Question

Assume that security returns are generated by the single-index model,

*R _{i}* =

where *R _{i}* is the excess return for security

Security | β_{i} |
E(R_{i}) |
σ(e_{i}) |
||

A |
0.8 | 10 | % | 25 | % |

B |
1.0 | 12 | 10 | ||

C |
1.2 | 14 | 20 | ||

**a.** If *σ _{M}* = 20%, calculate
the variance of returns of securities

**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.)**

Answer #1

Calculation is given in the below attached image

Please give upvote and and thank you for that in advance

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
0.6
7
%
16
%
B
0.9
10
7
C
1.2
13
10
If σM = 10%, calculate the variance of...

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
0.8
15
%
24
%
B
1.1
18
15
C
1.4
21
18
a. If σM = 20%, calculate
the variance...

Consider the two empirical models for excess returns (Ri-Rf) of
stocks A and B. The risk free rate (Rf) over the period was 6%, and
the market’s average return (Rm) was 14%.
Stock A
Stock B
Estimated market models
Ri-Rf= 1% + 1.2(Rm – Rf)
Ri-Rf = 2% + 0.8(Rm – Rf)
Standard deviation of excess returns
21.6%
24.9%
Find the following for each stock:
Alpha
Sharpe ratio
Treynor ratio
b) Based on your answers to part a), which stock...

Suppose that the index model for stocks A and B is estimated
from excess returns with the following results:
RA = 3.6% + 1.20RM + eA RB = –1.6% + 1.5RM + eB σM = 16%;
R-squareA = 0.25; R-squareB = 0.15
Break down the variance of each stock to the systematic and
firm-specific components. (Do not round intermediate calculations.
Calculate using numbers in decimal form, not percentages. Round
your answers to 4 decimal places.)

Suppose that the index model for stocks A and
B is estimated from excess returns with the following
results:
RA = 4.5% + 1.40RM +
eA
RB = –2.2% + 1.7RM +
eB
σM = 24%;
R-squareA = 0.30;
R-squareB = 0.20
Break down the variance of each stock to the systematic and
firm-specific components. (Do not round intermediate
calculations. Calculate using numbers in decimal
form, not percentages. Round your answers to 4
decimal places.)
Risk A
Risk B
Systematic...

Suppose that the index model for stocks A and
B is estimated from excess returns with the following
results:
RA = 5.0% + 1.30RM +
eA
RB = –2.0% + 1.6RM +
eB
σM = 20%;
R-squareA = 0.20;
R-squareB = 0.12
What is the standard deviation of each stock? (Do not round
intermediate calculations. Round your answers to 2 decimal
places.)
=

Suppose that the index model for stocks A and B is estimated
from excess returns with the following results:
RA = 5.0% + 1.30RM + eA
RB = –2.0% + 1.6RM + eB
σM = 20%; R-squareA = 0.20; R-squareB = 0.12
What is the standard deviation of each stock? (Do not round
intermediate calculations. Round your answers to 2 decimal
places.)
Stock A:
Stock B:

Suppose that the index model for stocks A and
B is estimated from excess returns with the following
results:
RA = 4.0% + 0.50RM +
eA
RB = –1.2% + 0.70RM +
eB
σM = 17%;
R-squareA = 0.26;
R-squareB = 0.18
What are the covariance and correlation coefficient between the
two stocks? (Do not round intermediate calculations.
Calculate using numbers in decimal form, not percentages. Round
your answers to 4 decimal places.)
Covariance:
Correlation coefficient:

Suppose that the index model for stocks A and
B is estimated from excess returns with the following
results:
RA = 2.0% + 0.40RM +
eA
RB = -1.8% + 0.9RM +
eB
σM = 15%;
R-squareA = 0.30;
R-squareB = 0.22
What is the covariance between each stock and the market index?
(Calculate using numbers in decimal form,
not percentages. Do not round your intermediate
calculations. Round your answers to 3 decimal places.)
Covariance
Stock A
Stock B

Suppose that the index model for stocks A and
B is estimated from excess returns with the following
results:
RA = 3.6% + 1.20RM +
eA
RB = -1.6% + 1.50RM +
eB
σM = 16%;
R-squareA = 0.25;
R-squareB = 0.15
What is the covariance between each stock and the market index?
(Calculate using numbers in decimal form,
not percentages. Do not round your intermediate
calculations. Round your answers to 3 decimal places.)
Covariance
Stock A
Stock B

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