Question
In: Finance
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 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?
Solutions
jeff jeffy answered 1 year 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
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...
Ri = αi + βiRM + ei where Ri is the excess return for security i...
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
0.5
13
%
26
%
B
0.9
17
12
C
1.3
21
21
a. If σM = 25%, calculate
the variance of returns of securities A, B, and
C.
b. Now...
The single-index model for stock i is Ri = 0.01+1.5RM + ei. The single-index model for...
The single-index model for stock i is Ri = 0.01+1.5RM + ei. The
single-index model for stock j is Rj = 0.02+0.8RM + ej. The
standard deviation of the market return is σM=0.2, the standard
deviation of ei is σei=0.3 and the standard deviation of ej is
σej=0.4. 1. Calculate the systematic risk, firm-specific risk, and
total risk of stock i.
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