Financial Theory I & II

Paul Söderlind1
17 January 2009

1University of St. Gallen. Address: s/bf-HSG, Rosenbergstrasse 52, CH-9000 St. Gallen,
Switzerland. E-mail: Paul.Soderlind@unisg.ch. I thank Felix Moldenhauer for comments and
help. Document name: Fin1MiQEFAll.TeX

Contents

1 Mean-Variance Frontier 4
1.1 Portfolio Return: Mean, Variance, and the Effect of Diversification . . 4
1.2 Mean-Variance Frontier of Risky Assets . . . . . . . . . . . . . . . . 8
1.3 Mean-Variance Frontier of Riskfree and Risky Assets . . . . . . . . . 17
1.4 Examples of Portfolio Weights from MV Calculations . . . . . . . . . 19
A A Primer in Matrix Algebra 22
B A Primer in Optimization 25
2 Index Models 28
2.1 The Inputs to a MV Analysis . . . . . . . . . . . . . . . . . . . . . . 28
2.2 Single-Index Models . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3 Estimating Beta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4 Multi-Index Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.5 Estimating Expected Returns . . . . . . . . . . . . . . . . . . . . . . 37
3 Risk Measures 39
3.1 Symmetric Dispersion Measures . . . . . . . . . . . . . . . . . . . . 39
3.2 Downside Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4 CAPM 47
4.1 Portfolio Choice with Mean-Variance Utility . . . . . . . . . . . . . . 47
4.2 Beta Representation of Expected Returns . . . . . . . . . . . . . . . 54
4.3 Market Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4 An Application of MV Portfolio Choice: International Assets . . . . . 58
5 Utility-Based Portfolio Choice 65
5.1 Utility Functions and Risky Investments . . . . . . . . . . . . . . . . 65
5.2 Utility Optimization and the Two-Fund Theorem . . . . . . . . . . . 71
5.3 Application of Normal Returns: Value at Risk, ES, Lpm and the Telser
Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.4 Behavioural Finance . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6 CAPM Extensions 91
6.1 Nonmarketable Assets . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.2 Heterogenous Investors . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.3 CAPM without a Riskfree Rate . . . . . . . . . . . . . . . . . . . . 99
6.4 Multi-Factor Models and APT . . . . . . . . . . . . . . . . . . . . . 102
6.5 Joint Portfolio and Savings Choice . . . . . . . . . . . . . . . . . . . 105
7 Investment for the Long Run 109
7.1 Time Diversification: Approximate Case . . . . . . . . . . . . . . . . 109
7.2 Time Diversification and the Growth-Optimal Portfolio: Lognormal
Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7.3 More General Utility Functions and Rebalancing . . . . . . . . . . . 121
8 Testing CAPM and Multifactor Models 124
8.1 Market Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
8.2 Several Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
8.3 Fama-MacBeth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
9 Performance Analysis 142
9.1 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 142
9.2 Performance Attribution . . . . . . . . . . . . . . . . . . . . . . . . 150
9.3 Style Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
10 Predicting Asset Returns 155
10.1 Asset Prices, Random Walks, and the Efficient Market Hypothesis . . 155
10.2 Autocorrelations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
10.3 Other Predictors and Methods . . . . . . . . . . . . . . . . . . . . . 166
10.4 Security Analysts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
10.5 Technical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
10.6 Spurious Regressions and In-Sample Overfit . . . . . . . . . . . . . 175
10.7 Empirical U.S. Evidence on Stock Return Predictability . . . . . . . . 181
11 Event Studies 185
11.1 Basic Structure of Event Studies . . . . . . . . . . . . . . . . . . . . 185
11.2 Models of Normal Returns . . . . . . . . . . . . . . . . . . . . . . . 187
11.3 Testing the Abnormal Return . . . . . . . . . . . . . . . . . . . . . . 190
11.4 Quantitative Events . . . . . . . . . . . . . . . . . . . . . . . . . . . 193