Question

Portfolio D has an expected return r_D= 10% and a standard deviation = 30%. Portfolio E has an expected return r_E = 20% and a standard deviation =40%. The correlation coefficient = +0.25. If I want to combine these 2 portfolios to earn an expected return r_p = 16%, what will be my portfolio standard deviation to the NEAREST xx.xx%?

a) 20.88%

b) 24.00%

c) 26.91%

d) 29.39%

e) None of the above

Answer 1

Answer:

Return for Porfolio D Rd=10%

Standard Deviation for D SDd=30%

Return for Porfolio E Re=20%

Standard Deviation for E SDe=40%

Correlation C=0.25

Expeted return Rp=16%

Let w1 is weight of D and w2 is weight of E

So that w1+w2=1 Eq 1

Rp=w1*Rd+w2*Re

16%=w1*10%+(1-w1)*20%

w1=40%

w2=60%

Portfolio Variance Vp=w1^2*SDd^2+w2^2*SDe^2+2*w1*w2*SDd*SDe*C

Vp=40%^2*30%^2+60%^2*40%^2+2*40%*60%*30%*40%*0.25

Vp=0.0864

Standrad deviation =SDp

SDp=29.39%