Question on Beta equation, derived, involving

cyber21

Just wondering if anyone has ever seen such a equation involving beta. I have absolutely no idea where it is derived from


Beta(1) = [ SD(1) * SD(2) * Corr(1,2) ] / Var(2)

?

johnnyBuz

Beta is simply covariance of an asset with the market divided by the asset's variance.

Covariance = Correlation x SD1 x SD2 which comes from Correlation = Covariance/(SD1xSD2)

Yep I've still got it.

amqata

this equation can be translated into [SD(1)* SD(2)* Cov(1,2)/SD(1)*SD(2)]/Var(2) (I)

(I)= Cov(1,2)/Var(2) (II)


Equation II is the correlation equation, which is what we call beta.

ogoluwa

Think of both correlation and beta as "scaled covariance". In the case of correlation, covariance is scaled by the prodict of the two assets' std deviations, while in the case of beta, covariance is scaled by the variance of the market. To relate them,

beta = correlation x [std(firm)/std(market)]

So, beta has both a "directional" component (i.e. correlation) and a dispersion component (the relative std deviations of the asset and the market). The correlation component also picks up the tuicghtness of the relationship between the asset and the market.