Is there a missing factor? A canonical correlation approach to factor models

A common question in asset pricing research is if a finite set of observable variables can completely capture the systematic or common variations in a large number of response variables. This paper provides a new approach to answer this question. A novelty is that common factors are extracted using canonical relations between response variables and observable factors. We show how these factors in combination with tests for the number of factors can be used to evaluate if a given set of macroeconomic and financial variables is sufficient to capture all the systematic variation in the response variables. We illustrate the usefulness of our methods by analyzing the systematic determinants of credit spreads of U.S. corporate bonds.