Question

Mr X can invest in two financial securities, security A and security B. The table below gives a description of the states of the world, their respective probabilities and the return of each security in each state. 

         State:                      Bear Normal Bull 

Probability of state          20%   40%  40%

Return of security A -       40%    0%   100% 

Return of security B        -6%    10%   20% 

a. Find the expected return and the standard deviation of returns of a portfolio which places weight 30% in security A and 70% in security B. 

b. risk-free interest rate is RF=2%, estimate the optimal risky portfolio for the investor when short sales are allowed. 

 c. Suppose that there is a third security, security C. Its return is -10% when the market is Bear, and 10% when the market is Normal. When the market is Bull, security C has 50% chance to give a return of 20% and 50% to give a return of 100%. Find the optimal risky portfolio for Mr X. when he can invest in securities A, B, and C and short sales are allowed.