Contents
Acknowledgements xi
Biographies xiii
Introduction 1
1 Presentation of the Portfolio Management Environment 3
1.1 The different categories of assets 3
1.1.1 Presentation of the different traditional asset classes 3
1.1.2 Alternative instruments 5
1.1.3 Grouping by sector 6
1.2 Definition of portfolio management 6
1.2.1 Passive investment management 6
1.2.2 Active investment management 8
1.3 Organisation of portfolio management and description of the investment
management process 8
1.3.1 The different phases of the investment management process 9
1.3.2 The multi-style approach 9
1.3.3 Performance analysis 10
1.4 Performance analysis and market efficiency 12
1.4.1 Market efficiency 12
1.4.2 Performance persistence 13
1.5 Performance analysis and the AIMR standards 16
1.6 International investment: additional elements to be taken
into account 20
1.7 Conclusion 22
Bibliography 22
2 The Basic Performance Analysis Concepts 25
2.1 Return calculation 25
2.1.1 Return on an asset 25
2.1.2 Portfolio return 27
2.1.3 International investment 33
vi Contents
2.1.4 Handling derivative instruments 38
2.1.5 The AIMR standards for calculating returns 40
2.2 Calculating relative return 43
2.2.1 Benchmarks 43
2.2.2. Peer groups 49
2.2.3. A new approach: Portfolio Opportunity Distributions 50
2.3 Definition of risk 51
2.3.1 Asset risk 52
2.3.2 Link between the variations in returns on two assets 54
2.3.3 Other statistical measures of risk 54
2.3.4 Risk indicators for fixed income investment 55
2.3.5 Foreign asset risk 55
2.3.6 The AIMR standards and risk 57
2.3.7 Generalisation of the notion of risk: Value-at-Risk 57
2.4 Estimation of parameters 63
2.4.1 Use of time-series 63
2.4.2 Scenario method 64
2.4.3 Forecast evaluation 64
2.5 Conclusion 66
Appendix 2.1 Calculating the portfolio return with the help of arithmetic
and logarithmic asset returns 66
Appendix 2.2 Calculating the continuous geometric rate of return for
the portfolio 67
Appendix 2.3 Stock exchange indices 68
Bibliography 74
3 The Basic Elements of Modern Portfolio Theory 77
3.1 Principles 77
3.1.1 Utility functions and indifference curves 78
3.1.2 Risk aversion 78
3.2 The Markowitz model 80
3.2.1 Formulation of the model 81
3.2.2 Choosing a particular portfolio on the efficient frontier 82
3.2.3 Impact of transaction costs when determining the optimal portfolio 83
3.2.4 International diversification and currency risk 83
3.3 Efficient frontier calculation algorithm 84
3.3.1 The Markowitz–Sharpe critical line algorithm 84
3.3.2 Other algorithms 85
3.4 Simplified portfolio modelling methods 85
3.4.1 Sharpe’s single-index model 85
3.4.2 Multi-index models 87
3.4.3 Simplified methods proposed by Elton and Gruber 88
3.5 Conclusion 89
Appendix 3.1 Resolution of the Markowitz problem 90
Bibliography 93
Contents vii
4 The Capital Asset Pricing Model and its Application to Performance
Measurement 95
4.1 The CAPM 95
4.1.1 Context in which the model was developed 95
4.1.2 Presentation of the CAPM 98
4.1.3 Modified versions of the CAPM 102
4.1.4 Conclusion 107
4.2 Applying the CAPM to performance measurement: single-index
performance measurement indicators 108
4.2.1 The Treynor measure 108
4.2.2 The Sharpe measure 109
4.2.3 The Jensen measure 110
4.2.4 Relationships between the different indicators and use of the
indicators 110
4.2.5 Extensions to the Jensen measure 112
4.2.6 The tracking-error 114
4.2.7 The information ratio 114
4.2.8 The Sortino ratio 115
4.2.9 Recently developed risk-adjusted return measures 116
4.3 Evaluating the management strategy with the help of models derived from
the CAPM: timing analysis 123
4.3.1 The Treynor and Mazuy (1966) method 124
4.3.2 The Henriksson and Merton (1981) and Henriksson (1984)
models 124
4.3.3 Decomposition of the Jensen measure and evaluation of timing 125
4.4 Measuring the performance of internationally diversified portfolios:
extensions to the CAPM 127
4.4.1 International Asset Pricing Model 128
4.4.2 McDonald’s model 128
4.4.3 Pogue, Solnik and Rousselin’s model 129
4.5 The limitations of the CAPM 129
4.5.1 Roll’s criticism 129
4.5.2 Conclusion 130
Bibliography 130
5 Developments in the Field of Performance Measurement 135
5.1 Heteroskedastic models 135
5.1.1 Presentation of the ARCH models 135
5.1.2 Formulation of the model for several assets 137
5.1.3 Application to performance measurement 140
5.2 Performance measurement method using a conditional beta 140
5.2.1 The model 140
5.2.2 Application to performance measurement 142
5.2.3 Model with a conditional alpha 144
5.2.4 The contribution of conditional models 145
viii Contents
5.2.5 Extensions to the model 145
5.2.6 Comparison with the first model 145
5.3 Performance analysis methods that are not dependent on the
market model 145
5.3.1 The Cornell measure 145
5.3.2 The Grinblatt and Titman measure and the positive period weighting
measure 146
5.3.3 Performance measure based on the composition of the portfolio:
Grinblatt and Titman study 147
5.4 Conclusion 148
Bibliography 148
6 Multi-factor Models and their Application to Performance Measurement 149
6.1 Presentation of the multi-factor models 149
6.1.1 Arbitrage models 149
6.1.2 Empirical models 151
6.1.3 Link between the two types of model 152
6.2 Choosing the factors and estimating the model parameters 152
6.2.1 Explicit factor models 153
6.2.2 Implicit or endogenous factor models 159
6.2.3 Comparing the different models 165
6.3 Extending the models to the international arena 166
6.3.1 The international arbitrage models 166
6.3.2 Factors that explain international returns 169
6.4 Applying multi-factor models 170
6.4.1 Portfolio risk analysis 171
6.4.2 Choice of portfolio 175
6.4.3 Decomposing the performance of a portfolio 175
6.4.4 Timing analysis 179
6.4.5 Style analysis 179
6.5 Summary and conclusion 189
Appendix 6.1 The principle of arbitrage valuation 190
Bibliography 192
7 Evaluating the Investment Management Process and Decomposing
Performance 195
7.1 The steps in constructing a portfolio 195
7.1.1 Asset allocation 195
7.1.2 Stock picking 210
7.2 Performance decomposition and analysis 210
7.2.1 Fama’s decomposition 210
7.2.2 Performance decomposition corresponding to the stages in the
investment management process 213
7.2.3 Technique of replicating portfolios for performance measurement 222
7.2.4 Comparison between the different performance decomposition
methods 223
Bibliography 223
Contents ix
8 Fixed Income Security Investment 229
8.1 Modelling yield curves: the term structure of interest rates 229
8.1.1 Yield to maturity and zero-coupon rates 229
8.1.2 Estimating the range of zero-coupon rates from the range of yields
to maturity 230
8.1.3 Dynamic interest rate models 232
8.2 Managing a bond portfolio 234
8.2.1 Quantitative analysis of bond portfolios 234
8.2.2 Defining the risks 235
8.2.3 Factor models for explaining yield curve shifts 236
8.2.4 Optimising a bond portfolio 238
8.2.5 Bond investment strategies 239
8.2.6 International fixed income security investment 240
8.3 Performance analysis for fixed income security portfolios 240
8.3.1 Performance attribution in comparison with a benchmark 241
8.3.2 The Lehman Brothers performance attribution model 241
8.3.3 Additive decomposition of a fixed income portfolio’s performance 243
8.3.4 International Performance Analysis (IPA) 244
8.3.5 Performance decomposition in line with the stages in the
investment management process 245
8.3.6 Performance decomposition for multiple currency portfolios 247
8.3.7 The APT model applied to fixed income security portfolios 248
8.3.8 The Khoury, Veilleux and Viau model 249
8.3.9 The Barra model for fixed income security portfolios 250
8.3.10 Decomposition with hedging of the exchange rate risk 251
Bibliography 251
Conclusion 253
Index 255