In: Finance

A stock's returns have the following distribution:

Demand for theCompany's Products |
Probability of ThisDemand Occurring |
Rate of Return IfThis Demand Occurs |

Weak | 0.1 | (36%) |

Below average | 0.1 | (15) |

Average | 0.3 | 16 |

Above average | 0.3 | 21 |

Strong | 0.2 | 56 |

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 variation:

Sharpe ratio:

**a**) **Expected Return**- It refers
to the sum of the average return of each stock multiplied by its
weight or probability.

E(R) = P_{1} * R_{1} + P_{2} *
R_{2} +.......P_{n *} R_{n}

where, P_{1} ,P_{2 ...}P_{n} =
Probabilty of return

R_{1} ,R_{2 ...}R_{n }=
Return expectation

Here, E(R) = (0.1* -36%) + (0.1 * -15%) + (0.3 * 16%) + (0.3 * 21%) + (0.2 * 56%)

= -0.036 - 0.015 + 0.048 + 0.063 + 0.112 = 0.172 or 17.2%

**b) Standard Deviation-** It is a measure of
volatility or risk. It is the squareroot of the variance.

_{p}
=
[P_{1} * (R_{1}- E(R))^{2} +
P_{2}* (R_{2}- E(R))^{2} + .........
Pn * Rn -
E(R))^{2}]

_{p}
= (0.1
* (-0.36-0.172)^{2}) + (0.1 * (-0.15-0.172)^{2}) +
(0.3 * (0.16-0.172)^{2}) + (0.3 * (0.21-0.172)^{2}
) + (0.2 * (0.56-0.172)^{2})

_{p}=
(0.0283 + 0.0103684 + 0.0000432 + 0.0004332 + 0.0301)

_{p}=
(0.0692448)

_{p}=
0.2631 or 26.31%

**c) Coefficient of variation** - It is the ratio
of standard deviation to the mean (expected return)

COV = SD/ expected return

COV = 26.3%/ 17.2% = 1.52

**d) Sharpe ratio** - The ratio is the average
return earned in excess of the risk-free rate per unit of
volatility or total risk

**Sharpe ratio = R _{p} - R_{f} /
_{p}**

where, R_{p} - Return on portfolio

R_{f} - Risk free rate

_{p
-} Standard deviation of portfolio

Sharpe ratio = R_{p} - R_{f} /
_{p}

= (0.172 - 0.03) / 0.263

= 0.53

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
(26%)
Below average
0.2
(14)
Average
0.3
10
Above average
0.3
21
Strong
0.1
73
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: %
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
(48%)
Below average
0.1
(15)
Average
0.3
11
Above average
0.3
40
Strong
0.2
65
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: %
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
-46%
Below average
0.1
-13
Average
0.4
14
Above average
0.3
34
Strong
0.1
56
=
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...

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
(28%)
Below average
0.1
(11)
Average
0.4
10
Above average
0.3
35
Strong
0.1
61
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: %
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
(14)
Average
0.3
13
Above average
0.3
31
Strong
0.2
63
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: %
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
(32%)
Below average
0.3
(14)
Average
0.4
11
Above average
0.1
36
Strong
0.1
55
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...

eBook Problem Walk-Through
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
(10)
Average
0.3
13
Above average
0.3
21
Strong
0.1
51
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...

eBook Problem Walk-Through
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
(48%)
Below average
0.1
(13)
Average
0.4
18
Above average
0.3
22
Strong
0.1
54
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...

Rand Inc. and McNally Corp. have the following probability
distribution of returns: Probability Rand Returns McNally
Returns
0.3 15% 12% 0.4 9 5 0.3 18 20
a) Calculate the expected rates of return for the two
stocks.
b) Calculate the standard deviation of returns for the two
stocks.
c) Calculate the expected return and standard deviation on a
portfolio P made up of 75%
invested in McNally stock and the remaining invested in Rand
stock.

Expected Returns: Discrete Distribution
The market and Stock J have the following probability
distributions:
Probability
rM
rJ
0.3
12%
21%
0.4
10
4
0.3
17
12
a.Calculate the expected rate of return for the market. Round
your answer to two decimal places.
%
b. Calculate the expected rate of return for Stock J. Round your
answer to two decimal places.
%
c. Calculate the standard deviation for the market. Round your
answer to two decimal places.
%
d. Calculate the...

ADVERTISEMENT

ADVERTISEMENT

Latest Questions

- Which of the following returns will give you the highest dollar amount after 6 years? 49%...
- I need to write a forum on lerner index from a managers perspective in economics not...
- Python acquired 75% of Slitherâ€™s stock for $316 million in cash on January 2, 2015. The...
- Explain the tax implications of working from home in Australia during the COVID-19 pandemic. Who is...
- Make a reasonable argument for the "Good Samaritan" doctrine as the best approach for this situations
- An industry has two firms. The inverse demand function for this industry is p = 74...
- 30-Sep The following information is available: Sales Revenue (net credit sales) 1,200 Accounts Receivable &nb

ADVERTISEMENT