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RA = 4.00% + 0.50RM + eA RB = -1.20% + 0.70RM + eB σM =...

RA = 4.00% + 0.50RM + eA RB = -1.20% + 0.70RM + eB σM = 17%; R-squareA = 0.26; R-squareB = 0.18

Assume you create portfolio P with investment proportions of 0.70 in A and 0.30 in B.

SD of portfolio?

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Answer #1

Variance of A=Beta A^2*Standard Deviation of M^2/Ra^2 =0.5^2*17%^2/0.26 =2.7788%
Standard Deviation of A =2.7788%^0.5 =16.6699%
Variance of B=Beta B^2*Standard Deviation of M^2/Rb^2 =0.7^2*17%^2/0.18 =7.8672%
Standard Deviation of B =7.8672%^0.5 =28.0486%
Covariance =Beta of A*Beta of B*Standard Deviation of M^2=0.50*0.70*17%^2 =0.010115

Variance of portfolio =Weight A^2*Variance of A +Weight B^2*Variance of B +2*Weight A*Weight B*Covariance
=0.7^2*2.7788%+0.3^2*7.8672%+2*0.7*0.3*0.010115=2.4945%

Standard Deviation =Variance^0.5 =2.4945%^0.5 =15.79%

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