Missing data is a prevalent, yet often ignored, feature of company fundamentals. In this paper, we document the structure of missing financial data and show how to systematically deal with it. In a comprehensive empirical study we establish four key stylized facts. First, the issue of missing financial data is profound:

it affects over 70% of firms that represent about half of the total market cap. Second, the problem becomes particularly severe when requiring multiple characteristics to be present. Third, firm fundamentals are not missing-at-random, invalidating traditional ad-hoc approaches to data imputation and sample selection. Fourth, stock returns themselves depend on missingness. We propose a novel imputation method to obtain a fully observed panel of firm fundamentals. It exploits both time-series and cross-sectional dependency of firm characteristics to impute their missing values, while allowing for general systematic patterns of missing data. Our approach provides a substantial improvement over the standard leading empirical procedures such as using cross-sectional averages or past observations. Our results have crucial implications for many areas of asset pricing.

When expected returns are linear in asset characteristics, the stochastic discount factor (SDF) that prices individual stocks can be represented as a factor model with GLS cross-sectional regression slope factors. Factors constructed heuristically by aggregating individual stocks into characteristics-based factor portfolios using sorting, characteristics-weighting, or OLS cross-sectional regression slopes do not span this SDF unless the covariance matrix of stock returns has a specific structure. These conditions are more likely satisfied when researchers use large numbers of characteristics simultaneously. Methods to hedge unpriced components of heuristic factor returns allow partial relaxation of these conditions. We also show the conditions that must hold for dimension reduction to a number of factors smaller than the number of characteristics to be possible without having to invert a large covariance matrix. Under these conditions, instrumented and projected principal components analysis methods can be implemented as simple PCA on certain portfolio sorts.

We study the size and drivers of non-standard errors (Menkveld et al., 2021) in portfolio sorts across 14 common methodological decision nodes and 40 sorting variables. These non-standard errors range between 0.05 and 0.26 percent and are, on average, larger than standard errors. Supposedly innocuous decisions cause large variation in estimated premiums, standard errors, non-standard errors, and t-statistics. The impact of decision nodes varies widely across sorting variables. Irrespective of choices in portfolio sorts, we find pervasively positive premiums and alphas for almost all sorting variables. This suggests that while the size of these premiums is uncertain, their sign is remarkably stable. Our code is publicly available.