CFA Level I, Port­fo­lio Manage­ment, Con­s­truc­tion of a Port­fo­lio — MC Question

Con­sider two shares, A and B, with a given return of 8 % and 4 %. The risks are given by 6 % for A and 3 % for B. The cova­ri­ance of the two returns of the two shares is given by ‑0.00144. The port­fo­lio of the two shares con­sists of 30 % of share A and 70 % of share B. The stan­dard devia­ti­on of the portfolio´s return is equal to

A. 2.45 %

B. 3.63 %

C. 1.27 %

Solu­ti­on: C. is correct.

We com­pu­te the vari­ance as 

variance_portfolio

= (w_A)^2*Var_A + (w_B)^2*Var_B + 2*(w_A)*(w_B)*Cov_(A,B)

= 0.3^2*0.06^2 + 0.7^2*0.03^2 + 2*0.3*0.7*(-0.00144)

= 0.0001602, lea­ding to a stan­dard devia­ti­on of 1.27 %.