Question

You are trying to build the best possible risky portfolio for your investment clients. You have two risky assets available to you: A risky stock with an expected excess return of 0.199 and a standard deviation of 0.01, and a risky bond with an expected excess return of 0.039, and a standard deviation of 0.916. If these two assets have a coefficient of correlation of 0.22, what proportion of the money you invest in risky assets should you put in the bond? An answer of 0 means invest no money in the bond, an answer of 1 means put all of your money in the bond. Please give your answer to three decimal places.

Answer 1

Solution:

Given:

Standard Deviation of Risky Asset () = 0.01

Standard Deviation of Bond () = 0.916

Coefficient of Correlation_(R,B) () = 0.22

Optimum weight of Risky Asset = {² - ( * * )} / {² + ² - (2 * * * )}

= {0.916² - (0.22 * 0.916 * 0.01)} / { 0.01² + 0.916² - (2* 0.22 * 0.916 * 0.01)}

= {0.839056 - 0.002015} / {0.0001 + 0.839056 - 0.00403}

= 0.837041 / 0.835126

= 1.002 i.e., 1

Therefore, Zero investment needed in the bond. All of the money will get invested in risky asset only.