Linear Factor Models in Finance (eBook)

Linear Factor Models in Finance 1
Contents 5
List of contributors 11
Introduction 15
1 Review of literature on multifactor asset pricing models 17
1.1 Theoretical reasons for existence of multiple factors 17
1.2 Empirical evidence of existence of multiple factors 21
1.3 Estimation of factor pricing models 21
Bibliography 25
2 Estimating UK factor models using the multivariate skew normal distribution 28
2.1 Introduction 28
2.2 The multivariate skew normal distribution and some of its properties 30
2.3 Conditional distributions and factor models 33
2.4 Data model choice and estimation 35
2.5 Empirical study 35
2.5.1 Basic return statistics 35
2.5.2 Overall model fit 37
2.5.3 Comparison of parameter estimates 39
2.5.4 Skewness parameters 40
2.5.5 Tau and time-varying conditional variance 41
2.6 Conclusions 43
Acknowledgement 43
References 43
3 Misspecification in the linear pricing model 46
3.1 Introduction 46
3.2 Framework 47
3.2.1 Arbitrage Pricing Theory 47
3.2.2 Multivariate F test used in linear factor model 48
3.2.3 Average F test used in linear factor model 50
3.3 Distribution of the multivariate F test statistics under misspecification 50
3.3.1 Exclusion of a set of factors from estimation 51
3.3.2 Time-varying factor loadings 57
3.4 Simulation study 59
3.4.1 Design 59
3.4.2 Factors serially independent 61
3.4.3 Factors autocorrelated 64
3.4.4 Time-varying factor loadings 65
3.4.5 Simulation results 66
3.5 Conclusion 73
Appendix: Proof of proposition 3.1 and proposition 3.2 75
4 Bayesian estimation of risk premia in an APT context 77
4.1 Introduction 77
4.2 The general APT framework 78
4.2.1 The excess return generating process (when factors are traded portfolios) 78
4.2.2 The excess return generating process (when factors are macroeconomic variables or non-traded portfolios) 80
4.2.3 Obtaining the (K x 1) vector of risk premia l 81
4.3 Introducing a Bayesian framework using a Minnesota prior (Litterman’s prior) 82
4.3.1 Prior estimates of the risk premia 83
4.3.2 Posterior estimates of the risk premia 86
4.4 An empirical application 88
4.4.1 Data 89
4.4.2 Results 90
4.5 Conclusion 93
References 93
Appendix 96
5 Sharpe style analysis in the MSCI sector portfolios: a Monte Carlo integration approach 99
5.1 Introduction 99
5.2 Methodology 100
5.2.1 A Bayesian decision-theoretic approach 101
5.2.2 Estimation by Monte Carlo integration 102
5.3 Style analysis in the MSCI sector portfolios 103
5.4 Conclusions 109
References 109
6 Implication of the method of portfolio formation on asset pricing tests 111
6.1 Introduction 111
6.2 Models 113
6.2.1 Asset pricing frameworks 113
6.2.2 Specifications to be tested 114
6.3 Implementation 115
6.3.1 Multivariate F test 115
6.3.2 Average F test 116
6.3.3 Stochastic discount factor using GMM with Hansen and Jagannathan distance 118
6.3.4 A look at the pricing errors under different tests 119
6.4 Variables construction and data sources 120
6.4.1 Data sources 120
6.4.2 Independent variables: excess market return, size return factor and book-to-market return factor 121
6.4.3 Dependent variables: size-sorted portfolios, beta-sorted portfolios and individual assets 125
6.5 Result and discussion 130
6.5.1 Formation of WT 130
6.5.2 Model 1 131
6.5.3 Model 2 139
6.5.4 Model 3 149
6.6 Simulation 154
6.7 Conclusion and implication 162
References 164
7 The small noise arbitrage pricing theory and its welfare implications 166
7.1 Introduction 166
7.2 167
7.3 171
References 172
List of symbols 173
8 Risk attribution in a global country-sector model 175
8.1 Introduction 175
8.2 Recent trends in the ‘globalization’ of equity markets 177
8.2.1 ‘Home bias' 178
8.2.2 The rise and rise of the multinational corporation 181
8.2.3 Increases in market concentration 183
8.3 Modelling country and sector risk 186
8.4 The estimated country and sector indices 192
8.5 Stock and portfolio risk attribution 197
8.6 Conclusions 204
8.7 Further issues and applications 205
8.7.1 Accounting for currency risk 205
8.7.2 Additional applications for this research 206
References 206
Appendix A: A detailed description of the identifying restrictions 209
Appendix B: The optimization algorithm 213
Appendix C: Getting the hedge right 215
9 Predictability of fund of hedge fund returns using DynaPorte 218
9.1 Introduction 218
9.2 Literature review 219
9.3 Methodology and data 220
9.4 Empirical results 220
9.5 Discussion 221
9.6 Conclusion 223
References 223
10 Estimating a combined linear factor model 226
10.1 Introduction 226
10.2 A combined linear factor model 227
10.3 An extended model 229
10.4 Model estimation 230
10.5 Conditional maximization 232
10.6 Heterogeneous errors 233
10.7 Estimating the extended model 234
10.8 Discussion 236
10.9 Some simulation evidence 237
10.10 Model extensions 238
10.11 Conclusion 239
References 240
11 Attributing investment risk with a factor analytic model 242
11.1 Introduction 242
11.2 The case for factor analytic models 243
11.2.1 Types of linear factor model 243
11.2.2 Estimation issues 244
11.3 Attributing investment risk with a factor analytic model 245
11.3.1 Which attributes can we consider? 246
11.4 Valuation attributes 247
11.4.1 Which attributes should we consider? 247
11.4.2 Attributing risk with valuation attributes 252
11.5 Category attributes 253
11.5.1 Which categories should we consider? 255
11.5.2 Attributing risk with categories 256
11.6 Sensitivities to macroeconomic time series 257
11.6.1 Which time series should we consider? 257
11.6.2 Attributing risk with macroeconomic time series 257
11.7 Reporting risk – relative marginals 258
11.7.1 Case study: Analysis of a UK portfolio 260
11.8 Conclusion 261
References 262
Appendix 263
12 Making covariance-based portfolio risk models sensitive to the rate at which markets reflect new information 265
12.1 Introduction 265
12.2 Review 266
12.3 Discussion 269
12.4 The model 270
12.5 A few examples 273
12.6 Conclusions 275
References 275
13 Decomposing factor exposure for equity portfolios 278
13.1 Introduction 278
13.2 Risk decomposition: cross-sectional characteristics 280
13.3 Decomposition and misspecification in the cross-sectional model: a simple example 285
13.3.1 Industry classification projected onto factor exposures 285
13.3.2 Incorporating expected return information 286
13.4 Summary and discussion 289
References 290
Index 293