Given That.docx

Given that, RA = 4.5% + 1.40RM + eA RB = –2.2% + 1.7RM + eB σM = 24%; R-squareA = 0.30; R-squareB = 0.20; wA = 0.60; wB = 0.40 Comparing above two equations with standard equation of Sharpe Index Model, Beta of Stock-A, A = 1.05 Beta of Stock-B, B = 1.2 Also, R-squareA = A x A x σM x σM /(σA x σA) 0.29 = 1.05 x 1.05 x 0.29 x 0.29 / (σA x σA) (σA x σA) = 0.0927 / 0.29 (σA x σA) = 0.3197 σA = 0.5654 Also, R-squareB = B x B x σM x σM /(σB x σB) 0.14 = 1.2 x 1.2 x 0.29 x 0.29 / (σB x σB) (σB x σB) = 0.1211 / 0.14 (σB x σB) = 0.8650 σB = 0.9301 Covariance (A,B) = A x B x σM x σM = 1.05 x 1.2 x 0.29 x 0.29 = 0.106 Correlation (A,B) = Covariance (A,B) / σA / σB = 0.106/ 0.5654/ 0.9301 = 0.2015 a.) σ2p = w2Aσ2A + w2Bσ2B + 2wAwBxCovariance(A,B) = 0.6*0.6*0.5654*0.6134 + 0.4*0.4*0.9123*0.9301+ 2*0.6*0.4*0.106 =

0.1249+ 0.1358+ 0.05088

=

0.31158 0.31158

σp = sqrt ( ) = 0.5582 Standard Deviation of Portfolio = 55.82% b.) Portfolio Beta,

p = wA A + wB B = 0.6 x 1.05 + 0.4 x 1.2

= 1.11 c.)

Variance of Stock-A, σA x σA = 0.3197 (calculated above) Variance of Stock-B, σB x σB = 0.8650 (calculated above) Variance of Portfolio, σP x σP =

d.) Covariance (P,M) =

P

x

M

0.31158 (calculated above)

x σM x σM

= 1.11 x 1.0 x 0.29 x 0.29 =

0.0934