Describing model relations: The case of the capital asset pricing model (CAPM) family in financial economics

The description of how individual models in families of models are related to each other is crucial for the general philosophical understanding of model-based scientific practice. We focus on the Capital Asset Pricing Models (CAPM) family, a cornerstone in financial economics, to provide a descriptive analysis of model relations within a family. We introduce the concepts of theoretical and empirical complementarity to characterise model relations. Our complementarity analysis of model relations has two types of payoff. Specifically regarding the CAPM, our analysis reveals why this model family, which has been empirically contested, has yet remained popular and important: the different models that have been added over time have made new empirically and theoretically complementary contributions to the model family. More generally, our analysis reveals the dynamic character of model-based scientific practice. Characterising relations between models as theoretically and/or empirically complementary yields three hitherto underappreciated lessons: (i) actual modelling purposes are not always primarily epistemic, (ii) a model's individual import is relative, not absolute, and (iii) there is an important interplay between theory and data models. Faithfully characterising scientific modelling in this way facilitates subsequent analysis of models' epistemic import.