd. One of Ed Thorp's theoretical contributions to the Kelly criterion literature is a 1969 paper in which he demonstrated the partial incompatibility of mean-variance analysis and the policy of maximizing the geometric mean. Thorp closes his article by declaring that 'the Kelly criterion should replace the Markowitz criterion as the guide to portfolio selection.'"
Perhaps no economist of the time would have dared such a heresy. It seems unlikely a major economic journal would have published such talk. Thorp's article appeared in the Review of the International Statistical Institute. Probably few economists saw it. In any event, few economists had heard of John Kelly. That was about to change.
  • There are less aggressive money management schemes that handle runs of bad luck better than the Kelly criterion does. Of course, they have a lower average compound return.

Utility Functions and Return on Investment

"It's a free country” (utility argument)
Latane felt that outside of the ivory tower, no one cares about utility functions, Return on investment is the portfolio manager's scorecard. Investors flock to a manager, or abandon him or her, because of that number. Is that not itself a reason for being interested in the system that maximizes compound return? Latané pointed out that 'it is difficult to identify the underlying utilities and to tell exactly when the utilities are being maximized in the case of a mutual fund or pension fund. The fund manager is cooking for an army. It's impractical to gauge everyone's taste for salt or risk.'"

Thorp and Markowitz on Compound Return

"Thorp was managing money not only for wealthy individuals but for corporate pensions and Harvard University's endowment. For most of these investors, Princeton-Newport was just one of many investments. The investors could do their own asset allocation. It was Thorp's job to provide an attractive financial product. Undoubtedly, investors judged the fund largely by its risk-adjusted return. In articles published in 1972 and 1976, Harry Markowitz made this point most forcefully. The utility function of a long-term investor should be denominated in compound return, not terminal wealth, Markowitz suggested."

The Debate on Average Compound Return

"What about the argument,' asked Merton and Samuelson (1974) 'that expected average compound return deserves analysis because such analysis may be relevant to those decision makers who just happen to be interested in average compound return? After some reflection, we think an appropriate reaction would go as in average-compound follows: It's a free country. Anybody can set up whatever criteria he wishes. However, the analyst who understands the implications of various criteria has the useful duty to help people clarify goals they will, on reflection, really want... In our experience, once understanding of the issues is realized, few decision makers retain their interest in average compound return."

Thorp's Real-World Experience with the Kelly Criterion

"Thorp reported that when he explained the Kelly criterion to investors, 'most people I talk to say 'Yeah, sounds great to me, I want that.' Thorp was in a better position to cite 'real world' results than anyone. His article 'Portfolio Choice and the Kelly Criterion' lists the performance record of 'a private institutional investor that decided to commit all its resources to convertible hedging and to use the Kelly criterion to allocate its assets.' This investor, Thorp now confirms, was his fund Convertible Hedge Associates. From November 1969 through December 1973, the fund's cumulative gain was 102.9 percent, versus a loss (-0.5 percent) for the Dow Jones average in the same period."

Risk Management and Betting Strategies

"- A Kelly's bettor’s wealth is more volatile than the Dow or S&P 500 have historically been. In an infinite series of serial Kelly bets, the chance of your bankroll ever dipping down to half its original size is 50%. A similar rule holds for any fraction 1/n. The chance of ever dipping to 1/3 of your original bankroll is 1/3. The chance of being reduced to 1% of your bankroll is 1%. 'Any way you slice it the Kelly bettor spends a lot of time being less wealthy than he was.' - A Kelly bettor has a 1/3 chance of halving the bankroll before doubling it. - The half Kelly bettor has only a 1/9 chance of halving before doubling. The half Kelly bettor halves risk but cuts expected return by one 1/4."

Thorp's Decision Against LTCM and the Overlap with Gambling

"Thorp decided not to put any of his money in LTCM He was concerned that Merton and Scholes, brilliant as they were, had little experience investing other people's money. It didn't help that Merton was second only to Samuelson as a critic of the Kelly criterion. Thorp also had heard that Meriwether was a 'martingale man.' 'The general chatter was that he was a high roller, and it wasn't clear that the size of his bets were justified,' Thorp recalled. 'The story was that if he got in the hole, if things went against him, he'd bet more. If things still went against him, he'd bet more.’ - There is much overlap between portfolio managers and serious gamblers. Whether this is good can be argued either way. William Ziemba believes that it is mostly good. Gambling provides the most important object lesson of all: going broke. There is no better way of demonstrating the need for money management than seeing your own money vanish while making positive-expectation bets. It is impossible to make the same point so viscerally with mere stochastic differential equations. As Fred Schwed, Jr., author of 'Where Are the Customers Yachts?,' put it back in 1940, 'Like all of life's rich emotional experiences, the full flavor of losing important money cannot be conveyed by literature.’”