© 2009 Elsevier Limited. All rights reserved.
Doi:10.1016/B978-0-12-374952-9.00006-3.

2010

Staying ahead on downside risk

Giuliano De Rossi

6

Executive Summary

Critics of the mean – variance approach have pointed out its shortcomings in count-

less academic papers. It is often argued that variance is a poor measure of risk

because it treats symmetrically positive and negative returns. I argue that this fea-

ture is likely to have an adverse effect on the performance of mean – variance strate-

gies when the distribution of asset returns changes rapidly over time. Nevertheless,

a standard approach that can supersede mean – variance is yet to emerge.

This chapter discusses the advantages of an alternative measure recently advo-

cated in the academic literature, expectile value at risk (EVaR). I illustrate a sim-

ple asset allocation procedure that incorporates a dynamic model of EVaR. The

information available from time series of returns of raw assets is used to learn

about the evolution of portfolio downside risk. Risk is then minimized by tar-

geting the predicted EVaR. The new approach to asset allocation allows for

changes in the overall distribution of asset returns while retaining a high degree

of tractability.

6.1 Introduction

The aim of this chapter is provide a simple methodology to deal with downside
risk at times when the distribution of asset returns experiences sudden and dra-
matic changes. The recent turmoil due to the credit crisis provides a remark-
able example of such an environment.
Most of the existing asset allocation and portfolio construction procedures
can be viewed as a way of finding the optimal balance between return and risk,
given the portfolio manager’s preferences. As a consequence, two intricately
intertwined aspects of the procedure are fundamental to the performance of a
trading strategy: how we measure risk and how we keep track of the changes
in the risk characteristics of a portfolio.
Return volatility is arguably the most widespread risk measure in this context,
partly due to the elegance and mathematical tractability of the mean – variance
framework. Another popular risk measure, which requires a somewhat greater
effort when used for asset allocation, is value at risk (VaR). Both these measures
have been criticized in the recent academic research on risk measurement. In
fact, Artzner, Delbaen, Eber, and Heath (1999) have drawn up a list of minimal