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
Funding Sources
DePaul University College of Science and Health
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.