Risk Limited Asset Allocation with a Budget Threshold Utility Function and Leptokurtotic Distributions of Returns

TL;DR

This paper introduces an analytical solution for single-horizon asset allocation considering a novel 'budget threshold utility' and return distributions with leptokurtosis, simplifying the understanding of risk costs in trading.

Contribution

It presents a new analytical approach to asset allocation with a piecewise-linear utility function and exogenous limits, highlighting a simple, interpretable structure.

Findings

Analytical solution derived for the utility maximization problem.

The solution incorporates a risk cost component.

Applicable to leptokurtotic return distributions.

Abstract

An analytical solution to single-horizon asset allocation for an investor with a piecewise-linear utility function, called herein the "budget threshold utility," and exogenous position limits is presented. The resulting functional form has a surprisingly simple structure and can be readily interpreted as representing the addition of a simple "risk cost" to otherwise frictionless trading.