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Unformatted text preview: Overview Portfolio Choice The EquityPremium Puzzle Eco331: Comparative Risk Aversion and Portfolio Choice Marciano Siniscalchi October 19, 2009 Overview Portfolio Choice The EquityPremium Puzzle Overview Review of key definitions The PortfolioChoice Problem Comparative Statics of Risk Aversion The EquityPremium Puzzle Overview Portfolio Choice The EquityPremium 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 riskaverse iff, for any X ∈ F , δ E [ X ] < X . Proposition An EU DM with preferences over F is riskaverse if and only if her Bernoulli utility function u is concave . Overview Portfolio Choice The EquityPremium Puzzle Review, cont.: Comparing Risk Attitudes Recall < is riskaverse iff, for all X ∈ F , C [ X ] ≤ E [ X ] . Definition Let u and v be continuous and strictly increasing. Then v is more riskaverse 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 riskaverse 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 EquityPremium Puzzle A simple PortfolioChoice 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.
 Spring '09
 Marciano
 Economics

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