© 2010 Elsevier Limited. All rights reserved.
Doi:10.1016/B978-0-12-374952-9.00011-7.

2010

Heuristic portfolio optimization:

Bayesian updating with the

Johnson family of distributions

Richard Louth

11

Executive Summary

This chapter seeks to advance the methodological basis for the use of

non-Gaussian alternatives to traditional mean – variance analysis for large-dimension

portfolio optimization problems. Through the application of a threshold accept-

ance algorithm and an appropriately chosen distribution from the Johnson family,

we show how portfolio weights for an otherwise computationally intensive asset

allocation problem can be obtained in a quick and efficient manner. The inherent

flexibility and generality of this approach is further illustrated by two practical

extensions. First, we introduce the idea of data reweighting as a simple and, most

importantly, computationally tractable method for improving the robustness of

our optimization algorithm. And second, we demonstrate how return forecasts

( “ alphas ” ) can be seamlessly incorporated into the estimation procedure via

Bayesian updating. In this case, we utilize an important property of the Johnson

family to build a model of the joint dependence between returns and their fore-

casts using the class of meta-elliptical distributions.

11.1 Introduction

Contrary to overwhelming empirical evidence, the most popular commercial port-
folio optimizers are still based on Gaussian fundamentals. For large-dimension
problems in particular, the lure of analytical tractability and computational
convenience afforded by Gaussianity appears too tempting to resist. Yet, the
recent financial turmoil has reignited the debate surrounding the adequacy
of the Gaussian paradigm and highlighted the potential dangers associated
with Gaussian assumptions in a non-Gaussian world. Moreover, the relent-
less nature of Moore’s Law means that computational barriers to alternative
approaches are continually being eroded as new algorithms are developed and
the power of parallel computing is realized.^1

1 In 1965, Intel cofounder Gordon Moore correctly predicted that the number of transistors that
can be placed on an integrated circuit would double approximately every 2 years ( Moore, 1965 ).