Part SixProbability Theory and Statistics
A Bayesian estimate of security beta β is obtained from its posterior distribution, which is approximately normal with mean
and variance
where b is the least-squares estimate of β in a linear regression, 
is the standard error of the estimate, and b′ and 
are the mean and standard deviation, respectively, of prior information about the company's beta. In the absence of more specific knowledge about the company, the parameters of the prior distribution can be set to the mean 
and standard deviation of the cross-sectional distribution of betas in the universe. (page 291)
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