Assume the CAPM is the correct asset pricing model.An asset has a standard deviation of 30% and the market has a standard deviation of 20%.What would the correlation of the asset with the market need to be if the asset were to have the same expected return as the risk-free asset?

A) $ -0.200 $
B) $ 0.000 $
C) $ 0.200 $
D) $ 0.300 $

Question

Assume the CAPM is the correct asset pricing model.An asset has a standard deviation of 30% and the market has a standard deviation of 20%.What would the correlation of the asset with the market need to be if the asset were to have the same expected return as the risk-free asset?

A) $ -0.200 $
B) $ 0.000 $
C) $ 0.200 $
D) $ 0.300 $

Quizplus · Accepted Answer

According to the CAPM,the risk of an asset is measured by beta,where the beta of the market is 1.Similarly,the beta of the risk-free asset must be zero (by definition it must have zero risk,and hence zero beta).Therefore,if an asset is to have the same return as that of the risk-free,then it must also have a beta of 0.Using equation 8.2,page 240,the beta of an asset is calculated as follows: F1F1F1S1F1F1F10_i = F1F1F1S1F1F1F10_imF1F1F1S1F1F1F10_i/F1F1F1S1F1F1F10_m.Given that F1F1F1S1F1F1F10_i= 0.30 and F1F1F1S1F1F1F10_m= 0.20,and F1F1F1S1F1F1F10_i = 1,then solving for F1F1F1S1F1F1F10_im gives a required correlation of 0.000.Intuitively this makes sense,as the risk-free asset should be constant regardless of the state of the world,and hence uncorrelated with the risky asset.

Assume the CAPM Is the Correct Asset Pricing Model −0.200 -0.200 −0.200

Assume the CAPM Is the Correct Asset Pricing Model $-0.200$