An Analysis of Risk and Pricing Anomalies

40 Pages Posted: 15 Mar 2000

See all articles by Tobias J. Moskowitz

Tobias J. Moskowitz

Yale University, Yale SOM; AQR Capital; National Bureau of Economic Research (NBER)

Date Written: September 1999


This paper examines the link between several well-known asset pricing anomalies and covariance risk. Estimating the time-series of the covariance matrix of asset returns via a multivariate GARCH model, I quantify the contribution made by each anomaly to the covariance matrix of asset returns, as well as its ability to forecast future covariances. I find that anomalous returns associated with firm size are closely linked to the covariance matrix, while those associated with book-to-market equity are weakly linked. However, returns associated with momentum do not appear related to covariance risk and do not forecast future covariances. Finally, despite its lack of predictive power on the cross-section of expected returns, the market portfolio is the single most important factor contributing to and forecasting covariance risk.

JEL Classification: G12

Suggested Citation

Moskowitz, Tobias J., An Analysis of Risk and Pricing Anomalies (September 1999). CRSP Working Paper No. 500. Available at SSRN: or

Tobias J. Moskowitz (Contact Author)

Yale University, Yale SOM ( email )

New Haven, CT 06520
United States


AQR Capital ( email )

Greenwich, CT
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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