# The Kelly Capital Growth Investment Criterion

This book is the definitive treatment of "Fortune's Formula," also described as "The Kelly Criterion", used by gamblers and investors alike to determine the optimal size of a series of bets.

This volume provides the definitive treatment of fortune’s formula or the Kelly capital growth criterion as it is often called. The strategy is to maximize long run wealth of the investor by maximizing the period by period expected utility of wealth with a logarithmic utility function. Mathematical theorems show that only the log utility function maximizes asymptotic long run wealth and minimizes the expected time to arbitrary large goals. In general, the strategy is risky in the short term but as the number of bets increase, the Kelly bettor’s wealth tends to be much larger than those with essentially different strategies. So most of the time, the Kelly bettor will have much more wealth than these other bettors but the Kelly strategy can lead to considerable losses a small percent of the time. There are ways to reduce this risk at the cost of lower expected final wealth using fractional Kelly strategies that blend the Kelly suggested wager with cash. The various classic reprinted papers and the new ones written specifically for this volume cover various aspects of the theory and practice of dynamic investing. Good and bad properties are discussed, as are fixed-mix and volatility induced growth strategies. The relationships with utility theory and the use of these ideas by great investors are featured.

“This is a fantastic reference covering the theory and practice of the field beautifully organized and produced. I have already used it and I will refer it to my students and colleagues.”

—Professor David G Luenberger, Stanford University

“This volume provides a fascinating historical account and critical assessment of the Kelly criterion (expected logarithmic utility maximization) as a universal criterion for the tradeoff between risk and return in portfolio management and gambling.”

—George M Constantinides, Leo Melamed Professor of Finance, The University of Chicago, USA

“This book provides a comprehensive survey of research and applications on the Kelly growth optimal strategy that maximizes the expected utility of the log of final wealth…This book provides a fine coverage of these topics from original sources and recent research publications.”

—Quantitative Finance

“For those who have heard of the Kelly mythos and want to explore the science behind it, this book will be an instant classic. The editors have collected all the pivotal original papers, spanning centuries and the rarely bridged gulf between theory and practice. This book is indispensable for anyone interested in Kelly’s legacy.”

—William Poundstone, Author of

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

“The present handbook assembles in an impressive way the classical papers and also provides the link to modern research. It also presents important papers with a critical view towards the Kelly criterion.”

—Professor Walter Schachermayer, Faculty of Mathematics, University of Vienna