Expectation and Optimal f : Expected Growth with and without Reinvestment for Discretely-Distributed Outcomes of Finite Length

22 Pages Posted: 15 Mar 2015 Last revised: 30 Jul 2018

Ralph Vince

Vince Strategies LLC

Date Written: July 29, 2018

Abstract

Presented is the formulation for determining the exact, expected growth-optimal fraction of equity to risk for all conditions, rather than merely the asymptotic growth-optimal fraction. The formulation presented represents the surface in the leverage space manifold, wherein the loci at the peak of the surface are those fractions for maximizing expected growth. Other criteria can be solved for upon the surface in the leverage space manifold utilizing the equation specified here. Of equal importance, since solving for the expected growth-optimal fraction involves a set of inputs and the "expectation" of those inputs, we see that the notion of mathematical expectation, as ubiquitously employed in numerous disciplines is also an asymptotic proxy for what an individual participant "expects" shall occur over a finite sequence of propositions. Thus, we determine what this expectation is over a finite sequence, demonstrate that it approaches the classical expectation as the length of the sequence becomes ever-longer, and see how this determination of "actual" expectation, versus the asymptotic "classical" one, is innately part of the human decision-making process.

Keywords: Growth-optimal portfolio, expectation, mathematical expectation, finite trials, gambling, risk management, Kelly Criterion, finite investment horizon, drawdown

JEL Classification: C02,C13,C44,C65,C70,C79,G02,G11,G12

Suggested Citation

Vince, Ralph, Expectation and Optimal f : Expected Growth with and without Reinvestment for Discretely-Distributed Outcomes of Finite Length (July 29, 2018). Available at SSRN: https://ssrn.com/abstract=2577782 or http://dx.doi.org/10.2139/ssrn.2577782

Ralph Vince (Contact Author)

Vince Strategies LLC ( email )

405 Lexington Ave - 26th fl
New York, NY 10174
United States

HOME PAGE: http://vinceprime.com

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