Suppose that in an efficient market there are three risky assets A, B and C with

Question

Suppose that in an efficient market there are three risky assets A, B and C with the following beta s and sigma_ij^2 s Assume that the pairwise correlations among epsilon_j s all equal to 0 and that the variance of the market portfolio is sigma_M^2 =0.025. Suppose now we have a portfolio with weights omega_A = 0.20, omega_B = 0.40 and omaega_c = 0.40 on these three assets. Compute Cov(R_A, R_B) Find the beta of this portfolio and the variance of the excess return on this portfolio. What proportion of the total risk of this portfolio is due to market risk?

Explanation / Answer

covariance = correlation cofficient × s.d of A × s.d of B

Beta of a stock = covariance of stock and market / variance of market

so beta = correlation cofficient of stock and market× s.d of stock × s.d of market / (s.d of market^2)

= correlation × s.d of stock/ s.d of market

Now the beta has to be solved for, to find the stocks S.D

However , correlation coefficient is missing in the sum

But process remains this

2.Beta of portfolio = weight of a*beta of A +weight of B *beta of B + weight of C * beta of C

=0.20×1.5+ 0.40×1.2+0.40×0.80

=1.1

Variance of portfolio = weight of stock × s.d of stock + 2* correlation cofficient*s. d of stock

Again since the correlation coffiecent is missing in the sum. But this is the way to calculate.

c. Total risk = systematic risk + unsystematic risk

=0.025 + (0.035+0.019+0.081)

=0.16

Systematic risk as a proportion os total risk is 0.025/0.16 =15.625%

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