Nº 20-119: Cross-Section Without Factors: Correlation Risk, Strings and Asset Prices

Many asset pricing theories treat the cross-section of returns volatility and correlations as two intimately related quantities driven by common factors, which hinders achieving a neat definition of a correlation premium. We formulate a model without factors, but with a continuum of securities that have returns driven by a string. In this model, the arbitrage restrictions require that any asset premium links to the granular exposure of the asset returns to shocks in all other asset returns: an average correlation premium. This premium is both statistically and economically significant, and considerably fluctuates, driven by time-varying correlations and global market developments. The model predictions also lead to uncover fresh properties of big stocks. Big stocks display a high degree of market connectivity in bad times, but they are safer than other stocks, thereby providing hedges against times of heightened correlations. Finally, the model also explains the time-series behavior of the premium for the risk of changes in asset correlations (the premium for correlation risk), including its inverse relation with realized correlations.