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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 , the Euler Equation for equilibrium asset pricing is 1 = E t h ( 1 + R i , t + 1 ) ( 1 + C t + 1 )- i where R i , t + 1 is the returns to the generic i th asset and 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- C t + 1- R i , t + 1 C t + 1 + ( + 1 ) 2 ( C t + 1 ) 2 so taking expectations and approximating the EE yields, E t R i , t + 1 + E t C t + 1 + ic- ( + 1 ) 2 2 c where = subjective discount rate, 1/ - 1 c = Var t ( C t + 1 ) ic = Cov t ( R i , t + 1 , C t + 1 ) . Hence the risk-free rate is R f , t + 1 = + E t C t + 1- ( + 1 ) 2 2 c and the equity premium for asset i is E t R i , t + 1- R f , t + 1 = ic ....
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