Given the following information, what is the expected return and standard deviat

Question

Given the following information, what is the expected return and standard deviation of a portfolio which is invested 30 percent in both stocks A and C, and 40 percent in stock B?

                State of                Probability of Rate of Return if State Occurs

Economy State of Economy                               Stock A                  Stock B                  Stock C

                Boom .10 .28                           .12                          .18

                Normal .75 .03                           .09                          .07

                Recession .15 -.40                           .05                       -.22

Explanation / Answer

Return Expected Return Stock A Stock B Stock C Probability Stock A Stock B Stock C Boom 0.28 0.12 0.18 0.1 0.028 0.012 0.018 Normal 0.03 0.09 0.07 0.75 0.0225 0.0675 0.0525 Recession -0.4 0.05 -0.22 0.15 -0.06 0.0075 -0.033 Total -0.95% 8.70% 3.75% Expected Expected Average Return Return Weight Return Formula Stock A -0.95% 30% -0.29% (-0.95% x 30%) Stock B 8.70% 60% 5.22% (8.70% x 60%) Stock C 3.75% 30% 1.13% (3.75 x 30%) Total 6.06% Average return of the portfolio = 6.06% Expected Expected Square of Return Return Weight Variance Formula Stock A -0.95% 30% 0.15% (-0.95-6.06)^2 x 30% Stock B 8.70% 60% 0.04% (8.70-6.06)^2 x 60% Stock C 3.75% 30% 0.02% (3.75-6.06)^2 x 30% Total 0.21% Standard Deviation = square root of 0.21% = 4.53%

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