Identifying Risk-Based Factors

44 Pages Posted: 18 Jul 2005

See all articles by Anchada Aida Charoenrook

Anchada Aida Charoenrook

Thammasat University

Jennifer S. Conrad

University of North Carolina Kenan-Flagler Business School

Date Written: June 2005


Existing studies find that size, book-to-market, and momentum explain the cross-section of average returns. Some studies also report evidence that suggests that liquidity risk is priced. There is an ongoing debate about whether these factors are related to fundamental risks. We propose a new test that examines whether a candidate variable meets a necessary condition to be considered a risk-based factor. We demonstrate that there must be a relationship between the conditional mean and conditional variance of the return on any factor-mimicking portfolio if the factor is a priced risk. In addition, the sign of the relation between the conditional mean and variance is given by the sign of the risk premium of the factor-mimicking portfolio. For a number of factors, including SMB, HML, UMD, and a liquidity factor, we test whether there is a reliable relation between the factor-mimicking portfolio's conditional variance and conditional mean. Our results suggest that the size and liquidity factors pass this 'necessary condition' to be considered a priced risk; the book-to-market factor passes the hurdle only during the latter part of the sample period (1963-2003). We find strong evidence that the variance of the momentum factor varies through time, but the relation between conditional variance and conditional mean is of the wrong sign. Thus, the evidence for momentum is not consistent with a risk-based explanation in the mean-variance setting.

Keywords: Asset pricing, multi-factor models, size, book-to-market, momentum, liquidity factor

JEL Classification: G12, G14

Suggested Citation

Charoenrook, Anchada Aida and Conrad, Jennifer S., Identifying Risk-Based Factors (June 2005). AFA 2006 Boston Meetings Paper. Available at SSRN: or

Anchada Aida Charoenrook (Contact Author)

Thammasat University ( email )

Thammasat Business School
2 Prachan Rd.
Bangkok, 10200
6686132215 (Phone)

Jennifer S. Conrad

University of North Carolina Kenan-Flagler Business School ( email )

Kenan-Flagler Business School
Chapel Hill, NC 27599-3490
United States

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