An Analytic Solution for Asset Allocation with a Multivariate Laplace Distribution

Abstract

In this short note the theory for multi-variate asset allocation with elliptically symmetric distributions of returns, as developed in the authors prior work, is specialized to the case of returns drawn from a multi-variate Laplace distribution. This analysis delivers a result closely, but not perfectly, consistent with the conjecture presented in the author's article Thinking Differently About Asset Allocation. The principal differences are due to the introduction of a term in the dimensionality of the problem, which was omitted from the conjectured solution, and a re-scaling of the variance due to varying parameterizations of the univariate Laplace distribution.

Keywords: utility theory, negative exponential utility, asset allocation strategy, trading strategy, portfolio theory, leptokurtosis, market returns

JEL Classification: G11