Operational risk with Excel and VBA

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Operational risk with Excel and VBA

Operational Risk

with Excel and VBA

Applied Statistical Methods

for Risk Management

NIGEL DA COSTA LEWIS

John Wiley & Sons, Inc.


Operational Risk

with Excel and VBA


John Wiley & Sons

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Operational Risk

with Excel and VBA

Applied Statistical Methods

for Risk Management

NIGEL DA COSTA LEWIS

John Wiley & Sons, Inc.


Copyright © 2004 by Nigel Da Costa Lewis. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data

Lewis, Nigel Da Costa.

Operational risk with Excel and VBA : applied statistical methods for

risk management / Nigel Da Costa Lewis.

p. cm.

“Published simultaneously in Canada.”

Includes index.

ISBN 0-471-47887-3

1. Risk management—Statistical methods. 2. Risk

management—Mathematical models. I. Title.

HD61 .L49 2004

658.15′5′0285554—dc22

2003023869

Printed in the United States of America.

10 9 8 7 6 5 4 3 2 1


In loving memory of my mother-in-law,

Lydora.

Her devotion and wisdom nurtured my wife

into becoming the encouraging source

of strength that she is today.

These qualities have inspired

and enabled me to complete this work.


Contents

Preface

Acknowledgments

xiii

xv

CHAPTER 1

Introduction to Operational Risk Management and Modeling

What is Operational Risk

The Regulatory Environment

Why a Statistical Approach to Operational Risk Management

Summary

Review Questions

Further Reading

CHAPTER 2

Random Variables, Risk indicators, and Probability

Random Variables and Operational Risk Indicators

Types of Random Variable

Probability

Frequency and Subjective Probability

Probability Functions

Case Studies

Case Study 2.1: Downtown Investment Bank

Case Study 2.2: Mr. Mondey’s OPVaR

Case Study 2.3: Risk in Software Development

Useful Excel Functions

Summary

Review Questions

Further Reading

1

1

3

5

6

6

6

7

7

8

9

11

13

16

17

20

20

24

24

25

26

vii


viii

CONTENTS

CHAPTER 3

Expectation, Covariance, Variance, and Correlation

Expected Value of a RandomVariable

Variance and Standard Deviation

Covariance and Correlation

Some Rules for Correlation, Variance, and Covariance

Case Studies

Case Study 3.1: Expected Time to Complete

a Complex Transaction

Case Study 3.2: Operational Cost of System Down Time

Summary

Review Questions

Further Reading

27

27

31

32

34

35

35

37

38

38

39

CHAPTER 4

Modeling Central Tendency and Variability of Operational Risk Indicators

Empirical Measures of Central Tendency

Measures of Variability

Case Studies

Case Study 4.1: Approximating Business Risk

Excel Functions

Summary

Review Questions

Further Reading

CHAPTER 5

Measuring Skew and Fat Tails of Operational Risk Indicators

Measuring Skew

Measuring Fat Tails

Review of Excel and VBA Functions for Skew and Fat Tails

Summary

Review Questions

Further Reading

CHAPTER 6

Statistical Testing of Operational Risk Parameters

Objective and Language of Statistical Hypothesis Testing

Steps Involved In Conducting a Hypothesis Test

Confidence Intervals

Case Study 6.1: Stephan’s Mistake

Excel Functions for Hypothesis Testing

41

41

43

44

44

47

47

48

49

51

51

54

57

58

58

58

59

59

61

64

65

67


Contents

ix

Summary

Review Questions

Further Reading

CHAPTER 7

Severity of Loss Probability Models

Normal Distribution

Estimation of Parameters

Beta Distribution

Erlang Distribution

Exponential Distribution

Gamma Distribution

Lognormal Distribution

Pareto Distribution

Weibull Distribution

Other Probability Distributions

What Distribution Best Fits My Severity of Loss Data

Case Study 7.1: Modeling Severity of Loss Legal

Liability Losses

Summary

Review Questions

Further Reading

CHAPTER 8

Frequency of Loss Probability Models

Popular Frequency of Loss Probability Models

Other Frequency of Loss Distributions

Chi-Squared Goodness of Fit Test

Case Study 8.1: Key Personnel Risk

Summary

Review Questions

Further Reading

CHAPTER 9

Modeling Aggregate Loss Distributions

Aggregating Severity of Loss and Frequency

of Loss Distributions

Calculating OpVaR

Coherent Risk Measures

Summary

Review Questions

Further Reading

67

68

68

69

69

72

72

77

77

78

80

81

81

83

84

86

91

91

92

93

93

98

100

102

103

103

103

105

105

108

110

112

112

112


x

CONTENTS

CHAPTER 10

The Law of Significant Digits and Fraud Risk Identification

The Law of Significant Digits

Benford’s Law in Finance

Case Study 10.1: Analysis of Trader’s Profit and Loss

Using Benford’s Law

A Step Towards Better Statistical Methods of Fraud Detection

Summary

Review Questions

Further Reading

CHAPTER 11

Correlation and Dependence

Measuring Correlation

Dependence

Stochastic Dependence

Summary

Review Questions

Further Reading

CHAPTER 12

Linear Regression in Operational Risk Management

The Simple Linear Regression Model

Multiple Regression

Prediction

Polynomial and Other Types of Regression

Multivariate Multiple Regression

Regime-Switching Regression

The Difference Between Correlation and Regression

A Strategy for Regression Model Building

in Operational Risk Management

Summary

Review Questions

Further Reading

CHAPTER 13

Logistic Regression in Operational Risk Management

Binary Logistic Regression

Bivariate Logistic Regression

Case Study 13.1: Nostro Breaks and Volume

in a Bivariate Logistic Regression

Other Approaches for Modeling Bivariate Binary Endpoints

113

113

116

116

118

120

120

120

121

121

132

134

136

136

136

137

137

148

153

155

155

157

158

159

159

159

160

161

161

165

172

173


Contents

xi

Summary

Review Questions

Further Reading

CHAPTER 14

Mixed Dependent Variable Modeling

A Model for Mixed Dependent Variables

Working Assumption of Independence

Understanding the Benefits of Using a WAI

Case Study 14.1: Modeling Failure in Compliance

Summary

Review Questions

Further Reading

CHAPTER 15

Validating Operational Risk Proxies Using Surrogate Endpoints

The Need for Surrogate Endpoints in OR Modeling

The Prentice Criterion

Limitations of the Prentice Criterion

The Real Value Added of Using Surrogate Variables

Validation Via the Proportion Explained

Limitations of Surrogate Modelling in Operational

Risk Management

Case Study 15.1: Legal Experience as a Surrogate Endpoint

for Legal Costs for a Business Unit

Summary

Review Questions

Further Reading

CHAPTER 16

Introduction to Extreme Value Theory

Fisher-Tippet–Gnedenko Theorem

Method of Block Maxima

Peaks over Threshold Modeling

Summary

Review Questions

Further Reading

CHAPTER 17

Managing Operational Risk with Bayesian Belief Networks

What is a Bayesian Belief Network

Case Study 17.1: A BBN Model for Software Product Risk

Creating a BBN-Based Simulation

176

177

177

179

179

181

184

184

185

186

186

187

187

188

191

193

196

200

201

202

202

202

203

203

205

206

207

207

207

209

209

212

215


xii

CONTENTS

Assessing the Impact of Different Managerial Strategies

Perceived Benefits of Bayesian Belief Network Modeling

Common Myths About BBNs—

The Truth for Operational Risk Management

Summary

Review Questions

Further Reading

CHAPTER 18

Epilogue

Winning the Operational Risk Argument

Final Tips on Applied Operational Risk Modeling

Further Reading

Appendix

Statistical Tables

Cumulative Distribution Function of the Standard

Normal Distribution

Chi-Squared Distribution

Student’s t Distribution

F Distribution

Notes

Bibliography

About the CD-ROM

Index

216

218

222

224

224

224

225

225

226

226

227

227

230

232

233

237

245

255

259


Preface

CHAPTER 1: Preface

ntil a few year ago most banks and other financial institutions paid little

U attention to measuring or quantifying operational risk. In recent years

this has changed. Understanding and managing operational risk are essential

to a company’s future survival and prosperity. With the regulatory spotlight

on operational risk management, there has been ever-increasing

attention devoted to the quantification of operational risks. As a result we

have seen the emergence of a wide array of statistical methods for measuring,

modeling, and monitoring operational risk. Working out how all these

new statistical tools relate to one another and which to use and when is a

not a straightforward issue.

Although a handful of books explain and explore the concept of operational

risk per se, it is often quite difficult for a practicing risk manager to

turn up a quickly digestible introduction to the statistical methods that can

be used to model, monitor, and assess operational risk. This book provides

such an introduction, using Microsoft Excel and Visual Basic For Applications

(VBA) to illustrate many of the examples. It is designed to be used “on

the go,” with minimal quantitative background. Familiarity with Excel or

VBA is a bonus, but not essential. Chapter sections are generally short—

ideal material for the metro commute into and from work, read over lunch,

or dipped into while enjoying a freshly brewed cup of coffee. To improve

your understanding of the methods discussed, case studies, examples, interactive

illustrations, review questions, and suggestions for further reading

are included in many chapters.

In writing this text I have sought to bring together a wide variety of statistical

methods and models that can be used to model, monitor, and assess

operational risks. The intention is to give you, the reader, a concise and

applied introduction to statistical modeling for operational risk management

by providing explanation, relevant information, examples, and interactive

illustrations together with a guide to further reading. In common

xiii


xiv

PREFACE

with its sister book Applied Statistical Methods for Market Risk Management

(Risk Books, March 2003), this book has been written to provide the

time-starved reader, who may not be quantitatively trained, with rapid and

succinct introduction to useful statistical methods that must otherwise be

gleaned from scattered, obscure, or mathematically obtuse sources. In this

sense, it is not a book about the theory of operational risk management or

mathematical statistics per se, but a book about the application of statistical

methods to operational risk management.

Successful modeling of operational risks is both art and science. I hope

the numerous illustrations, Excel examples, case studies, and VBA code listings

will serve both as an ideas bank and technical reference. Naturally, any

such compilation must omit some models and methods. In choosing the

material, I have been guided both by the pragmatic “can do” requirement

inherent in operational risk management, and by my own practical experience

gained over many years working as a statistician and quantitative

analyst in the City of London, on Wall Street, at the quantitative research

boutique StatMetrics, and in academia. Thus, this is a practitioners’ guide

book. Topics that are of theoretical interest but of little practical relevance

or methods that I have found offer at best a marginal improvement over the

most parsimonious alternative are ignored. As always with my books on

applied statistical methods, lucidity of style and simplicity of expression

have been my twin objectives.

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