Question

20. Portfolio risk You can form a portfolio of two assets, A and B, whose returns have the following characteristics: Stock Expected Return Standard Deviation Correlation A 10% 20% 0.5 If you demand an expected return of 12%, what are the portfolio weights? What is the portfolio's standard deviation?

I understand that the weights are .6 and .4, not sure how to get that from .12=(Wa)(.1)+(1-Wa)(.15)

Answer 1

Weight of Stock A = W_a

Therefore, Stock B = 1 - W_a

Now,

0.12 = (W_a)(0.10) + (1-W_a)(0.15)

0.12 = 0.10W_a + 0.15 - 0.15W_a

0.12 - 0.15 = -0.05W_a

W_a = 0.03 / 0.05

W_a = 0.6

W_b = 1 - W_a

= 1 - 0.6

W_b = 0.4

Portfolio Standard Deviation

$\sqrt{W_{a}^{2} \sigma^{2}(k_{a}) + W_{b}^{2} \sigma^{2}(k_{b}) + 2W_{a}W_{b}R(k_{a}k_{b})\sigma(k_{a})\sigma(k_{b}) }$

$\sqrt{(0.6)^{2} (0.2)^{2} + (0.4)^{2} (0.4)^{2} + 2*0.6*0.4*0.5*0.2*0.4 }$

$\sqrt{0.0144 + 0.0256 + 0.0192 }$

0.2433 or 24.33%