Eco 525 Financial Economics I Lecture 04 State price BETA Model Prof Markus K Brunnermeier 10 01 Lecture 04 State price Beta Model Slide 04 1 Eco 525 Financial Economics I Overview Risk adjustment in payoffs Risk adjustment in returns State price beta model Different specific asset pricing models 10 01 Lecture 04 State price Beta Model Slide 04 2 Eco 525 Financial Economics I Risk adjustment in payoffs p E mxj E m E x Cov m x Since 1 E mR the risk free rate is Rf 1 E m p E x Rf Cov m x Remarks i If risk free rate does not exist Rf is the shadow risk free rate ii In general Cov m x 0 which lowers price and increases return 10 01 Lecture 04 State price Beta Model Slide 04 3 Eco 525 Financial Economics I Risk adjustment in Returns E mRj 1 Rf E m 1 E m Rj Rf 0 E m E Rj Rf Cov m Rj 0 E Rj Rf Cov m Rj E m also holds for portfolios h 2 Note risk correction depends only on Cov of payoff return with discount factor Only compensated for taking on systematic risk not idiosyncratic risk 10 01 Lecture 04 State price Beta Model Slide 04 4 Eco 525 Financial Economics I State price BETA Model shrink axes by factor c2 X let underlying asset be x 1 2 1 R R m m m c1 p 1 priced with m 10 01 Lecture 04 State price Beta Model Slide 04 5 Eco 525 Financial Economics I State price BETA Model E Rj Rf Cov m Rj E m 2 also holds for all portfolios h and we can replace m with m Suppose i Var m 0 and ii R m with 0 E Rh Rf Cov R Rh E R 2 Define h Cov R Rh Var R for any portfolio h Regression Rhs h h R s s with Cov R E 0 10 01 Lecture 04 State price Beta Model Slide 04 6 Eco 525 Financial Economics I State price BETA Model 2 for R E R Rf Cov R R E R Var R E R 2 for Rh E Rh Rf Cov R Rh E R h Var R E R E Rh Rf h E R Rf where h Cov R Rh Var R very general but what is R in reality 10 01 Lecture 04 State price Beta Model Slide 04 7 Eco 525 Financial Economics I Different Asset Pricing Models pt E mt 1 xt 1 where mt 1 f f asset pricing model General Equilibrium f MRS Factor Pricing Model a b1 f1 t 1 b2 f2 t 1 CAPM a b1 f1 t 1 a b1 RM 10 01 Lecture 04 E Rh Rf h E R Rf where h Cov R Rh Var R CAPM R Rf a b1RM a b1Rf where RM return of market portfolio Is b1 0 State price Beta Model Slide 04 8 Eco 525 Financial Economics I Different Asset Pricing Models Theory All economics and modeling is determined by mt 1 a b f Entire content of model lies in restriction of SDF Empirics m which is a portfolio payoff prices as well as m which is e g a function of income investment etc measurement error of m is smaller than for any m Run regression on returns portfolio payoffs e g Fama French three factor model 10 01 Lecture 04 State price Beta Model Slide 04 9