eco331-06-PortfolioChoiceHandout

eco331-06-PortfolioChoiceHandout - Overview Portfolio...

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Unformatted text preview: Overview Portfolio Choice The Equity-Premium Puzzle Eco331: Comparative Risk Aversion and Portfolio Choice Marciano Siniscalchi October 19, 2009 Overview Portfolio Choice The Equity-Premium Puzzle Overview Review of key definitions The Portfolio-Choice Problem Comparative Statics of Risk Aversion The Equity-Premium Puzzle Overview Portfolio Choice The Equity-Premium Puzzle Review of Definitions and Results Prizes X ; discrete r.v.’s F . Certainty Equivalent : C [ X ]. Definition A DM with preferences < on F is risk-averse iff, for any X ∈ F , δ E [ X ] < X . Proposition An EU DM with preferences over F is risk-averse if and only if her Bernoulli utility function u is concave . Overview Portfolio Choice The Equity-Premium Puzzle Review, cont.: Comparing Risk Attitudes Recall < is risk-averse iff, for all X ∈ F , C [ X ] ≤ E [ X ] . Definition Let u and v be continuous and strictly increasing. Then v is more risk-averse than u if and only if, for all X ∈ F , C v [ X ] ≤ C u [ X ]. Proposition Let u, v be twice differentiable & strictly increasing. Then the following are equivalent: (1) v is more risk-averse than u . (2) There exists a concave, strictly increasing function g : u ( X ) → R such that, for all x ∈ X v ( x ) = g ( u ( x )) . (3) For all x ∈ X ,- v 00 ( x ) v ( x ) ≥ - u 00 ( x ) u ( x ) . Overview Portfolio Choice The Equity-Premium Puzzle A simple Portfolio-Choice Problem Initial wealth...
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This note was uploaded on 11/17/2009 for the course ECONOMICS 331 taught by Professor Marciano during the Spring '09 term at Northwestern.

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eco331-06-PortfolioChoiceHandout - Overview Portfolio...

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