Question

Given the following probability distribution, what are the expected return and the standard |

deviation of returns for Security J? |

State Pi rj |

1 0.2 12% |

2 0.3 4% |

3 0.5 17% |

Group of answer choices

12.10%; 5.93%

12.30%; 5.63%

12.40%; 5.63%

12.30%; 5.93%

12.10%; 5.63%

Suppose you hold a diversified portfolio consisting of a $6,485 invested equally |

in each of 20 different common stocks. The portfolio’s beta is 0.81. Now |

suppose you decided to sell one of your stocks that has a beta of 1.4 and to |

use the proceeds to buy a replacement stock with a beta of 1.6. What would |

the portfolio’s new beta be? |

Group of answer choices

1.02

0.82

0.92

1.12

0.72

A stock has an expected return of 19.1 percent. The beta of the stock is 2.15 and the |

risk-free rate is 2.9 percent. What is the market risk premium? |

Group of answer choices

7.63%

7.53%

7.23%

7.33%

7.43%

Your portfolio consists of $31,232 invested in a stock that has a beta = 1.9, |

$45,024 invested in a stock that has a beta = 1, and $93,754 invested in a |

stock that has a beta = 1.8. The risk-free rate is 5%. Last year this portfolio had |

a required return of 8.3%. This year nothing has changed except that the market |

risk premium has increased by 3.8%. What is the portfolio’s current required rate |

of return? |

Group of answer choices

14.6%

14.3%

14.4%

14.7%

14.5%

Answer #1

**Solution 1.>**

Expected Return = Sum of (probabilities*return)

= (0.2*12%)+(0.3*4%)+(0.5*17%)

= **12.1%**

Standard deviation:

State | Return | Mean | (return - mean) | (return - mean)^2 |

1 | 12 | 12.1 | -0.1 | 0.01 |

2 | 4 | -8.1 | 65.61 | |

3 | 17 | 4.9 | 24.01 |

Variance = 0.01+65.61+24.01/3 = 29.877

standard deviation = variance^0.5 = 29.877^0.5 =
**5.465**

**Hence, the correct option is (E)**

**Solution 2.>**

New Beta : 0.81 - 1.4*(1/20) + 1.6*(1/20)

: 0.82

**Hence, the correct option is (B)**

**Solution 3.>**

Using CAPM model,

Expected Return = Risk-free rate + Beta * ( Market Risk Premium )

19.1% = 2.9% + 2.15(MRP)

MRP = 0.0753 or **7.53%**

**Hence, the correct option is (B)**

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