Contents
Acknowledgments 2
Preface 8
Part I. Asset pricing theory 12
1 Consumption-based model and overview 13
1.1 Basic pricing equation 14
1.2 Marginal rate of substitution/stochastic discount factor 16
1.3 Prices, payoffs and notation 17
1.4 Classic issues in finance 20
1.5 Discount factors in continuous time 33
1.6 Problems 38
2 Applying the basic model 41
2.1 Assumptions and applicability 41
2.2 General Equilibrium 43
2.3 Consumption-based model in practice 47
2.4 Alternative asset pricing models: Overview 49
2.5 Problems 51
3 Contingent Claims Markets 54
3.1 Contingent claims 54
3.2 Risk neutral probabilities 55
3.3 Investors again 57
3.4 Risk sharing 59
3.5 State diagram and price function 60
4 The discount factor 64
4.1 Law of one price and existence of a discount factor 64
4.2 No-Arbitrage and positive discount factors 69
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4.3 An alternative formula, and x∗ in continuous time 74
4.4 Problems 76
5 Mean-variance frontier and beta representations 77
5.1 Expected return - Beta representations 77
5.2 Mean-variance frontier: Intuition and Lagrangian characterization 80
5.3 An orthogonal characterization of the mean-variance frontier 83
5.4 Spanning the mean-variance frontier 88
5.5 A compilation of properties of R∗,Re∗ and x∗ 89
5.6 Mean-variance frontiers for m: the Hansen-Jagannathan bounds 92
5.7 Problems 97
6 Relation between discount factors, betas, and mean-variance frontiers 98
6.1 From discount factors to beta representations 98
6.2 From mean-variance frontier to a discount factor and beta representation 101
6.3 Factor models and discount factors 104
6.4 Discount factors and beta models to mean - variance frontier 108
6.5 Three riskfree rate analogues 109
6.6 Mean-variance special cases with no riskfree rate 115
6.7 Problems 118
7 Implications of existence and equivalence theorems 120
8 Conditioning information 128
8.1 Scaled payoffs 129
8.2 Sufficiency of adding scaled returns 131
8.3 Conditional and unconditional models 133
8.4 Scaled factors: a partial solution 140
8.5 Summary 141
8.6 Problems 142
9 Factor pricing models 143
9.1 Capital Asset Pricing Model (CAPM) 145
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9.2 Intertemporal Capital Asset Pricing Model (ICAPM) 156
9.3 Comments on the CAPM and ICAPM 158
9.4 Arbitrage Pricing Theory (APT) 162
9.5 APT vs. ICAPM 171
9.6 Problems 172
Part II. Estimating and evaluating asset pricing models 174
10 GMM in explicit discount factor models 177
10.1 The Recipe 177
10.2 Interpreting the GMM procedure 180
10.3 Applying GMM 184
11 GMM: general formulas and applications 188
11.1 General GMM formulas 188
11.2 Testing moments 192
11.3 Standard errors of anything by delta method 193
11.4 Using GMM for regressions 194
11.5 Prespecified weighting matrices and moment conditions 196
11.6 Estimating on one group of moments, testing on another. 205
11.7 Estimating the spectral density matrix 205
11.8 Problems 212
12 Regression-based tests of linear factor models 214
12.1 Time-series regressions 214
12.2 Cross-sectional regressions 219
12.3 Fama-MacBeth Procedure 228
12.4 Problems 234
13 GMM for linear factor models in discount factor form 235
13.1 GMM on the pricing errors gives a cross-sectional regression 235
13.2 The case of excess returns 237
13.3 Horse Races 239
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13.4 Testing for characteristics 240
13.5 Testing for priced factors: lambdas or b’s? 241
13.6 Problems 245
14 Maximum likelihood 247
14.1 Maximum likelihood 247
14.2 ML is GMM on the scores 249
14.3 When factors are returns, ML prescribes a time-series regression 251
14.4 When factors are not excess returns, ML prescribes a cross-sectional
regression 255
14.5 Problems 256
15 Time series, cross-section, and GMM/DF tests of linear factor models 258
15.1 Three approaches to the CAPM in size portfolios 259
15.2 Monte Carlo and Bootstrap 265
16 Which method? 271
Part III. Bonds and options 284
17 Option pricing 286
17.1 Background 286
17.2 Black-Scholes formula 293
17.3 Problems 299
18 Option pricing without perfect replication 300
18.1 On the edges of arbitrage 300
18.2 One-period good deal bounds 301
18.3 Multiple periods and continuous time 309
18.4 Extensions, other approaches, and bibliography 317
18.5 Problems 319
19 Term structure of interest rates 320
19.1 Definitions and notation 320
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19.2 Yield curve and expectations hypothesis 325
19.3 Term structure models – a discrete-time introduction 327
19.4 Continuous time term structure models 332
19.5 Three linear term structure models 337
19.6 Bibliography and comments 348
19.7 Problems 351
Part IV. Empirical survey 352
20 Expected returns in the time-series and cross-section 354
20.1 Time-series predictability 356
20.2 The Cross-section: CAPM and Multifactor Models 396
20.3 Summary and interpretation 409
20.4 Problems 413
21 Equity premium puzzle and consumption-based models 414
21.1 Equity premium puzzles 414
21.2 New models 423
21.3 Bibliography 437
21.4 Problems 440
22 References 442
Part V. Appendix 455
23 Continuous time 456
23.1 Brownian Motion 456
23.2 Diffusion model 457
23.3 Ito’s lemma 460
23.4 Problems 462