On the Dynamics of Changing Correlations: Identification and Stock Returns
Previously circulated as: "Correlation, causation, and stock returns" and "Size-Related Risk Premiums", Discussion Papers on Business and Economics, University of Southern Denmark, 3/2018
78 Pages Posted: 21 Nov 2017 Last revised: 2 Jul 2020
Date Written: July 2, 2020
Riskier firms have lower prices (and higher book-to-market) exclusively due to the present value identity (while book equity is only a relatively bad proxy for expected cash flows). This theoretically explains (i) why the difference between the value and the size premiums significantly decreases and becomes negative as the price of risk increases, (ii) why the SMB returns explain none of the variation in the HML returns for portfolios formed in low price of risk states while a strong factor structure exists for the remaining portfolios, and (iii) why only among these portfolios formed in high price of risk states, the SMB returns span (without being spanned by) the HML returns. The hypothesis that there are (even indirect) stable economic relations between risk and market capitalization ("size") or book-to-market - often treated as an axiom in Finance - is theoretically inconsistent with the present value identity, especially for market capitalization, and also with the empirical evidence, under very general conditions. Inevitably, regressions that rely on size-related portfolios do not produce valid unconditional models of returns.
Keywords: Size premium, value premium, correlation, causation, missing risk
JEL Classification: G11, G12, G14
Suggested Citation: Suggested Citation