This note is one of a series about the books that have informed and inspired my life and work. Click here for the previous book, A Demon Of Our Own Design.
Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street brings together gaming, mathematics, and investing in a fascinating and applicable story. The fast-paced tale begins with the history of the "private wire" in gaming, an informational edge that allows one party to bet with a durable advantage. From there, it leaps to Bell Labs in 1956 where Claude Shannon essentially invented information theory, the mathematic work that gave birth to our modern digital age. Connecting Shannon to a web of geniuses and gangsters, William Poundstone puts forth a new theory of gambling.
What was applicable? The life changing idea in this book, for me, is the Kelly formula, the system that we use for sizing all of our investment exposures.
Almost everyone who gambles eventually loses their money. Once a gambler is bankrupt, the game ends. The most obvious way to avoid this outcome is to not play. However, if someone has a real edge, what are they supposed to do with it? Size a bet at zero and throw away the edge? Size it at 100% of one's bankroll and risk a significant chance of bankruptcy? In short, to what use should you put an advantage, if you have one?
A scientist at Bell Labs, John Kelly, Jr., solved this riddle. According to the Kelly formula, one should wager the fraction of one's bankroll on a bet equal to your edge over the odds. In market parlance, the correct percentage of a portfolio's equity allocated to a position should be based upon the variance of the probability of the upside over the downside compared to the market price all divided by the market's implied probability, which is the odds that the capital markets offer.
where: f* is the fraction of the current bankroll to wager
b is the net odds received on the wager
p is the probability of winning
q is the probability of losing, which is 1 − p
Without a private wire or a similar advantage, one's edge is zero. If you do not know anything that is not already priced into the market, then the Kelly formula will size a bet at zero. The formula also allows for uncertainty, which reduces edge and therefore position size. Return is maximized when the edge is highest. Ultimately, information equals money (pages 72-75 are key in explaining the formula). As an edge becomes recognized and understood by the market, position sizes should converge upon zero.
The caveat is that the Kelly formula does not guarantee that you will make money on any given bet. Kelly is a survival mechanism by which you will win or lose in the short term, but you will always survive. When you survive until the long-term, you will eventually get approximately an outcome equal to the expected value of your investments.
The Kelly formula is so unbelievably potent because it maximizes profit while at the same time minimizing the chance of ruin. In short, it is safe and lucrative. It grows wealth faster than any alternative. Both overbetting and underbetting Kelly lead to a lower return. Fixed wagers lead to less return. "Bet-it-all" tactics tend to lead to nearly instant ruin. Martingale, a mean reversion system which works for a while, eventually falls to Kelly as well. At its heart, Kelly works because of the law of large numbers, which says that the percentage of a given outcome approaches the expected percentage as the number of iterations increases. Kelly sizes positions so that you stay alive long enough for the law of large numbers to work its magic. In the long run, Kelly sizing is unbeatable.
In 1956 two Bell Labs scientists discovered the scientific formula for getting rich. One was mathematician Claude Shannon, neurotic father of our digital age, whose genius is ranked with Einstein's. The other was John L. Kelly Jr., a Texas-born, gun-toting physicist. Together they applied the science of information theory--the basis of computers and the Internet--to the problem of making as much money as possible, as fast as possible.