CHAPTER 2
Incorporating
Diversification into
Risk Management
Amiyatosh Purnanandam, Mitch Warachka, Yonggan Zhao
and William T. Ziemba∗2.1 INTRODUCTION
Risk measurement is of fundamental importance to financial practice. Given
the widespread usage of Value-at-Risk (VaR), firms actively manage their
risk. Unfortunately, VaR is not derived from fundamental economic princi-
ples and may lead to sub-optimal decisions as shown by Shapiro and Basak
(2001).
Substantial progress in the academic risk management literature began
withArtzner, Delbaen, Eber and Heath (1999), abbreviatedADEH hereafter,
who develop an axiomatic framework for risk measurement. Their axioms
stem from intuitive economic principles that define a coherent risk mea-
sure. The intent of ADEH is to provide a regulator with a methodology for
determining the riskfree capital requirements of a firm, conditional on their
existing portfolio. Indeed, a coherent risk measure is defined as the mini-
mum amount of riskfree capital a portfolio requires to become acceptable to
the regulator.
∗Mitch Warachka and Yonggan Zhao gratefully acknowledge financial support from the
Wharton-SMU Research Center, Singapore Management University, and the Center for
Research in Financial Services, Nanyang Technological University. William T. Ziemba acknowl-
edgesfinancialsupportfromtheNaturalSciencesandEngineeringResearchCouncilofCanada.
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