We investigate pricing factors for corporate bonds in the six largest international markets. Our econometric analysis shows that small sample sizes severely compromise pricing tests of bond portfolios. Using Barillas and Shanken (2017) tests and global portfolios, we reject standard corporate bond factor models in favor of a model featuring the global corporate bond market, a global maturity spread factor, and a global liquidity spread factor. This model prices various cross-sections well, except for Japanese Yen bonds, where including a local market factor improves fit. All returns are hedged in US dollars, as hedged portfolios outperform unhedged ones.

We show that investors treat individual stocks as weak substitutes, and that this weak substitutability explains the existence of the “factor zoo” in expected stock returns. In classical asset-pricing models, substitutability is strong: when relative expected returns change, investors readily reallocate across assets that covary. In this case, there would be no factor zoo: differences in expected returns would be explained by the few factors that drive most covariance across stocks. In contrast, we show that substitutability is empirically weak in investor holdings data. We demonstrate that this weak substitutability gives rise to the factor zoo: expected returns depend on many factors, including those that drive little covariance across stocks.

We simulate data from well-known economic frameworks in which the true conditional SDF can be calculated. We examine multiple factor construction methodologies in these simulated economies, estimating the SDF by linear regression on past factor returns. Creating many factors using nonlinear combinations of characteristics as portfolio weights and then using shrinkage in the regression (complexity) works well. However, a latent factor model with fewer factors than characteristics (instrumented principal components) also works well. Classical methods do not perform well.