Beta as a Random Coefficient

17 Pages Posted: 31 Mar 2015 Last revised: 12 Apr 2019

See all articles by Frank J. Fabozzi

Frank J. Fabozzi

EDHEC Business School

Jack Clark Francis

Zicklin School of Business, Baruch College

Date Written: March 5, 1978


The results suggest that the beta systematic risk measure calculated with the well-known single index market model (SIMM) may be a random coefficient. This would explain why the average NYSE stock has less than half of its total risk explained by market forces — the true beta is moving randomly while the OLS beta is a point estimate which is invariant over the sample period. The OLS residual variance is biased upward by the beta coefficient's rigidity. Furthermore, it is expected that the problems caused by the OLS coefficient rigidity will increase with the length of the sample time span used to estimate the SIMM, because in the long run all betas will experience changes. These findings have serious implications for past and future research.

Keywords: Beta, random coefficient, point estimate

Suggested Citation

Fabozzi, Frank J. and Francis, Jack Clark, Beta as a Random Coefficient (March 5, 1978). Journal of Financial and Quantitative Analysis (JFQA), March 1978, pages 101-115, Available at SSRN:

Frank J. Fabozzi

EDHEC Business School ( email )

215 598-8924 (Phone)

Jack Clark Francis (Contact Author)

Zicklin School of Business, Baruch College ( email )

One Bernard Baruch Way
New York, NY 10010
United States
646-312-3462 (Phone)

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