Optimal Level of Leverage using Numerical Methods

Advances in computer software and in agent-based computational finance allow the use of numerical methods in order to optimize different type of functions. In this paper we propose a numerical method in order to find the level of leverage that maximizes the geometric mean of a series of historical daily returns. One of the advantages of the use of numerical methods is that it requires less assumption than analytical methods with closed-form solutions. Furthermore, after running an experiment, the analysis of the results demonstrates that the use of numerical methods yields a higher geometric mean than the use of analytical method based on the assumption of a geometric Brownian motion. JEL Classification: C61