Cross-Section Without Factors: Correlation Risk, Strings and Asset Prices

Many asset pricing theories treat the cross-section of expected returns, volatility and correlations as quantities driven by common factors. We formulate and estimate a model without such factors, but with a continuum of securities that have returns driven by a string. Our 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. The model predictions uncover fresh properties of big stocks. Big stocks display a high degree of market connectivity in bad times, but also work as correlation hedges: they contribute to a negative fraction of the average correlation premium, and portfolios that are more exposed to them command a lower premium. The string model performs at least as well as many existing linear factor models.