Question

The market portfolio has an expected return of 11.0 percent and a standard deviation of 21.0 percent. The risk-free rate is 4.0 percent. |

a. |
What is the expected return on a well-diversified portfolio with
a standard deviation of 8.0 percent? |

Expected return | % |

b. |
What is the standard deviation of a well-diversified portfolio
with an expected return of 19.0 percent? |

Standard deviation | % |

Answer #1

R_{m} = 11%

R_{f} = 4%

a.

For well diversified portfolio,

Correlation Coefficient = 1

Beta_{p} = 0.08/0.21 = 0.38

Using CAPM model,

Expected return of Portfolio = R_{f} +
Beta(R_{m} - R_{f})

Expected Return of Portfolio = 0.04 + 0.38(0.11 - 0.04)

Expected Return of Portfolio = 6.66%

b.

Expected Return = 0.19

Using CAPM model,

Expected return of Portfolio = R_{f} +
Beta(R_{m} - R_{f})

Beta = (0.19 - 0.04)/(0.11 - 0.04) = 2.14

For well diversified portfolio,

Correlation Coefficient = 1

Beta = Standard Deviation of Portfolio/Standard Deviation of market

Standard Deviation of Portfolio = 2.14 * 0.21

Standard Deviation of Portfolio = 44.94%

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