Asset Pricing for Idiosyncratically Incomplete Markets

Abstract

We present a rigorous analysis of idiosyncratically incomplete markets with heterogeneous agents. Our model is an extension of the classic Constantinides and Duffie (1996) that, among other important differences, allows for trade. We rigorously expand asset returns in the idiosyncratic risk and heterogeneity and then extract important economic information from the coefficients. In particular, we give a rational factor analysis of idiosyncratic risk. We calculate the response of some thirteen well known stylized facts to both idiosyncratic risk and heterogeneity. Of particular interest, we identify an explicit mechanism through which the growth rate of idiosyncratic risk increases equity returns and their volatility, but, (in stark contrast to models without trade) at the same time, leaves risk free rates virtually unchanged. Among other results, we find (to our own surprise) that the equity premium increases relative to the background complete market when the idiosyncratic risk process is (contradicting the conventional wisdom) procyclical and its growth rate is above an explicit threshold. We also show that countercyclicity of the idiosyncratic risk process forces term premia to be negative, contrary to empirical data, and also forces countercyclicity of price dividend ratios, again, contrary to empirical data.