1.1 Random Variables and Distributions . . . . . . . . 5

1.2 Moments . . . . . . . . . . . . .. . . . . . . . . . . . . . 11

1.3 Distributions Commonly Used in Tests . . . . . . 14

1.4 Normal Distribution of the Sample Mean as an Approximation . . . . 17

A Statistical Tables 19

2 Least Squares Estimation 22

2.1 Least Squares . . . . . . . . . . . . . . . . 22

2.2 Hypothesis Testing . . . . . . .  . . . . . 43

2.3 Heteroskedasticity . . . . . . . .  . . . . . 53

2.4 Autocorrelation . . . . . . . .. . . . . . . . 56

A A Primer in Matrix Algebra 59

A Statistical Tables 64

3.1 Misspecifying the Set of Regressors . . . 67

3.2 Comparing Non-Nested Models . . . . . . 68

3.3 Non-Linear Models . . . . . . . . . . 68

3.4 Outliers . . .. . . 69

3.5 Estimation on Subsamples . .. . . 69

4.1 Properties of the OLS Estimator when “Gauss-Markov” Is False . . . 80

4.2 Motivation of Asymptotics . . . . . . 80

4.3 Asymptotics: Consistency . . . . . . 80

4.4 When LS Cannot be Saved . . .  . . . 82

4.5 Asymptotic Normality . . .  . . . . 87

5 Index Models 89

5.1 The Inputs to a MV Analysis . .. . . 89

5.2 Single-Index Models . . . . . . . 90

5.3 Estimating Beta . . . . . . . . 95

5.4 Multi-Index Models . . . . . . . . 97

6 Testing CAPM and Multifactor Models 106

6.1 Market Model . . . . .. . 106

A Statistical Tables 124

7 Time Series Analysis 127

7.1 Descriptive Statistics . . . . . .. . . 127

7.2 Stationarity . . . . . . . . . .  . . 128

7.3 White Noise . . . . . . . . . . . 129

7.4 Autoregression (AR) . . . . . .  . . . 129

7.5 Moving Average (MA) . . . . .  . . . 138

7.6 ARMA(p,q) . . . . . . . . . . . . 139

7.7 VAR(p) . . . . . . . . .  . . . 140

7.8 Impulse Response Function . . . . . . . . 142

7.9 Non-stationary Processes . . . . . 144

2

8 Predicting Asset Returns 155

8.1 Autocorrelations . . . . . . . . . . . . . . 155

8.2 Other Predictors and Methods . . . . . . . . . . . 163

8.3 Out-of-Sample Forecasting Performance . . . .  . . . 166

9.1 Maximum Likelihood . . . . . . . . 185

9.2 Key Properties of MLE . . . . . . . . . . . 191

9.3 Three Test Principles . . . . . . . . . . 192

10 ARCH and GARCH 194

10.1 Heteroskedasticity . . . . .. . . 194

10.2 ARCH Models . . . . . . . . . . . 200

10.3 GARCH Models . . . . . . . . . 203

10.4 Non-Linear Extensions . . . . .. . . 206

10.5 (G)ARCH-M . . . . . .  . . . . . 208

10.6 Multivariate (G)ARCH . . . . .. . . 209

11 Risk Measures 214

11.1 Value at Risk . . . . . . .  . . . 214

11.2 Expected Shortfall . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

11.3 Target Semivariance (Lower Partial 2nd Moment) and Max Drawdown 223

12 Return Distributions (Univariate) 229

12.1 Estimating and Testing Distributions . . . . . .. . . . 229

12.2 Tail Distribution . . . . . . . . . . . . 242

13.1 Recap of Univariate Distributions . . . . . .  . . . 252

13.2 Exceedance Correlations . . . . . . . 252

13.3 Beyond (Linear) Correlations . . . . . . 254

13.4 Copulas . . . . . . .  . . . . 260

13.5 Joint Tail Distribution . . . . .. . . . 267

14 Option Pricing and Estimation of Continuous Time Processes 274

14.1 The Black-Scholes Model . . . . . . . . . . . . . . . . . . . . . . . . 274

14.2 Estimation of the Volatility of a Random Walk Process . . . . . . . . 282

15 Event Studies 289

15.1 Basic Structure of Event Studies . . .. . . . . 289

15.2 Models of Normal Returns . .  . . . . . 291

15.3 Testing the Abnormal Return . .  . . . . 295

15.4 Quantitative Events . . . . . .  . . . 297

16 Kernel Density Estimation and Regression 299

16.1 Non-Parametric Regression . . . . .  . . 299

16.2 Examples of Non-Parametric Estimation . . . . 307

17.1 Monte Carlo Simulations . . . . . . . . 313

17.2 Bootstrapping . . . . . .. . . . . 317

18.1 Introduction to Panel Data . . . . . . . . 322

18.2 Fixed Effects Model . . . . .  . . . 322

18.3 Random Effects Model . . . . . . . 326

19.1 Binary Choice Model . . . . . . . 329

19.2 Truncated Regression Model . . . . .. . . 336

19.3 Censored Regression Model (Tobit Model) . . . . . . . 340