Estimation of Kelly fraction from Historical Returns

Session Title

Session 2-3-E: Mathematics and Statistics I

Presentation Type

Paper Presentation

Location

Park MGM, Las Vegas, NV

Start Date

24-5-2023 1:30 PM

End Date

24-5-2023 3:00 PM

Disciplines

Probability | Statistical Models | Statistics and Probability

Abstract

It is well-known that the long-term growth rate for a series of independent and identically distributed bets is maximized by maximizing expected log utility. This is known as the Kelly criterion. It has many optimality properties but is usually considered to overwhelm individual risk tolerances. Blackjack teams and other advantage gamblers typically practice a fraction of the Kelly optimal to decrease riskiness. We use a discrete optimization model to estimate the historical Kelly fraction and then compare it to an earlier Geometric Brownian Motion model. We present an estimator for the historical Kelly fraction employed and its variance for a time series of independent i.i.d. bets. Simulations and historical data from a range of sources are examined.

Keywords

Kelly criterion, optimal betting, proportional betting, Kelly fraction

Author Bios

William Chin, Ph. D.

Professor

Dept. of Mathematical Sciences

DePaul University

Chicago, Illinois

Funding Sources

DePaul University College of Science and Health

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May 24th, 1:30 PM May 24th, 3:00 PM

Estimation of Kelly fraction from Historical Returns

Park MGM, Las Vegas, NV

It is well-known that the long-term growth rate for a series of independent and identically distributed bets is maximized by maximizing expected log utility. This is known as the Kelly criterion. It has many optimality properties but is usually considered to overwhelm individual risk tolerances. Blackjack teams and other advantage gamblers typically practice a fraction of the Kelly optimal to decrease riskiness. We use a discrete optimization model to estimate the historical Kelly fraction and then compare it to an earlier Geometric Brownian Motion model. We present an estimator for the historical Kelly fraction employed and its variance for a time series of independent i.i.d. bets. Simulations and historical data from a range of sources are examined.