Contents

Cover

Title Page

Copyright

CHAPTER 6: Risk and Uncertainty

6.1 INTRODUCTION

6.2 MEASURES OF DISPERSION

6.3 PROBABILITY METRICS AND DISPERSION MEASURES

6.4 MEASURES OF RISK

6.5 RISK MEASURES AND DISPERSION MEASURES

6.6 RISK MEASURES AND STOCHASTIC ORDERS

6.7 SUMMARY

6.8 TECHNICAL APPENDIX

Copyright © 2011 by John Wiley & Sons, Inc. All rights reserved.

Disclaimer. This content is excerpted from Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures, by Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi (978-0-470-05316-4, 2008), with permission from the publisher John Wiley & Sons. You may not make any other use, or authorize others to make any other use of this excerpt, in any print or non-print format, including electronic or multimedia.

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

There has been major debate on the differences and common features of risk and uncertainty. Both notions are related but they do not coincide. Risk is often argued to be a subjective phenomenon involving exposure and uncertainty. That is, generally, risk may arise whenever there is uncertainty. This Wiley Global Finance Executive Select content focuses on the quantifiable aspects of risk and includes discussion of key concerns, specifically measures of dispersion (deviation), probability metrics, measures of risk (Value-at-Risk), stochastic orders, and more. This is advanced content for portfolio managers, sophisticated financial readers and investors, institutional risk officers, and perpetual students of risk.

Derived from Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi. Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures. Hoboken, NJ: John Wiley & Sons, Inc., 2008. 978-0-470-05316-4; 382 pp.

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CHAPTER 6

Risk and Uncertainty

6.1 INTRODUCTION

There has been a major debate on the differences and common features of risk and uncertainty. Both notions are related but they do not coincide. Risk is often argued to be a subjective phenomenon involving and . That is, generally, risk may arise whenever there is uncertainty.