Optimal trading quantity integration as a basis for optimal portfolio management

Abstract

The author in this paper points out the reason behind calculating and using optimal trading quantity in conjunction with Markowitz’s Modern portfolio theory. In the opening part the author presents an example of calculating optimal weights using Markowitz’s Mean-Variance approach, followed by an explanation of basic logic behind optimal trading quantity. The use of optimal trading quantity is not limited to systems with Bernoulli outcome, but can also be used when trading shares, futures, options etc. Optimal trading quantity points out two often-overlooked axioms: (1) a system with negative mathematical expectancy can never be transformed in a system with positive mathematical expectancy, (2) by missing the optimal trading quantity an investor can turn a system with positive expectancy into a negative one. Optimal trading quantity is that quantity which maximizes geometric mean (growth function) of a particular system. To determine the optimal trading quantity for simpler systems, with a very limited number of outcomes, a set of Kelly’s formulas is appropriate. In the conclusion the summary of the paper is presented.

Keywords

• Optimal portfolio
• Trading
• Optimal trading quantity
• Game theory