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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 ....

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?

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E(r) = \sum_{i=1}^{n} [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%

\sigmaP = [\sum_{i=1}^{n}{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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