# eppuzzle - E CON 714 M ACROECONOMIC T HEORY II TA T IM L EE...

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E CON 714: M ACROECONOMIC T HEORY II TA: T IM L EE M ARCH 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 . The average returns on stock is about 7% and 3-month T-bills is about 1% in the past century. Even if stock returns are perfectly correlated with aggregate consumption (which they aren’t), sigma 2 c

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