Towards a New Stock Trading Model for a Kelly Betting Practitioner

The takeoff for this paper is the voluminous body of literature on Kelly Betting in the context of stock market trading. As far as motivation for this work is concerned, the following point is central: The vast preponderance of this literature begins by assuming some “underlying” theoretical model for stock prices, such as Geometric Brownian Motion (GBM), and typically uses empirical data to numerically estimate the parameters entering these dynamics on the way to constructing a trading strategy. In contrast to this literature, our approach in this paper has three salient features: First, no functional form such as GBM for the stock price dynamics is assumed. Second, in our new model for updating the account value, the number of shares held and the cash balance from stage k to k + 1 is entirely data driven based on empirical values of the quadruple (open, low, high, close) of the realized prices in each period. Third, this update is customized to the order type being submitted by the trader. Whereas the special case of a market order replicates results in existing papers, new state equations arise for other types of “contingent orders” that practitioners typically submit. Within this new framework, in this initial piece of work, similar to a number of existing papers in the control literature, we view Kelly’s betting fraction K as a feedback gain. Then, unlike existing papers, an optimal gain is obtained by maximizing a metric that we call the Empirical Logarithmic Growth (ELG). The paper also includes a backtesting simulation to illustrate the use of our new model for market and limit orders and includes suggestions for future research aimed at the practitioner’s needs.