On the Insignificant Cross-Sectional Risk-Return Relationship

Gerald H. L. Cheang, Joseph C. S. Kang, Michael Z. F. Li

Nanyang Business School, Nanyang Technological University, Singapore City, Singapore.

DOI: 10.4236/jmf.2012.21004                

Abstract

In their paper, “On the Cross-sectional Relation between Expected Returns and Betas”, Roll and Ross (1994) demonstrated that the expected returns and betas can have zero relationship even when the underlying market portfolio proxies are nearby the efficient frontier. In this note, we provide the mathematical details that lead to their conclusion and further show that their claim needs not hold for the entire set of MV portfolios.

Keywords

CAPM; Portfolio Theory; Mathematical Finance; Market Risk and Expected Return; Cross-Sectional Relationship; Theory and Evidence; Mathematical Derivation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	E. F. Fama and K. R. French, “The Cross-Section of Expected Stock Returns,” Journal of Finance, Vol. 47, No. 2, 1992, pp. 427-466. doi:10.2307/2329112
[2]	R. Roll and S. A. Ross, “On the Cross-Sectional Relation between Expected Returns and Betas,” Journal of Finance, Vol. 49, No. 1, 1994, pp. 101-121. doi:10.2307/2329137