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Theory of Asset Pricing
George Pennacchi
December 2006
ii
Contents
Preface
I
xiii
Single-Period Portfolio Choice and Asset Pricing
1 Expected Utility and Risk Aversion
1
3
1.1
Preferences when Returns Are Uncertain . . . . . . . . . . . . . .
4
1.2
Risk Aversion and Risk Premia . . . . . . . . . . . . . . . . . . .
14
1.3
Risk Aversion and Portfolio Choice . . . . . . . . . . . . . . . . .
25
1.4
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
1.5
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
2 Mean-Variance Analysis
2.1
37
Assumptions on Preferences and Asset Returns . . . . . . . . . .
39
2.2 Investor Indifference Relations . . . . . . . . . . . . . . . . . . . .
43
2.3 The Efficient Frontier . . . . . . . . . . . . . . . . . . . . . . . .
47
2.3.1
A Simple Example . . . . . . . . . . . . . . . . . . . . . .
47
2.3.2
Mathematics of the Efficient Frontier . . . . . . . . . . . .
51
2.3.3
Portfolio Separation . . . . . . . . . . . . . . . . . . . . .
55
2.4 The Efficient Frontier with a Riskless Asset . . . . . . . . . . . .
59
2.4.1
An Example with Negative Exponential Utility . . . . . .
iii
65
iv
CONTENTS
2.5
An Application to Cross-Hedging . . . . . . . . . . . . . . . . . .
68
2.6
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
2.7
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
3 CAPM, Arbitrage, and Linear Factor Models
3.1
77
The Capital Asset Pricing Model . . . . . . . . . . . . . . . . . .
79
3.1.1
Characteristics of the Tangency Portfolio . . . . . . . . .
80
3.1.2
Market Equilibrium . . . . . . . . . . . . . . . . . . . . .
82
Arbitrage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
3.2.1
Examples of Arbitrage Pricing . . . ....