A general proof that diversification pays, even with contagion

The swiftness with which risk spreaded throughout the market lead to a shift to a more connection-based approach to financial regulation. This change in focus has implications on the desirability portfolio diversification from society's perspective. Indeed while the individually risk reducing effect of diversification has been known since Markowitz (1952), it also forms connections between investors through common asset holdings, who have been identified as a major carrier of contagion in the presence of fire sales. The paper takes a first step towards quantifying this contagion externality diversification and compares it to its individual risk-reducing effect. We do so through the distribution of the vector of investor wealth, where marginal densities capture the former effect, while the latter is embedded in the dependence structure. Covariance matrices between investors are obtained from a micro-founded model that captures the contagion steeming from cross asset holding, which translates into a linear system of N recurrence equations of price returns. This paper is in its preliminary stages, comments are very welcome.