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%. What is the portfolio weight of Origami in the optimal risky portfolio?

Answer 1

Portfolio weight in Origami = ((Expected return on Origami - Risk free rate)  * (Standard Deviation of Gamiori)² - ((Expected return on Gamiori - Risk free rate) * Standard Deviation of Origami * Standard Deviation of Gamiori * Correlation between Origami & Gamiori))) / ((Expected return on Origami - Risk free rate) * (Standard Deviation of Gamiori)² + (Expected return on Gamiori - Risk free rate)  * (Standard Deviation of Origami)²  - ((Expected return on Origami - Risk free rate + Expected return on Gamiori - Risk free rate) * Standard Deviation of Origami * Standard Deviation of Gamiori * Correlation between Origami & Gamiori))

Portfolio weight in Origami = ((13% - 4%) * (10%)² - ((6% - 4%) * 20% * 10% * 0.30)) / ((13% - 4%) * (10%)² + (6% - 4%) * (20%)² - ((13% - 4% + 6% - 4%) * 20% * 10% * 0.30))

Portfolio weight in Origami = 75%