Question
In: Finance
***Please show the math! Thank you! Assume that security returns are generated by the single-index model,...
***Please show the math! Thank you!
Assume that security returns are generated by the single-index model,
Ri = αi +
βiRM + ei
where Ri is the excess return for security
i and RM is the market’s excess
return. The risk-free rate is 3%. Suppose also that there are three
securities A, B, and C, characterized by
the following data:
| Security | βi | E(Ri) | σ(ei) | ||
| A | 1.0 | 10 | % | 23 | % |
| B | 1.3 | 13 | 9 | ||
| C | 1.6 | 16 | 18 | ||
a. If σM = 20%, calculate the variance of returns of securities A, B, and C.
|
b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number.)
|
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Solutions
jeff jeffy answered 1 week agoRelated Solutions
Assume that security returns are generated by the single-index model, Ri = αi + βiRM +...
Assume that security returns are generated by the single-index
model,
Ri = αi +
βiRM + ei
where Ri is the excess return for security
i and RM is the market’s excess
return. The risk-free rate is 4%. Suppose also that there are three
securities A, B, and C, characterized by
the following data:
Security
βi
E(Ri)
σ(ei)
A
1.3
14%
27%
B
1.5
16
13
C
1.7
18
22
a. If σM = 22%, calculate
the variance of returns...
Assume that security returns are generated by the single-index model, Ri = αi + βiRM +...
Assume that security returns are generated by the single-index
model, Ri = αi + βiRM + ei where Ri is the excess return for
security i and RM is the market’s excess return. The risk-free rate
is 2%. Suppose also that there are three securities A, B, and C,
characterized by the following data: Security βi E(Ri) σ(ei) A 0.7
7 % 20 % B 0.9 9 6 C 1.1 11 15
a. If σM = 16%, calculate the variance...
Assume that security returns are generated by the single-index model, Ri = αi + βiRM +...
Assume that security returns are generated by the single-index
model,
Ri = αi +
βiRM + ei
where Ri is the excess return for security
i and RM is the market’s excess
return. The risk-free rate is 2%. Suppose also that there are three
securities A, B, and C, characterized by
the following data:
Security
βi
E(Ri)
σ(ei)
A
1.2
12
%
25
%
B
1.3
13
11
C
1.4
14
20
a. If σM = 23%, calculate
the variance...
Assume that security returns are generated by the single-index model, Ri = αi + βiRM +...
Assume that security returns are generated by the single-index
model,
Ri = αi +
βiRM + ei
where Ri is the excess return for security
i and RM is the market’s excess
return. The risk-free rate is 2%. Suppose also that there are three
securities A, B, and C, characterized by
the following data:
Security
βi
E(Ri)
σ(ei)
A
1.3
13
%
22
%
B
1.5
15
13
C
1.7
17
16
a. If σM = 20%, calculate
the variance...
Assume that security returns are generated by the single-index model, Ri = αi + βiRM +...
Assume that security returns are generated by the single-index
model,
Ri = αi +
βiRM + ei
where Ri is the excess return for security
i and RM is the market’s excess
return. The risk-free rate is 4%. Suppose also that there are three
securities A, B, and C, characterized by
the following data:
Security
βi
E(Ri)
σ(ei)
A
1.3
14%
27
%
B
1.5
16%
13
%
C
1.7
18%
22
%
a. If σM = 22%, calculate
the...
Assume that security returns are generated by the single-index model, Ri = αi + βiRM +...
Assume that security returns are generated by the single-index
model,
Ri = αi +
βiRM + ei
where Ri is the excess return for security
i and RM is the market’s excess
return. The risk-free rate is 3%. Suppose also that there are three
securities A, B, and C, characterized by
the following data:
Security
βi
E(Ri)
σ(ei)
A
1.0
10
%
23
%
B
1.3
13
9
C
1.6
16
18
a. If σM = 20%, calculate
the variance...
Assume that security returns are generated by the single-index model, Ri = αi + βiRM +...
Assume that security returns are generated by the single-index
model,
Ri = αi +
βiRM + ei
where Ri is the excess return for security
i and RM is the market’s excess
return. The risk-free rate is 3%. Suppose also that there are three
securities A, B, and C, characterized by
the following data:
Security
βi
E(Ri)
σ(ei)
A
1.4
14
%
23
%
B
1.6
16
14
C
1.8
18
17
a. If σM = 22%, calculate
the variance...
Assume that security returns are generated by the single-index model, Ri = αi + βiRM +...
Assume that security returns are generated by the single-index
model, Ri = αi + βiRM + ei where Ri is the excess return for
security i and RM is the market’s excess return. The risk-free rate
is 2%. Suppose also that there are three securities A, B, and C,
characterized by the following data: Security βi E(Ri) σ(ei) A 0.8
10 % 25 % B 1.0 12 10 C 1.2 14 20
a. If σM = 20%, calculate the variance...
Problem 10-8 Assume that security returns are generated by the single-index model, Ri = αi +...
Problem 10-8
Assume that security returns are generated by the single-index
model,
Ri = αi +
βiRM + ei
where Ri is the excess return for security
i and RM is the market’s excess
return. The risk-free rate is 3%. Suppose also that there are three
securities A, B, and C, characterized by
the following data:
Security
βi
E(Ri)
σ(ei)
A
1.5
6
%
29
%
B
1.7
8
15
C
1.9
10
24
a. If σM = 26%, calculate...
***Please show your math work, thank you! Assume that stock market returns have the market index...
***Please show your math work, thank you!
Assume that stock market returns have the market index as a
common factor, and that all stocks in the economy have a beta of
2.0 on the market index. Firm-specific returns all have a standard
deviation of 32%.
Suppose that an analyst studies 20 stocks and finds that
one-half of them have an alpha of +3.0%, and the other half have an
alpha of −3.0%. Suppose the analyst invests $1.0 million in an...
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