You want to invest $20,000 in a portfolio consisting of three stocks - Stock M,

Question

You want to invest $20,000 in a portfolio consisting of three stocks - Stock M, Stock D, and Stock G. The percentage investment is as follows: Stock M 40%, Stock D 35% and Stock G 25%. The expected return for each of these stocks under the three possible economic states is given below.

                                                                          Stock M            Stock D           Stock G

                        Economy – Booming                     20%                  -7%                 10%

                        Economy – Stagnant                     15%                  12%                  7%

                        Economy – Recession                   -10%                 16%                 12%

The probability of Booming Economy is 20%, the probability of stagnant economy is 50% and the probability of Recession is 30%.

Compute the following.

Expected returns for the three investments Stock M, Stock D, and Stock G.

Standard deviation of the returns for the three investments Stock M, Stock D, and Stock G.

Coefficient of Variation of returns for the three investments Stock M, Stock D, and Stock G.

Expected return of the Portfolio.

Standard Deviation of the expected portfolio return.

Explanation / Answer

Expected Return Stock M= 20*.2+15*.5-10*.3 = 8.5% Stock D= -7*.2+12*.5+16*.3 = 9.4% Stock G= 10*.2+7*.5+12*.3 = 9.1% Portfolio Return = 8.5*.4+9.4*.35+9.1*.25                                     = 3.4+3.29+2.275    Portfolio Return= 8.965%

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