© 2009 Elsevier Limited. All rights reserved.
Doi:10.1016/B978-0-12-374952-9.00002-6.

2010

Novel approaches to portfolio

construction: multiple risk models

and multisolution generation

Sebastian Ceria , Francois Margot , Anthony Renshaw

and Anureet Saxena

2

Executive Summary

This chapter highlights several novel methods for portfolio optimization. One

approach involves using more than one risk model and a systematic calibration

procedure is described for incorporating more than one risk model in a portfolio

construction strategy. The addition of a second risk model can lead to better over-

all performance than one risk model alone provided that the strategy is calibrated

so that both risk models affect the optimal portfolio solution. In addition, the

resulting portfolio is no more conservative than the portfolio obtained with one

risk model alone.

The second approach addresses the issue of generating multiple interesting

solutions to the portfolio optimization problem. It borrows the concept of “ elas-

ticity ” from Economics, and adapts it within the framework of portfolio optimiza-

tion to evaluate the relative significance of various constraints in the strategy. By

examining heatmaps of portfolio characteristics derived by perturbing constraints

with commensurable elasticities, it offers insights into trade-offs associated with

modifying constraint bounds. Not only do these techniques assist in enhancing

our understanding of the terrain of optimal portfolios, they also offer the unique

opportunity to visualize trade-offs associated with mathematically intractable

metrics such as transfer coefficient. A carefully designed case study elucidates the

practical utility of these techniques in generating multiple interesting solutions to

portfolio optimization.

These methods are representative of Axioma’s new approach to portfolio con-

struction that creates real-world value in optimized portfolios.

2.1 Introduction

Optimization as an applied discipline has a history spanning more than six
decades. Although highly successful in a variety of real-world applications such
as supply chain management, manufacturing, scheduling, etc., the penetration