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Unformatted text preview: ECON 714: MACROECONOMIC THEORY II TA: TIM LEE MARCH 28, 2010 Equity Premium Puzzle Under standard CRRA preferences with parameter γ , the Euler Equation for equilibrium asset pricing is 1 = β E t h ( 1 + R i , t + 1 ) ( 1 + Δ C t + 1 )- γ i where R i , t + 1 is the returns to the generic i th asset and Δ C t + 1 = C t + 1 / C t- 1. Taylor Approximation Taking a 2nd order Taylor Expansion around [ 0, 0 ] inside the brackets yields 1 + R i , t + 1- γ Δ C t + 1- γ R i , t + 1 Δ C t + 1 + γ ( γ + 1 ) 2 ( Δ C t + 1 ) 2 so taking expectations and approximating the EE yields, E t R i , t + 1 ≈ ρ + γ E t Δ C t + 1 + γσ ic- γ ( γ + 1 ) 2 σ 2 c where ρ = subjective discount rate, 1/ β- 1 σ c = Var t ( Δ C t + 1 ) σ ic = Cov t ( R i , t + 1 , Δ C t + 1 ) . Hence the risk-free rate is R f , t + 1 = ρ + γ E t Δ C t + 1- γ ( γ + 1 ) 2 σ 2 c and the equity premium for asset i is E t R i , t + 1- R f , t + 1 = γσ ic ....
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This note was uploaded on 06/19/2011 for the course ECON 714 taught by Professor Staff during the Spring '08 term at University of Wisconsin.
- Spring '08