1 GMM Estimation of the Mean-Variance Frontier 4 1.1 GMM Estimation of Means and Covariance Matrices . . . . . . . . . 4 1.2 Asymptotic Distribution of the GMM Estimators . . . . . . . . . . . 6 1.3 Mean-Variance Frontier . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Predicting Asset Returns 13 2.1 A Little Financial Theory and Predictability . . . . . . . . . . . . . . 13 2.2 Prices, Returns, and Predictability . . . . . . . . . . . . . . . . . . . 17 2.3 Autocorrelations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4 Other Predictors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.5 Trading Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.6 Maximally Predictable Portfolio . . . . . . . . . . . . . . . . . . . . 36 2.7 Technical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.8 Empirical U.S. Evidence on Stock Return Predictability . . . . . . . . 40 3 Linear Factor Models 44 3.1 Testing CAPM (Single Excess Return Factor) . . . . . . . . . . . . . 44 3.2 Testing Multi-Factor Models (Factors are Excess Returns) . . . . . . 55 3.3 Testing Multi-Factor Models (General Factors) . . . . . . . . . . . . 60 3.4 Fama-MacBeth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 A Coding of the GMM Problem in Section 3.2 66 A.1 Exactly Identified System . . . . . . . . . . . . . . . . . . . . . . . . 66 A.2 Overidentified system . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 Linear Factor Models in SDF Form 71 4.1 Estimating SDF Models . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.2 SDF Models versus Linear Factor Models Again . . . . . . . . . . . 75 4.3 Conditional SDF Models . . . . . . . . . . . . . . . . . . . . . . . . 76 4.4 Linear SDF,Linear Factor Model . . . . . . . . . . . . . . . . . . 79 5 Weighting Matrix in GMM 83 5.1 Arguments for a Prespecified Weighting Matrix . . . . . . . . . . . . 83 5.2 Near Singularity of the Weighting Matrix . . . . . . . . . . . . . . . 83 5.3 Very Different Variances . . . . . . . . . . . . . . . . . . . . . . . . 84 5.4 (E xt x0t )−1 as Weighting Matrix . . . . . . . . . . . . . . . . . . . . . 85 6 Consumption-Based Asset Pricing 90 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 6.2 Problems with the Consumption-Based Asset Pricing Model . . . . . 91 6.3 Assets in Simulation Models . . . . . . . . . . . . . . . . . . . . . . 114 6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 A Data Appendix 129 B Econometrics Appendix 130 7 ARCH and GARCH 139 7.1 Heteroskedasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 7.2 ARCH Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 7.3 GARCH Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 7.4 Non-Linear Extensions . . . . . . . . . . . . . . . . . . . . . . . . . 147 7.5 Stochastic Volatility Models . . . . . . . . . . . . . . . . . . . . . . 148 7.6 (G)ARCH-M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 7.7 Multivariate (G)ARCH . . . . . . . . . . . . . . . . . . . . . . . . . 151 8 Financial Applications of ARCH and GARCH Models 157 8.1 “Fundamental Values and Asset Returns in Global Equity Markets,” by Bansal and Lundblad . . . . . . . . . . . . . . . . . . . . . . . . 157
8.2 “A Closed-Form GARCH Option Valuation Model” by Heston and Nandi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 9 Yield Curve Models 169 9.1 Basic Facts About Yield Curves . . . . . . . . . . . . . . . . . . . . 169 9.2 SDF and Yield Curve Models . . . . . . . . . . . . . . . . . . . . . . 170 9.3 Affine Yield Curves: Overview . . . . . . . . . . . . . . . . . . . . . 172 9.4 Affine Yield Curves: Unconditional Gaussian Models . . . . . . . . . 174 9.5 Affine Yield Curves: Conditional Gaussian Models . . . . . . . . . . 184 9.6 Estimating Yield Curve Models . . . . . . . . . . . . . . . . . . . . . 190 9.7 Summary of Some Empirical Findings . . . . . . . . . . . . . . . . . 194 10 Kernel Density Estimation and Regression 200 10.1 Non-Parametric Regression . . . . . . . . . . . . . . . . . . . . . . . 200 10.2 Estimating and Testing Distributions . . . . . . . . . . . . . . . . . . 207 10.3 “Testing Continuous-Time Models of the Spot Interest Rate,” by Ait- Sahalia (1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 10.4 “Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices,” by Ait-Sahalia and Lo (1998) . . . . . . . . . . . . 212
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