Fortune’s Formula: How the Pros Wager Using the Kelly Capital Growth Investment Criterion?

Many top investors in the futures market and in sports betting use Kelly investing since it maximizes long run growth almost surely. The idea goes back to Daniel Bernoulli in 1738 who postulated that there was declining marginal utility in wealth and it might be equal to the reciprocal of current wealth. Thus expected log was the chosen utility function. Kelly in 1956 showed its use in investments. For many applications it results in not diversifying investments but instead focusing on a small number of best opportunities. It is a risky but wise strategy. But is very risky short term since it has essentially zero Arrow-Pratt absolute risk aversion. So in some cases fractional Kelly, which blends full Kelly with cash, might be better. That gives more security but less wealth long term. Fractional Kelly is associated with negative power utility when the assets are log normal and approximate otherwise for non lognormal assets. We discuss lottery applications and good versus bad properties of the strategies.