Question

A portfolio has the following stocks:

Stock | Amount Invested | Stock's Beta |

A | $2,000 | 1.4 |

B | $8,000 |
1.2 |

C | $15,000 | 1.6 |

Suppose that the risk-free rate of return is 4% and the market return is 20%.

(1) What are the weights for Stocks A, B and C, respectively? (

2) What is the portfolio’s beta?

(3) What is the expected return for Stock A?

(4) What is the expected return for the portfolio?

Answer #1

1. Weights for stock A B and C.

Stock | Amount invested | weight |

A | $2,000 | ($2,000/25,000)=>0.08 |

B | $8,000 | ($8,000/25,000)=>0.32 |

C | $15,000 | ($15,000/25,000)=>0.60 |

Total | $25,000 | 1.00 |

2. Portfolio Beta = sum of (weight * stock beta)

=> (0.08*1.40) + (0.32*1.20) + (0.60*1.60)

=>1.456.

3.expected return for stock A

=> risk free rate + beta*(market return - risk free rate)

=>4%+1.4*(20%-4%)

=>4% +22.4%

=>26.4%.

4.expected return for the portfolio = risk free rate + beta*(market return - risk free rate)

=>4%+1.456*(20%-4%)

=>4% + 23.296%

=>27.296%

=>27.30%.

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