Monte Carlo Portfolio Optimization for General Investor Risk-Return Objectives and Arbitrary Return Distributions: a Solution for Long-only Portfolios

TL;DR

This paper introduces a Monte Carlo sampling approach for portfolio optimization that accommodates complex risk measures and arbitrary return distributions, offering a flexible and scalable alternative to traditional methods.

Contribution

It develops a Monte Carlo-based framework for portfolio optimization that handles general risk functions and return distributions, extending beyond classical Gaussian assumptions.

Findings

Effective for quadratic risk-return functions like VaR and CVaR

Comparable results to traditional Mean-Variance and CVaR optimization

Demonstrates scalability using grid computing technology

Abstract

We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random portfolios may be generated. A practical scheme for the long-only fully-invested problem is developed and tested for the classic QP application. The advantage of Monte Carlo methods is that they may be extended to risk functions that are more complicated functions of the return distribution, and that the underlying return distribution may be computed without the classical Gaussian limitations. The optimization of quadratic risk-return functions, VaR, CVaR, may be handled in a similar manner to variability ratios such as Sortino and Omega, or mathematical constructions such as expected utility and its behavioural finance extensions. Robustification is also possible. Grid computing technology is an excellent platform for the development of such computations due to the intrinsically parallel nature of the computation, coupled to the requirement to transmit only small packets of data over the grid. We give some examples deploying GridMathematica, in which various investor risk preferences are optimized with differing multivariate distributions. Good comparisons with established results in Mean-Variance and CVaR optimization are obtained when ``edge-vertex-biased'' sampling methods are employed to create random portfolios. We also give an application to Omega optimization.