An asset has a standard deviation of 30% and a correlation with the market portfolio of 0.60.If the market has a standard deviation of 30%,how much lower is the beta of the asset relative to the market?

A) $ 0.05 $
B) $ 0.10 $
C) $ 0.18 $
D) $ 0.40 $

Question

An asset has a standard deviation of 30% and a correlation with the market portfolio of 0.60.If the market has a standard deviation of 30%,how much lower is the beta of the asset relative to the market?

A) $ 0.05 $
B) $ 0.10 $
C) $ 0.18 $
D) $ 0.40 $

Quizplus · Accepted Answer

Using equation 8.2,the beta of an asset is calculated as the covariance of the asset divided by the market variance.However,the equation can also be rewritten as follows: F1F1F1S1F1F1F10_i =F1F1F1S1F1F1F10_imF1F1F1S1F1F1F10_i/F1F1F1S1F1F1F10_m.Given that F1F1F1S1F1F1F10_im= 0.60,F1F1F1S1F1F1F10_i= 0.30 and F1F1F1S1F1F1F10_m= 0.30,then the beta of the asset is equal to 0.60.Therefore,since the market has a beta of 1,the asset's beta is 0.40 lower than the beta of the market.

An Asset Has a Standard Deviation of 30% and a Correlation