Quantitative Portfolio Optimisation, Asset Allocation and Risk Management (Finance and Capital Markets)

461 Pages·2003·4.22 MB·English

by  Mikkel Rasmussen

QUANTITATIVE PORTFOLIO
OPTIMISATION, ASSET
ALLOCATION AND
RISK MANAGEMENT
Mikkel Rasmussen
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Quantitative Portfolio Optimisation,
Asset Allocation and Risk Management
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QUANTITATIVE PORTFOLIO
OPTIMISATION, ASSET
ALLOCATION AND
RISK MANAGEMENT
Mikkel Rasmussen
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© Mikkel Rasmussen 2003
All rights reserved.No reproduction,copy or transmission of this
publication may be made without written permission.
No paragraph of this publication may be reproduced,copied or transmitted
save with written permission or in accordance with the provisions of the
Copyright,Designs and Patents Act 1988,or under the terms of any licence
permitting limited copying issued by the Copyright Licensing Agency,90
Tottenham Court Road,London W1T 4LP.
Any person who does any unauthorised act in relation to this publication
may be liable to criminal prosecution and civil claims for damages.
The author has asserted his right to be identified as the author of this work
in accordance with the Copyright,Designs and Patents Act 1988.
First published 2003 by
PALGRAVE MACMILLAN
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PALGRAVE MACMILLAN is the global academic imprint of the Palgrave
Macmillan division of St.Martin’s Press,LLC and of Palgrave Macmillan Ltd.
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and other countries.Palgrave is a registered trademark in the European
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ISBN 1–4039–0458–8 hardback
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managed and sustained forest sources.
A catalogue record for this book is available from the British Library.
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Editing and origination by Aardvark Editorial,Mendham,Suffolk
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Printed and bound in Great Britain by
Antony Rowe Ltd,Chippenham and Eastbourne
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CONTENTS
List of Figures ix
List of Tables xiv
PART I A BASIS FOR QUANTITATIVE MANAGEMENT
AND ANALYSIS 1
Chapter 1 Asset Management Basics 3
Introduction 3
Asset Management Objectives 4
The Case for Quantitative Management 4
Structure of this Book 6
Chapter 2 Asset Returns 9
Defining Investment Returns 9
Examples from the Real World 12
Excess Returns and Risk-free Rates 18
Residual/Abnormal Returns 19
Time-weighted Returns (TWR) 20
Summary 20
Appendix 20
Chapter 3 Asset Risk 23
Risk is Not Just a Four-letter Word 23
Defining Risk 26
ABrief Note on Normality 35
Summary 37
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CONTENTS
Chapter 4 Asset Pricing 38
Pricing and Valuation 38
Determining the Discount Rate 39
The Dividend Discount Model (DDM) 41
The Discounted Cash Flow Model (DCF) 43
Old vs. New Economy – AValuation Example 50
Implied Growth Rates 59
The Capital Asset Pricing Model (CAPM) 63
The Security Market Line (SML) 63
The Characteristic Line (CL) 66
The Arbitrage Pricing Theory (APT) 68
Summary 70
PART II MODERN PORTFOLIO THEORY 71
Chapter 5 Portfolio Characterisation 73
Introduction 73
Portfolio Return – The Sum of its Parts 74
Portfolio Risk – Less Than the Sum of its Parts 75
The Nature of Diversification 87
Summary 91
Appendix 92
Chapter 6 Quantitative Portfolio Optimisation and
Efficient Portfolios 97
Portfolio Efficiency 97
Quantitative Portfolio Optimisation 99
The Efficient Frontier 111
Benefits from International Diversification 117
Optimisation and Diversification 125
Summary 127
Appendix 128
Chapter 7 Estimating Model Parameters 138
Expected Return and Risk 138
The CAPM Revisited 139
Factor Models – The APT Revisited 143
Volatility and Correlation 146
Return Distributions (Risk Characterisation) 153
The Correlation Structure 158
Summary 162
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CONTENTS
PART III ASSET ALLOCATION 165
Chapter 8 Investment Objectives and Benchmark Selection 167
The Investment Policy Statement 167
Choosing the Benchmark 171
Summary 175
Chapter 9 Quantitative Portfolio Construction and
Asset Allocation 177
The Asset Allocation Decision 177
Traditional Portfolio Construction Techniques 178
Quantitative Portfolio Optimisation for Asset Allocation 186
Introducing an MSCI Global Sector Model 194
Summary 199
Chapter 10 Quasi-Random Monte Carlo Simulated Asset
Allocation (QRMCSAA) 201
Quantitative Optimisation and Monte Carlo Simulations 201
The Efficient Ridge 205
The Quasi-Random Monte Carlo Simulated
Asset Allocation 215
Summary 223
Appendix 225
Chapter 11 Refining the QRMCSAA Model 239
Bayesian Priors and Stein Estimators 239
Optimal Return Shrinkage 242
Optimal Covariance Matrix Shrinkage 255
Summary 270
Chapter 12 Strategic and Tactical Asset Allocation 273
Introduction 273
SAAvs. TAA– Theory 274
SAAvs. TAA– Practice 281
Summary 290
Chapter 13 Sector Rotation 291
The Sector Rotation Framework 291
Conceptual Framework 293
ANote on Determining Appropriate Model Inputs 299
Asset Allocation Through the Business Cycle 303
Summary 313
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CONTENTS
PART IV QUANTITATIVE RISK MANAGEMENT 315
Chapter 14 Tracking Error and Information Ratio 317
Definitions of Tracking Error 317
Risk Geometry 320
Information Ratio 324
Active Management Value Added 327
Summary 330
Chapter 15 Sector Risk Model 332
The Global Perspective 332
Risk Characterisation 333
Constructing the Model 340
Portfolio Risk-Management Implications 345
MSCTR and MSCAR for the Global Sector Model 347
The Efficient Ridge Revisited 359
General Thoughts on Active Risk Management 364
Summary 375
Appendix 15A: Sector Indices and Volatilities 377
Appendix 15B: Sector Returns 380
Appendix 15C: Sector Return Distributions 383
Appendix 15D: Portfolio Volatility and Tracking Error 386
Appendix 15E: Portfolio Beta 389
Chapter 16 Value-at-Risk (VaR) and Extreme Value Theory (EVT) 392
The Basics 392
Variance–Covariance VaR 395
Historical Simulation of VaR 396
Multivariate Normal Distributions 404
Monte Carlo Simulated VaR 414
VaR Along the Efficient Frontier 415
Marginal Contributions to VaR 416
Extreme Value Theory (EVT) 419
Summary 421
Appendix 16A: Sector Tail Return Frequencies 423
Appendix 16B: Sector Multivariate Normal Distribution 426
Appendix 16C: Sector Extreme Value Charts 429
Appendix Notation 432
Glossary 434
Index 441
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LIST OF FIGURES
2.1 The compounding effect 11
2.2 Performance of the DJIA, the S&P500 and the NASDAQ Composite
Index, 1995/1–2002/4 (daily observations) 12
2.3 Daily returns on the Dow Jones Industrial Average, 1995/1–2002/4 13
2.4 Daily returns on the S&P500, 1995/1–2002/4 14
2.5 Daily returns on the NASDAQ Composite, 1995/1–2002/4 14
2.6 Annualised returns on the Dow Jones Industrial Average, S&P500
Index and NASDAQ Composite Index, 1995–2001 15
2.7 Average annual returns on the Dow Jones Industrial Average,
S&P500 and the NASDAQ Composite Index, 1995–2001 16
2.8 Average annual returns on the FTSE100, DAX30, Tokyo SE and
Hang Seng Indices, 1995/1–2002/5 17
2.9 Monthly excess returns on IBM vs. the S&P500, 1995/1–2002/4 19
3.1 Hypothetical monthly performance of two global equity funds 25
3.2 Variance (average of the sum of squared deviations from the mean) 27
3.3 Three-month moving average of three-month volatilities, based
on daily observations 1995/1–2001/5 31
3.4 Normal, skewed and kurtotic return distributions 35
4.1 Discounting $1,000,000 at different discount rates over 30 years 49
4.2 Company A: FCFs, present value of FCFs and terminal value 52
4.3 Sensitivity – Company A: short-term growth and discount rate 52
4.4 Sensitivity – Company A: perpetual growth and discount rate 53
4.5 Sensitivity – Company A: short-term growth and perpetual growth 54
4.6 Company B: FCFs, present value of FCFs and terminal value 56
4.7 Sensitivity – Company B: short-term growth and discount rate 57
4.8 Sensitivity – Company B: discount rate and perpetual growth 58
4.9 Sensitivity – Company B: short-term growth and perpetual growth 58
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