Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street

In the most direct human terms, LTCM’s problem was group-think. Under John Meriwether, there was an organizational culture in which questions of risk were pressed only so far. This appears to have led to systematically rosy projections. Too little of the fund’s brainpower went to skeptical probing of what could have gone wrong.

The best you can do right now is to choose a portfolio with the highest geometric mean of the probability distribution of outcomes, as computed from current means, variances, and other statistics. The returns and volatility of your investments will change with time. When they do, you should adjust your portfolio accordingly, again with the sole obj

Latané called his approach to portfolio design the geometric mean criterion. He demonstrated that it is a myopic strategy. A “near-sighted” strategy sounds like a bad thing, but as economists use it, it’s good. It means that you don’t have to have a crystal ball on what the market is going to do in the future in order to make good decisions now. Th

The core of John Kelly’s philosophy of risk can be stated without math. It is that even unlikely events must come to pass eventually. Therefore, anyone who accepts small risks of losing everything will lose everything, sooner or later. The ultimate compound return rate is acutely sensitive to fat tails.

Life is short, and the stock market is a slow game. In blackjack, it’s double or nothing every forty seconds. In the stock market, it generally takes years to double your money—or to lose practically everything. No buy-and-hold stock investor lives long enough to have a high degree of confidence that the Kelly system will pull ahead of all others.

When faced with a choice of wagers or investments, choose the one with the highest geometric mean of outcomes. This rule, of broader application than the edge/odds Kelly formula for bet size, is the Kelly criterion.

For reasons mathematical, psychological, and sociological, it is a good idea to use a money management system that is relatively forgiving of estimation errors.

Within a few years as U.S. Attorney, Giuliani was probably the nation’s best-known crime-fighter since J. Edgar Hoover. That was due both to how many important convictions he secured and to his genius for promoting them. Though Giuliani expanded the U.S. Attorney’s office to 132 assistants, he presented himself as the iconic figurehead of that offi

The infinite expectation is a big problem for anyone who wants to use math to decide what to do in the real world. It implies that no amount of money is too much to pay for the privilege of playing this game. Were a casino to charge a million dollars to play this game, rational customers should jump at the chance, it would seem. Same if the casino