Question

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?

Answer #1

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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