Question

A) We have the following **historical** returns on
a portfolio. Assume the monthly risk-free rate in the same time
period was 3%. Estimate the Sharpe ratio of this portfolio.

month | return |

1 | 10% |

2 | 5% |

3 | -2% |

4 | 3% |

5 | 15% |

B) Consider the same historical record above, what is the stock's geometric average monthly return in that time period?

Answer #1

Answer A.

Expected Return = [0.10 + 0.05 + (-0.02) + 0.03 + 0.15] /
5

Expected Return = 0.31 / 5

Expected Return = 0.062 or 6.20%

Variance = [(0.10-0.062)^2 + (0.05-0.062)^2 + (-0.02-0.062)^2 +
(0.03-0.062)^2 + (0.15-0.062)^2] / 4

Variance = 0.01708 / 4

Variance = 0.00427

Standard Deviation = (0.00427)^(1/2)

Standard Deviation = 0.0653 or 6.53%

Sharpe Ratio = [Expected Return - Risk-free Rate] / Standard
Deviation

Sharpe Ratio = (0.062 - 0.03) / 0.0653

Sharpe Ratio = 0.49

Answer B.

Geometric Return = [(1+0.10) * (1+0.05) * (1-0.02) * (1+0.03) *
(1+0.15)]^(1/5) - 1

Geometric Return = 1.340736^(1/5) - 1

Geometric Return = 1.0604 - 1

Geometric Return = 0.0604 or 6.04%

We have the following historical returns on a
portfolio. Assume the monthly risk-free rate in the same time
period was 3%. Estimate the Sharpe ratio of this portfolio.
Round your answer to 4 decimal places. For example if your
answer is 3.205%, then please write down 0.0321.
month
return
1
10%
2
5%
3
-2%
4
3%
5
15%

A stock's returns have the following distribution:
Demand for the
Company's Products
Probability of This
Demand Occurring
Rate of Return If
This Demand Occurs
Weak
0.1
(34%)
Below average
0.1
(15)
Average
0.4
13
Above average
0.3
23
Strong
0.1
62
1.0
Assume the risk-free rate is 3%. Calculate the stock's expected
return, standard deviation, coefficient of variation, and Sharpe
ratio. Do not round intermediate calculations. Round your answers
to two decimal places.
Stock's expected return: %
Standard deviation: %
Coefficient of...

A stock's returns have the following distribution:
Demand for the
Company's Products
Probability of This
Demand Occurring
Rate of Return If
This Demand Occurs
Weak
0.1
(38%)
Below average
0.2
(15)
Average
0.3
12
Above average
0.3
36
Strong
0.1
61
1.0
Assume the risk-free rate is 2%. Calculate the stock's expected
return, standard deviation, coefficient of variation, and Sharpe
ratio. Do not round intermediate calculations. Round your answers
to two decimal places.
Stock's expected return:
Standard deviation:
Coefficient of...

A stock's returns have the following distribution: Demand for
the Company's Products Probability of This Demand Occurring Rate of
Return If This Demand Occurs Weak 0.1 (42%) Below average 0.2 (15)
Average 0.3 17 Above average 0.3 36 Strong 0.1 63 1.0 Assume the
risk-free rate is 2%.
Calculate the stock's expected return, standard deviation,
coefficient of variation, and Sharpe ratio. Do not round
intermediate calculations. Round your answers to two decimal
places. Stock's expected return: % Standard deviation: %...

A stock's returns have the following distribution:
Demand for the
Company's Products
Probability of This
Demand Occurring
Rate of Return If
This Demand Occurs
Weak
0.1
(38%)
Below average
0.3
(9)
Average
0.4
15
Above average
0.1
21
Strong
0.1
71
1.0
Assume the risk-free rate is 4%. Calculate the stock's expected
return, standard deviation, coefficient of variation, and Sharpe
ratio. Do not round intermediate calculations. Round your answers
to two decimal places.
Stock's expected return: _____ %
Standard deviation:...

A stock's returns have the following distribution:
Demand for the
Company's Products
Probability of This
Demand Occurring
Rate of Return If
This Demand Occurs
Weak
0.1
(44%)
Below average
0.1
(15)
Average
0.4
18
Above average
0.3
39
Strong
0.1
58
1.0
Assume the risk-free rate is 2%. Calculate the stock's expected
return, standard deviation, coefficient of variation, and Sharpe
ratio. Do not round intermediate calculations. Round your answers
to two decimal places.
Stock's expected return: %
Standard deviation: %
Coefficient of...

A stock's returns have the following distribution:
Demand for the
Company's Products
Probability of This
Demand Occurring
Rate of Return If
This Demand Occurs
Weak
0.2
(36%)
Below average
0.1
(7)
Average
0.3
18
Above average
0.2
27
Strong
0.2
48
1.0
Assume the risk-free rate is 3%. Calculate the stock's expected
return, standard deviation, coefficient of variation, and Sharpe
ratio. Do not round intermediate calculations. Round your answers
to two decimal places.
Stock's expected return: %
Standard deviation: %
Coefficient of...

A stock's returns have the following distribution:
Demand for the
Company's Products
Probability of This
Demand Occurring
Rate of Return If
This Demand Occurs
Weak
0.1
(40%)
Below average
0.4
(10)
Average
0.3
10
Above average
0.1
37
Strong
0.1
48
1.0
Assume the risk-free rate is 3%. Calculate the stock's expected
return, standard deviation, coefficient of variation, and Sharpe
ratio. Do not round intermediate calculations. Round your answers
to two decimal places.
Stock's expected return: %
Standard deviation: %...

A stock's returns have the following distribution:
Demand for the
Company's Products
Probability of This
Demand Occurring
Rate of Return If
This Demand Occurs
Weak
0.1
(24%)
Below average
0.1
(13)
Average
0.3
12
Above average
0.3
29
Strong
0.2
48
1.0
Assume the risk-free rate is 3%. Calculate the stock's expected
return, standard deviation, coefficient of variation, and Sharpe
ratio. Do not round intermediate calculations. Round your answers
to two decimal places.
Stock's expected return: %
Standard deviation: %
Coefficient of...

A stock's returns have the following distribution:
Demand for the
Company's Products
Probability of This
Demand Occurring
Rate of Return If
This Demand Occurs
Weak
0.1
(38%)
Below average
0.1
(13)
Average
0.4
12
Above average
0.3
30
Strong
0.1
62
1.0
Assume the risk-free rate is 3%. Calculate the stock's expected
return, standard deviation, coefficient of variation, and Sharpe
ratio. Do not round intermediate calculations. Round your answers
to two decimal places.
Stock's expected return: %
Standard deviation: %
Coefficient of...

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