Optimal Portfolio Weight Calculation Based on Risky Assets

What is the portfolio weight of origami in the optimal risky portfolio?

a) 12.19% b) 60.26% c) 47.78% d) 9.34%

Final answer:

The portfolio weight of origami in the optimal risky portfolio, based on the given returns, standard deviations, and correlation, is approximately 60.26%.

In constructing the optimal risky portfolio with two risky assets, origami and gamiori, certain calculations need to be made. Origami has an expected return of 13% with a standard deviation of 20%, while 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, and the risk-free rate of return is 2%.

To determine the portfolio weight of origami in the optimal risky portfolio, we use the formula:

w_opt = (E[R_1 - R_f] - rho * Sigma_2 * E[R_2 - R_f]) / ((1 - rho) * Sigma_1 * Sigma_2)

Substitute in the given values and calculate:

w_opt = (0.13 - 0.02 - 0.30*0.10*(0.06 - 0.02)) / ((1 - 0.30) * 0.20 * 0.10)

After calculation, the portfolio weight of origami in the optimal risky portfolio is approximately 60.26%, which corresponds to option b.

This portfolio weight indicates the proportion of origami that should be included in the optimal risky portfolio to achieve the desired balance between risk and return.