Quantitative Portfolio Optimisation, Asset Allocation and Risk Management

453 Pages·2003·51.34 MB·English

by  Mikkel Rasmussen (auth.)

Quantitative Portfolio Optimisation,
Asset Allocation and Risk Management
QUANTITATIVE PORTFOLIO
OPTIMISATION, ASSET
ALLOCATION AND
RISK MANAGEMENT
Mikkel Rasmussen
*
© Mikkel Rasmussen 2003
Softcover reprint of the hardcover 1st edition 2003 978-1-4039-0458-4
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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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Union and other countries.
ISBN 978-1-349-50944-7 ISBN 978-0-230-51285-6 (eBook)
DOI 10.1057/9780230512856
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Transferred to Digital Printing 2008
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/A bnormal 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
A Brief Note on Normality 35
Summary 37
t v)
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 -A Valuation 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
t
V-h~
CONTENTS
PART Ill 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
SAA vs. TAA-Theory 274
SAA vs. TAA-Practice 281
Summary 290
Chapter 13 Sector Rotation 291
The Sector Rotation Framework 291
Conceptual Framework 293
A Note on Determining Appropriate Model Inputs 299
Asset Allocation Through the Business Cycle 303
Summary 313
fvnt
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 1S 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 lSE: 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 ~1
Appendix 16A: Sector Tail Return Frequencies ~3
Appendix 16B: Sector Multivariate Normal Distribution ~6
Appendix 16C: Sector Extreme Value Charts ~9
Appendix Notation 432
Glossary 434
Index 441
LIST OF FIGURES
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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 FTSE1 00, 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 8: FCFs, present value of FCFs and terminal value 56
4.7 Sensitivity - Company 8: short-term growth and discount rate 57
4.8 Sensitivity - Company 8: discount rate and perpetual growth 58
4.9 Sensitivity-Company 8: short-term growth and perpetual growth 58
f ix)
LIST OF FIGURES
4.10 Framework for calculating implied growth rates 60
4.11 Implied 10 -year growth rate, Sony Corp. 61
4.12 Discounted earnings per share, Sony Corp. 61
4.13 Sensitivity analysis - Sony Corp. 62
4.14 The Security Market Line 65
4.15 The revised Security Market Line 66
4.16 The Characteristic Line- Sony vs. TOPIX, 1995/1-2002/5 67
5.1 Correlation coefficient of +1 77
5.2 Correlation coefficient of 0 78
5.3 Correlation coefficient of -1 79
5.4 Diversification at work- 2-asset portfolio 88
5.5 Portfolio volatility as 70 MSCI world stocks are successively added 90
6.1 Asset and minimum-variance portfolio volatilities 105
6.2 Asset and minimum-variance portfolio Sharpe Ratios 105
6.3 Return/risk combinations with correlation coefficient of -Q.5 112
6.4 The efficient frontier for a five-asset portfolio 113
6.5 Correlation matrix - four US equity indices and cash 115
6.6 Efficient frontier-four US equity indices and cash 115
6.7 Correlation matrix - four US equity indices, MSCI-W ex US and cash 119
6.8 Efficient frontier-five US equity indices, MSCI-W ex US and cash 120
6.9 Sharpe Ratios for the two efficient frontiers 121
6.10 The efficient surface - varying minimum cash position 124
6.11 Volatility of optimised portfolio as 70 randomly chosen stocks
are successively added to the portfolio 125
6.12 Number of stocks included in the minimum-variance portfolio
as the 70 randomly chosen stocks become available 127
7.1 Asset Allocation Line - one risky asset A and the market portfolio M 141
7.2 60-day moving average volatility of the S&P500, 1996/1-2002/5 147
7.3 Exponentially weighted volatility of the S&P500, 1996/1-2002/5 149
7.4 Weighting schemes (per cent) of different forecast methods 152
7.5 Return frequency distribution for the S&P500, 1995/1-2002/5 154
7.6 Return frequency distribution for the NASDAQ, 1995/1-2002/5 154
7.7 Return frequency distribution for the TOPIX, 1995/1-2002/5 155
7.8 3-month correlation coefficients for the Dow jones, 1995/4-2002/4 159
7.9 Distribution of correlation coefficients - Dow jones and TOPIX 160
9.1 Efficient frontier-five US equity indices, MSCI-W ex US and cash 187
9.2 Asset allocation along the efficient frontier, 3D 190
9.3 Asset allocation along the efficient frontier, cumulative percentages 191
9.4 Correlation matrix - MSCI Global Sector Model 197
9.5 The efficient frontier- MSCI Global Sector Model 197
9.6 Asset allocation topography along the efficient frontier 198
9.7 Expected Sharpe Ratio along the efficient frontier 199
10.1 Monte Carlo Simulation of portfolio returns 204
10.2 Return distributions for 10 MSCI global sectors, 1995/1-2002/5 207
10.3 Return distribution, minimum-variance portfolio 208
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