Question

A portfolio has 40% of its value in IBM shares and the rest in Microsoft (MSFT). The volatility of IBM and MSFT are 35% and 30%, respectively, and the correlation between IBM and MSFT is 0.4. What is the standard deviation of the portfolio? A. 22.83% B. 29.55% C. 30.89% D. 26.86%

Answer 1

Wieght in IBM Share (WB) = 40%

Weight in Microsoft(WM) = 60%

Standard Deviation of IBM(B)   = 35%

Standard Deviation of Microsft(M) = 30%

$S.D.= \sqrt{(W)_{B}^{2}*(\sigma )^{2}_{B}+(W)_{M}^{2}*(\sigma )^{2}_{M}+2W_{B}W_{M}R_{B}R_{M}\rho _{BM}}$

$S.D.= \sqrt{(0.40)^2(35)^2+(0.60)^2(30)^2+2*0.40*0.60*35*30*0.4}$

$S.D.= \sqrt{196 + 324 + 201.6}=\sqrt{721.6}$

S.D. = 26.86%

Option D