Optimizing Optimization: The Next Generation of Optimization Applications and Theory (Quantitative Finance)

(Romina) #1

© 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

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