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Advanced Modelling in Finance

using Excel and VBA

Wiley Finance Series

Operational Risk: Measurement and Modelling

Jack King

Advance Credit Risk Analysis: Financial Approaches and Mathematical Models to Assess, Price and

Manage Credit Risk

Didier Cossin and Hugues Pirotte

Dictionary of Financial Engineering

John F. Marshall

Pricing Financial Derivatives: The Finite Difference Method

Domingo A Tavella and Curt Randall

Interest Rate Modelling

Jessica James and Nick Webber

Handbook of Hybrid Instruments: Convertible Bonds, Preferred Shares, Lyons, ELKS, DECS and

Other Mandatory Convertible Notes

Izzy Nelken (ed)

Options on Foreign Exchange, Revised Edition

David F DeRosa

The Handbook of Equity Derivatives, Revised Edition

Jack Francis, William Toy and J Gregg Whittaker

Volatility and Correlation in the Pricing of Equity, FX and Interest-Rate Options

Riccardo Rebonato

Risk Management and Analysis vol. 1: Measuring and Modelling Financial Risk

Carol Alexander (ed)

Risk Management and Analysis vol. 2: New Markets and Products

Carol Alexander (ed)

Implementing Value at Risk

Philip Best

Credit Derivatives: A Guide to Instruments and Applications

Janet Tavakoli

Implementing Derivatives Models

Les Clewlow and Chris Strickland

Interest-Rate Option Models: Understanding, Analysing and Using Models for Exotic Interest-Rate

Options (second edition)

Riccardo Rebonato

Advanced Modelling in Finance

using Excel and VBA

Mary Jackson

and

Mike Staunton

JOHN WILEY & SONS, LTD

Chichester

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Weinheim

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Toronto

Copyright?2001 by John Wiley & Sons, Ltd,

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British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

ISBN 0 471 49922 6

Typeset in 10/12pt Times by Laserwords Private Limited, Chennai, India Printed and bound in Great Britain by Bookcraft (Bath) Ltd, Midsomer-Norton This book is printed on acid-free paper responsibly manufactured from sustainable forestry, in which at least two trees are planted for each one used for paper production.

Contents

Prefacexi

Acknowledgementsxii

1 Introduction1

1.1 Finance insights 1

1.2 Asset price assumptions 2

1.3 Mathematical and statistical problems 2

1.4 Numerical methods 2

1.5 Excel solutions 3

1.6 Topics covered 3

1.7 Related Excel workbooks 5

1.8 Comments and suggestions 5

Part One Advanced Modelling in Excel7

2 Advanced Excel functions and procedures9

2.1 Accessing functions in Excel 9

2.2 Mathematical functions 10

2.3 Statistical functions 12

2.3.1 Using the frequency function 12

2.3.2 Using the quartile function 14

2.3.3 Using Excel"s normal functions 15

2.4 Lookup functions 16

2.5 Other functions 18

2.6 Auditing tools 19

2.7 Data Tables 20

2.7.1 Setting up Data Tables with one input 20

2.7.2 Setting up Data Tables with two inputs 22

2.8 XY charts 23

2.9 Access to Data Analysis and Solver 26

2.10 Using range names 27

2.11 Regression 28

2.12 Goal Seek 31

vi Contents

2.13 Matrix algebra and related functions 33

2.13.1 Introduction to matrices 33

2.13.2 Transposing a matrix 33

2.13.3 Adding matrices 34

2.13.4 Multiplying matrices 34

2.13.5 Matrix inversion 35

2.13.6 Solving systems of simultaneous linear equations 36

2.13.7 Summary of Excel"s matrix functions 37

Summary 37

3 Introduction to VBA39

3.1 Advantages of mastering VBA 39

3.2 Object-oriented aspects of VBA 40

3.3 Starting to write VBA macros 42

3.3.1 Some simple examples of VBA subroutines 42

3.3.2 MsgBox for interaction 43

3.3.3 The writing environment 44

3.3.4 Entering code and executing macros 44

3.3.5 Recording keystrokes and editing code 45

3.4 Elements of programming 47

3.4.1 Variables and data types 48

3.4.2 VBA array variables 48

3.4.3 Control structures 50

3.4.4 Control of repeating procedures 51

3.4.5 Using Excel functions and VBA functions in code 52

3.4.6 General points on programming 53

3.5 Communicating between macros and the spreadsheet 53

3.6 Subroutine examples 56

3.6.1 Charts 56

3.6.2 Normal probability plot 59

3.6.3 Generating the efficient frontier with Solver 61

Summary 65

References 65

Appendix 3A The Visual Basic Editor 65

Stepping through a macro and using other

debug tools 68 Appendix 3B Recording keystrokes in 'relative references" mode 69

4 Writing VBA user-defined functions73

4.1 A simple sales commission function 73

4.2 Creating Commission(Sales) in the spreadsheet 74

4.3 Two functions with multiple inputs for valuing options 75

4.4 Manipulating arrays in VBA 78

4.5 Expected value and variance functions with array inputs 79

4.6 Portfolio variance function with array inputs 81

4.7 Functions with array output 84

4.8 Using Excel and VBA functions in user-defined functions 85

Contents vii

4.8.1 Using VBA functions in user-defined functions 85

4.8.2 Add-ins 86

4.9 Pros and cons of developing VBA functions 86

Summary 87

Appendix 4A Functions illustrating array handling 88 Appendix 4B Binomial tree option valuation functions 89

Exercises on writing functions 94

Solution notes for exercises on functions 95

Part Two Equities99

5 Introduction to equities101

6 Portfolio optimisation103

6.1 Portfolio mean and variance 103

6.2 Risk-return representation of portfolios 105

6.3 Using Solver to find efficient points 106

6.4 Generating the efficient frontier (Huang and Litzenberger"s

approach) 109

6.5 Constrained frontier portfolios 111

6.6 Combining risk-free and risky assets 113

6.7 Problem One-combining a risk-free asset with a risky asset 114

6.8 Problem Two-combining two risky assets 115

6.9 Problem Three-combining a risk-free asset with a risky portfolio 117

6.10 User-defined functions in Module1 119

6.11 Functions for the three generic portfolio problems in Module1 120

6.12 Macros in ModuleM 121

Summary 123

References 123

7 Asset pricing125

7.1 The single-index model 125

7.2 Estimating beta coefficients 126

7.3 The capital asset pricing model 129

7.4 Variance-covariance matrices 130

7.5 Value-at-Risk 131

7.6 Horizon wealth 134

7.7 Moments of related distributions such as normal and lognormal 136

7.8 User-defined functions in Module1 136

Summary 138

References 138

8 Performance measurement and attribution139

8.1 Conventional performance measurement 140

8.2 Active-passive management 141

8.3 Introduction to style analysis 144

viii Contents

8.4 Simple style analysis 145

8.5 Rolling-period style analysis 146

8.6 Confidence intervals for style weights 148

8.7 User-defined functions in Module1 151

8.8 Macros in ModuleM 151

Summary 152

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