Question

Consider two risky securities A and B, as well as a risk-free bond. Their average returns and standard deviations are presented in the table below. The correlation between the Securities A and B is 0.3.

Average Return Standard Deviation

Security A 8% 12%

Security B 13% 20%

Risk-free bond 5% 0%

a) What is the average return and standard deviation of an equally-weighted portfolio in A and B?

b) Assume that the portfolio from a) is the efficient market portfolio M. If the covariance between Security A and the efficient market portfolio M is Cov (A,M) =

0.0108, and the covariance between Security B and the efficient market portfolio M Cov (B, M) is 0.0236, what is the expected return of Securities A and B, according to the CAPM?

c) What are the Jensen’s alphas of the two securities? Based on the alphas, how can

investors improve their portfolio performance?

Answer 1

a.

given,

Equally weight portfolio of A and B

Therefore,

$w_A=0.5$

$w_B=0.5$

correlation A and B = 0.3

expected return $=w_a\times r_a+w_b\times r_b$

$=0.5 \times \frac{8}{100}+0.5\times \frac{13}{100} =0.105$

=10.5%

standard deviation

$=\sqrt{w_a^2\times σ_a^2+ w_b^2\times σ_b^2+2\times σ_a\times σ_b\times w_a \times w_b\times correl}$

$=\sqrt{0.5^2\times 12^2+0.5^2 \times 20^2 +2 \times 0.5 \times 0.5 \times 12 \times 20 \times 0.3}$

=13.12%