Asset pricing I: Pricing Models

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Asset pricing I: Pricing Models

Markus K. Brunnermeier a.y. 2014/2015

Contents

1 Introduction

8

1.1 Market Efficiency . . . . . . . . . . . . . . . 10

1.1.1 Dividend/Price Ratio and Stock Prices . . . . . . . . . . . . . . . . . 11

1.1.2 Size and Book to Market as drivers of Stock Returns . . . . . . . . . . . 11

1.1.3 Winners and Losers . . . . . . . . . 12

1.1.4 Event Studies . . . . . . . . . . . . 13

1.1.5 Government Bonds . . . . . . . . . 16

1.1.6 Corporate Bonds . . . . . . . . . . 17

1.1.7 Derivatives Pricing . . . . . . . . . 18

1.2 Stocks and Macroeconomic Factors . . . . 19

1.2.1 Measuring Risk with Covariance . 20

1.3 The 2013 Nobel Prize in Economics . . . . 21

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2 One Period Model

24

2.1 General Security Structure . . . . . . . . . 28

2.2 Derivatives . . . . . . . . . . . . . . . . . . 29

2.2.1 Forward Contracts . . . . . . . . . 29

2.2.2 Options . . . . . . . . . . . . . . . . 30

2.3 Back to Security Structures . . . . . . . . 32

2.3.1 Prices . . . . . . . . . . . . . . . . . 33

3 Pricing in the One Period Model

35

3.1 Forwards Revisited . . . . . . . . . . . . . . 36

3.1.1 Prepaid Forwards . . . . . . . . . . 36

3.1.2 Forwards . . . . . . . . . . . . . . . 37

3.2 Options Revisited . . . . . . . . . . . . . . 38

3.2.1 Option Price Boundaries . . . . . . 38

3.2.2 Time to Expiration . . . . . . . . . 39

3.2.3 Strike Price . . . . . . . . . . . . . . 39

3.3 Back to the One Period Model . . . . . . . 40

3.3.1 State Prices . . . . . . . . . . . . . . 41

3.3.2 The Fundamental Theorem of Finance . . . . . . . . . . . . . . . . . 42

3.3.3 State Prices and Incomplete Markets . . . . . . . . . . . . . . . . . . 43

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3.4 Asset Pricing Formulas . . . . . . . . . . . 44

3.4.1 State Price Model . . . . . . . . . . 44

3.4.2 Stochastic Discount Factor . . . . . 45

3.4.3 Equivalent Martingale Measure . . 46

3.4.4 State-Price Beta Model . . . . . . 47

3.5 Recovering State Prices from Option Prices 48

4 Risk Preferences and Expected Utility Theory 55 4.1 State-by-State Dominance . . . . . . . . . 55 4.2 Stochastic Dominance . . . . . . . . . . . . 57 4.3 Von Neumann Morgenstern Expected Utility Theory . . . . . . . . . . . . . . . . . . . 60 4.4 Representation of Preferences . . . . . . . 61 4.5 Risk Aversion, Concavity, Certainty Equivalent . . . . . . . . . . . . . . . . . . . . . . 64 4.6 Measures of Risk Aversion . . . . . . . . . 66 4.7 Risk Aversion and Portfolio Allocation . . 68 4.8 Alternative Theories . . . . . . . . . . . . . 70 4.9 Savings . . . . . . . . . . . . . . . . . . . . . 71 4.10 Mean-Variance Preferences . . . . . . . . . 73

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5 General Equilibrium, Efficiency and the

Equity Premium Puzzle

77

5.1 Pareto Efficiency . . . . . . . . . . . . . . . 79

5.2 The Sharpe Ratio, Bonds and the Equity Premium Puzzle . . . . . . . . . . . . . . . 81

5.3 Adding Expected Utility . . . . . . . . . . 83

5.4 The Equity Premium Puzzle . . . . . . . . 84

5.5 Empirical Estimation: Generalized Method of Moments . . . . . . . . . . . . . . . . . . 85

6 Mean-Variance Analysis and CAPM

87

6.1 The Traditional Derivation of CAPM . . . 88

6.1.1 Two Fund Separation . . . . . . . . 95

6.1.2 Equilibrium leads to CAPM . . . . 96

6.2 The Modern Approach . . . . . . . . . . . 98

6.2.1 Pricing and Expectation Kernel . 102

6.2.2 Beta Pricing . . . . . . . . . . . . . 105

6.3 Testing CAPM . . . . . . . . . . . . . . . . 106

6.4 Practical Issues . . . . . . . . . . . . . . . . 107

6.4.1 Estimating Means . . . . . . . . . . 107

6.4.2 Estimating Variances . . . . . . . . 107

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