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

摘要

We develop the idea of using Monte Carlo sampling of random portfolios tosolve portfolio investment problems. In this first paper we explore the needfor more general optimization tools, and consider the means by whichconstrained random portfolios may be generated. A practical scheme for thelong-only fully-invested problem is developed and tested for the classic QPapplication. The advantage of Monte Carlo methods is that they may be extendedto risk functions that are more complicated functions of the returndistribution, and that the underlying return distribution may be computedwithout the classical Gaussian limitations. The optimization of quadraticrisk-return functions, VaR, CVaR, may be handled in a similar manner tovariability ratios such as Sortino and Omega, or mathematical constructionssuch as expected utility and its behavioural finance extensions.Robustification is also possible. Grid computing technology is an excellentplatform for the development of such computations due to the intrinsicallyparallel nature of the computation, coupled to the requirement to transmit onlysmall packets of data over the grid. We give some examples deployingGridMathematica, in which various investor risk preferences are optimized withdiffering multivariate distributions. Good comparisons with established resultsin Mean-Variance and CVaR optimization are obtained when ``edge-vertex-biased''sampling methods are employed to create random portfolios. We also give anapplication to Omega optimization.