Beta as a Random Coefficient
17 Pages Posted: 31 Mar 2015 Last revised: 12 Apr 2019
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
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