An Analytic Derivation and Comments on Betting Against Beta 
DengTa Chen 
Wang Yanan Institute for Studies in Economics, Xiamen University 
4/29/2014 10:11:16 PM 

Abstract： 
I present a closed form solution to the OLG model in Frazzini and Pedersen (2014), and find that their OLG model of heterogeneous investors results in the zerobeta CAPM. I prove that the optimal amount to invest in risky assets for an investor is determined exactly by her risk aversion, margin requirement and wealth. Thus every investor's optimal portfolio is explicitly solved and the market portfolio is easily aggregated on the meanvariance frontier. Working with the analytic formulas, I provide a rigorous derivation of their theoretical results and discuss the implications of the Zfactor, which is market neutral, and must be the second factor other than the market factor in capital asset pricing. 
Keyword： 
Zerobeta Portfolio, CAPM, Heterogeneous Investors, Zfactor 
