Question

Historical Returns: Expected and Required Rates of Return

You have observed the following returns over time:

Year |
Stock X |
Stock Y |
Market |

2009 | 14% | 15% | 13% |

2010 | 20 | 7 | 9 |

2011 | -15 | -8 | -12 |

2012 | 4 | 2 | 2 |

2013 | 24 | 13 | 18 |

Assume that the risk-free rate is 4% and the market risk premium is 6%. Do not round intermediate calculations.

- What is the beta of Stock X? Round your answer to two decimal
places.

- What is the beta of Stock Y? Round your answer to two decimal
places.

- What is the required rate of return on Stock X? Round your
answer to one decimal place.

% - What is the required rate of return on Stock Y? Round your
answer to one decimal place.

% - What is the required rate of return on a portfolio consisting
of 80% of Stock X and 20% of Stock Y? Round your answer to one
decimal place.

%

Answer #1

Stock X | ||||||

Year | Year | Stock | Deviation=Return-Expected return | Deviation^2 | ||

2009 | 1 | 14.00% | 4.600% | 0.212% | ||

2010 | 2 | 20.00% | 10.600% | 1.124% | ||

2011 | 3 | -15.00% | -24.400% | 5.954% | ||

2012 | 4 | 4.00% | -5.400% | 0.292% | ||

2013 | 5 | 24.00% | 14.600% | 2.132% | ||

Total | 47.00% | Total | 9.712% | |||

Expected return= | 47%/5 | |||||

So the expected return is 9.4% | ||||||

Variance in return | 9.712%/5 | |||||

Variance in return | 1.9424% | |||||

Standard deviation | '1.9424%^(0.5) | |||||

Standard deviation | 13.94% |

Stock Y | ||||||

Year | Year | Stock | Deviation=Return-Expected return | Deviation^2 | ||

2009 | 1 | 15.00% | 9.200% | 0.846% | ||

2010 | 2 | 7.00% | 1.200% | 0.014% | ||

2011 | 3 | -8.00% | -13.800% | 1.904% | ||

2012 | 4 | 2.00% | -3.800% | 0.144% | ||

2013 | 5 | 13.00% | 7.200% | 0.518% | ||

Total | 29.00% | Total | 3.428% | |||

Expected return= | 29%/5 | |||||

So the expected return is 5.8% | ||||||

Variance in return | 3.428%/5 | |||||

Variance in return | 0.6856% | |||||

Standard deviation | '0.6856%^(0.5) | |||||

Standard deviation | 8.28% |

Market | ||||||

Year | Year | Stock | Deviation=Return-Expected return | Deviation^2 | ||

2009 | 1 | 13.00% | 7.000% | 0.490% | ||

2010 | 2 | 9.00% | 3.000% | 0.090% | ||

2011 | 3 | -12.00% | -18.000% | 3.240% | ||

2012 | 4 | 2.00% | -4.000% | 0.160% | ||

2013 | 5 | 18.00% | 12.000% | 1.440% | ||

Total | 30.00% | Total | 5.420% | |||

Expected return= | 30%/5 | |||||

So the expected return is 6% | ||||||

Variance in return | 5.42%/5 | |||||

Variance in return | 1.0840% | |||||

Standard deviation | '1.084%^(0.5) | |||||

Standard deviation | 10.41% |

Calculation of BETA

Beta Security= | Co-variance with Market/Market Variance | ||||||

Year | Market deviation | X deviation | Market D * Stock X deviation | Y deviation | Market D * Stock Y deviation | ||

2011 | 7.00% | 4.60% | 0.32% | 9.20% | 0.64% | ||

2012 | 3.00% | 10.60% | 0.32% | 1.20% | 0.04% | ||

2013 | -18.00% | -24.40% | 4.39% | -13.80% | 2.48% | ||

2014 | -4.00% | -5.40% | 0.22% | -3.80% | 0.15% | ||

2015 | 12.00% | 14.60% | 1.75% | 7.20% | 0.86% | ||

Total | 7.00% | Total | 4.18% | ||||

Stock X | Stock Y | ||||||

Co-variance with market= | 7%/(5-1) | 4.18%/(5-1) | |||||

Co-variance with market= | 1.75% | 1.05% | |||||

BETA= | 1.75%/1.084% | 1.05%/1.084% | |||||

BETA= | 1.61 | 0.97 |

Required return | Risk-free rate + Beta * Market premium | |

Stock X | Stock Y | |

Required return | 4%+1.61*6% | 4%+0.97*6% |

Required return | 13.66% | 9.82% |

Portfolio return | |||

Stock X | Stock Y | Total | |

Required return | 13.66% | 9.82% | |

Weight | 80% | 20% | |

Required return*weight | 10.92800% | 1.96400% | 12.89% |

So required return on portfolio will be 12.89% | |||

Historical Returns: Expected and Required Rates of Return
You have observed the following returns over time:
Year
Stock X
Stock Y
Market
2009
16%
14%
13%
2010
19
6
9
2011
-15
-2
-13
2012
2
1
1
2013
23
11
18
Assume that the risk-free rate is 3% and the market risk premium
is 6%. Do not round intermediate calculations.
What is the beta of Stock X? Round your answer to two decimal
places.
What is the beta of...

Historical Returns: Expected and Required Rates of Return
You have observed the following returns over time:
Year
Stock X
Stock Y
Market
2011
15%
14%
10%
2012
19
6
12
2013
-17
-3
-12
2014
3
2
3
2015
19
12
17
Assume that the risk-free rate is 6% and the market risk premium
is 6%. Do not round intermediate calculations.
What is the beta of Stock X? Round your answer to two decimal
places.
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Historical Returns: Expected and Required Rates of Return
You have observed the following returns over time:
Year
Stock X
Stock Y
Market
2012
16%
15%
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2013
21
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11
2014
-16
-6
-11
2015
3
3
1
2016
22
12
13
Assume that the risk-free rate is 4% and the market risk premium
is 7%. Do not round intermediate calculations.
What is the beta of Stock X? Round your answer to two decimal
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Problem 2-14
Historical Returns: Expected and Required Rates of Return
You have observed the following returns over time:
Year
Stock X
Stock Y
Market
2011
16%
12%
13%
2012
19
7
10
2013
-15
-2
-14
2014
4
1
1
2015
24
9
17
Assume that the risk-free rate is 4% and the market risk premium
is 7%. Do not round intermediate calculations.
What is the beta of Stock X? Round your answer to two decimal
places.
What is...

Historical Returns: Expected and Required Rates of Return
You have observed the following returns over time:
Year
Stock X
Stock Y
Market
2012
16%
12%
14%
2013
18
6
8
2014
-16
-4
-14
2015
5
2
3
2016
21
11
16
Assume that the risk-free rate is 6% and the market risk premium
is 6%. Do not round intermediate calculations.
What is the beta of Stock X? Round your answer to two decimal
places.
What is the beta of...

Historical Returns: Expected and Required Rates of Return
You have observed the following returns over time:
Year
Stock X
Stock Y
Market
2012
16%
14%
14%
2013
21
7
11
2014
-14
-3
-10
2015
5
2
1
2016
21
9
17
Assume that the risk-free rate is 3% and the market risk premium
is 6%. Do not round intermediate calculations.
What is the beta of Stock X? Round your answer to two decimal
places.
What is the beta of...

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Historical Returns: Expected and Required Rates of Return
You have observed the following returns over time:
Year
Stock X
Stock Y
Market
2012
15%
12%
12%
2013
18
8
9
2014
-14
-3
-14
2015
4
1
1
2016
20
12
18
Assume that the risk-free rate is 3% and the market risk premium
is 7%. Do not round intermediate calculations.
What is the beta of Stock X? Round your answer to two decimal
places.
What is the...

eBook
Problem 6-14
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You have observed the following returns
over time:
Year
Stock X
Stock Y
Market
2012
14%
11%
11%
2013
17
7
11
2014
-13
-2
-11
2015
4
2
1
2016
21
8
15
Assume that the risk-free rate is 3%
and the market risk premium is 6%. Do not round intermediate
calculations.
What is the beta of Stock X? Round your
answer to two decimal places.
What is...

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Stock R has a beta of 1.9, Stock S has a beta of 0.65, the
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You have observed the following returns over time:
Year
Stock X
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Problem 6-13
Historical Realized Rates of Return
Stocks A and B have the following historical returns:
Year
2012
-24.70%
-14.40%
2013
22.75
23.00
2014
11.75
37.10
2015
-2.50
-6.10
2016
31.50
-0.80
Assume that someone held a portfolio consisting of 50% of Stock
A and 50% of Stock B. What would have been the realized rate of
return on the portfolio in each year? What would have been the
average return on the portfolio during this period? Round your
answers...

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