Question

The correlation between the fund returns is 0.1560. What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds?

Answer 1

Answer:

The answer is given below

Explanation:

The question is not complete. Given that:

$E(r_s)=11\%,E(r_b)=8\%, \sigma(r_s)=33\%,\sigma(r_b)=25\%$, ρ = 0.1560

From the covariance matrix, Cov (B, S) = $\rho*\sigma_b*\sigma_s=0..1560*33*25=128.7$

The minimum-variance portfolio is gotten using the formula:

$w_{min}(S)=\frac{\sigma_B^2-Cov(B,S)}{\sigma_S^2+\sigma_B^2-2Cov(B,S)}=\frac{(25^2)-128.7}{33^2+25^2-2(128.7)}=\frac{625-128.7}{225+1089-257.4}=0.4697\\\\w_{min}(B)=\frac{\sigma_S^2-Cov(B,S)}{\sigma_S^2+\sigma_B^2-2Cov(B,S)}=\frac{(33^2)-128.7}{33^2+25^2-2(128.7)}=\frac{1089-128.7}{225+1089-257.4}=0.9089$

the expected return for the minimum-variance portfolio is:

$E(r_{min})=w_{min}S*E(r_s)+w_{min}B*E(r_b)=11*0.4697+0.9089*8=12.44\%$

the standard deviation for the minimum-variance portfolio is:

$\sigma_{min}=[w_S^2\sigma_s^2+w_B^2\sigma_B^2+2w_Bw_SCov(B,S)]^\frac{1}{2} =[0.4687^2*33^2+0.9089^2*25^2+2*0.9089*0.4687*128.7]^\frac{1}{2}=29.41\%$