Question

Drew can design a risky portfolio based on two risky assets, Origami and Gamiori. Origami has an expected return of 13% and a standard deviation of 20%. Gamiori has an expected return of 6% and a standard deviation of 10%. The correlation coefficient between the returns of Origami and Gamiori is 0.30. The risk-free rate of return is 4%. If Drew invests 30% money in Gamiori and the remaining in Origami, what is the standard deviation of his portfolio?

Answer 1

Variance of portfolio = [((Weight in Gamiori)^2 * (Standard Deviation of Gamiori^2)] + [((Weight in Origami)^2 * (Standard Deviation of Origami^2)] + 2 Weight in Gamior*Weight in Origami* Cov between Origami and Gamiori

coefficient between the returns of Origami and Gamiori = Cov between Origami and Gamiori / ( standard deviation of Origami* standard deviation of Gamiori

0.30 = Cov between Origami and Gamiori/ (0.20*0.10)

0.006 = Cov between Origami and Gamiori

Variance of portfolio = 0.3²0.1² + 0.7²0.2₂² + (2*0.3*0.7*0.006)

= 0.0009 + 0.0196 + 0.00252

= 0.02302

Standard Deviation of portfolio = Variance of portfolio^(1/2)

= 0.02302^(1/2)

= 0.1517 or 15.17%