In this article, we shed more light on the covariances versus characteristics debate by investigating the explanatory power of the instrumented principal component analysis (IPCA), recently proposed by Kelly et al. (2019). They conclude that characteristics are covariances because there is no residual return predictability from characteristics above and beyond that in factor loadings. Our findings indicate that there is no residual return predictability from factor loadings above and beyond that in characteristics either. In particular, we find that stock returns are best explained by characteristics (characteristics are characteristics) and that a one-factor IPCA model is sufficient to explain stock risk (characteristics are covariances). We therefore conclude that characteristics are covariances or characteristics, depending on whether the goal is to explain stock returns or risk.
cross-section of stock returns covariances characteristics IPCA