TY - JOUR

T1 - On the Spurious Correlation Between Sample Betas and Mean Returns

AU - Levy, Moshe

PY - 2012/9

Y1 - 2012/9

N2 - Cornerstone asset pricing models, such as capital asset pricing model (CAPM) and arbitrage pricing theory (APT), yield theoretical predictions about the relationship between expected returns and exposure to systematic risk, as measured by beta(s). Numerous studies have investigated the empirical validity of these models. We show that even if no relationship holds between true expected returns and betas in the population, the existence of low-probability extreme outcomes induces a spurious correlation between the sample means and the sample betas. Moreover, the magnitude of this purely spurious correlation is similar to the empirically documented correlation, and the regression slopes and intercepts are very similar as well. This result does not necessarily constitute evidence against the theoretical asset pricing models, but it does shed new light on previous empirical results, and it points to an issue that should be carefully considered in the empirical testing of these models. The analysis points to the dangers of relying on simple least squares regression for drawing conclusions about the validity of equilibrium pricing models.

AB - Cornerstone asset pricing models, such as capital asset pricing model (CAPM) and arbitrage pricing theory (APT), yield theoretical predictions about the relationship between expected returns and exposure to systematic risk, as measured by beta(s). Numerous studies have investigated the empirical validity of these models. We show that even if no relationship holds between true expected returns and betas in the population, the existence of low-probability extreme outcomes induces a spurious correlation between the sample means and the sample betas. Moreover, the magnitude of this purely spurious correlation is similar to the empirically documented correlation, and the regression slopes and intercepts are very similar as well. This result does not necessarily constitute evidence against the theoretical asset pricing models, but it does shed new light on previous empirical results, and it points to an issue that should be carefully considered in the empirical testing of these models. The analysis points to the dangers of relying on simple least squares regression for drawing conclusions about the validity of equilibrium pricing models.

KW - CAPM

KW - asset pricing

KW - beta

KW - spurious correlation

UR - http://www.scopus.com/inward/record.url?scp=84864687970&partnerID=8YFLogxK

U2 - 10.1080/1350486X.2011.624824

DO - 10.1080/1350486X.2011.624824

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AN - SCOPUS:84864687970

SN - 1350-486X

VL - 19

SP - 341

EP - 360

JO - Applied Mathematical Finance

JF - Applied Mathematical Finance

IS - 4

ER -