Consider the following information on a portfolio of three stocks:
State of Economy | Probability of State of Economy | Stock A Rate of Return | Stock B Rate of Return | Stock C Rate of Return |
Boom | .15 | .05 | .21 | .18 |
Normal | .80 | .08 | .15 | .07 |
Recession | .05 | .12 | -.22 | -.02 |
The portfolio is invested 35 percent in each Stock A and Stock B and 30 percent in Stock C. If the expected T-bill rate is 3.90 percent, what is the expected risk premium on the portfolio? What is the standard deviation of the portfolio?
E(r) = [Pi x Ri]
E(rA) = [0.15 x 5%] + [0.80 x 8%] + [0.05 x 12%] = 0.75% + 6.40% + 0.60% = 7.75%
E(rB) = [0.15 x 21%] + [0.80 x 15%] + [0.05 x -22%] = 3.15% + 12.00% - 1.10% = 14.05%
E(rC) = [0.15 x 18%] + [0.80 x 7%] + [0.05 x -2%] = 2.70% + 5.60% - 0.10% = 8.20%
E(rP) = [0.35 x 7.75%] + [0.35 x 14.05%] + [0.30 x 8.20%] = 2.71% + 4.92% + 2.46% = 10.09%
E(RP) = E(rP) - rF = 10.09% - 3.90% = 6.19%
P = [{Pi x (E(rP) - Ri)^{2}}]^{1/2}
= [{0.35 x (10.09% - 7.75%)^{2}} + {0.35 x (10.09% - 14.05%)^{2}} + {0.30 x (10.09% - 8.20%)^{2}}]^{1/2}
= [1.92%^{2} + 5.49%^{2} + 1.07%^{2}]^{1/2} = [8.48%^{2}]^{1/2} = 2.91%
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