On the Dynamics of Changing Correlations: Identification and Stock Returns

Abstract

Riskier firms have lower prices - and higher book-to-market - exclusively due to the present value identity. For a small subset of firms, book equity is a good proxy for expected cash flows. This is why (i) the difference between the value and size premiums significantly decreases and becomes negative with the price of risk; (ii) among portfolios formed in low price of risk states, SMB returns explain none of the variation in HML returns; (iii) for the remaining portfolios, a strong factor structure exists; (iv) only among these portfolios, SMB returns span HML returns; and (v) the same SMB portfolios span the (stock) market portfolio. The hypothesis of (even indirect) stable economic relations between risk and market capitalization ("size") or book-to-market is theoretically inconsistent with the present value identity and inconsistent with the empirical evidence under fairly general conditions. There are no "missing factors" which size or book-to-market proxy for: 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