Question
In: Finance
Consider the following situation: State of Economy Probability of State of Economy Returns if State Occurs...
Consider the following situation:
|
State of Economy |
Probability of State of Economy |
Returns if State Occurs |
||
|
Stock A |
Stock B |
Stock C |
||
|
Boom |
20% |
25% |
10% |
5% |
|
Recession |
80% |
-30% |
5% |
10% |
The expected return on the market portfolio is 7% and the US Treasury bill yields 3%. The capital market is currently in equilibrium.
Show your work. Do not use excel.
- (5 points) Which stock has the most systematic risk? Provide all the steps and equations.
- (5 points) Which stock has the most unsystematic risk? Explain why. Provide all the steps and equations.
- (10 points) What is the standard deviation of a portfolio which is comprised of $8,400 invested in stock A, $3,600 in stock B, and $8,000 in stock C?
- (5 points) If the expected inflation rate is 2.5%, what is the exact expected real return on the portfolio of part (c)?
Solutions
Expert Solution
| a) Systematic Risk = Beta | |||||||
| Returns if State Occurs | Expected Return | ||||||
| State of Economy | Probability of State of Economy | Stock A | Stock B | Stock C | Prob. x Stock A 's Return | Prob. x Stock A 's Return | Prob. x Stock A 's Return |
| Boom | 20.00% | 25.00% | 10.00% | 5.00% | 5.00% | 2.00% | 1.00% |
| Recession | 80.00% | -30.00% | 5.00% | 10.00% | -24.00% | 4.00% | 8.00% |
| Total | -19.00% | 6.00% | 9.00% | ||||
| According CAPM Expected Return E(R)= Risk free Rate + Beta x (Market Return - Risk free Rate) | |||||||
| Risk Free Rate RF = | 3.00% | ||||||
| Return on market RM | 7.00% | ||||||
| Stock A 's Beta = -19% - 3% = Beta x (7% -3%) | -5.5 | ||||||
| Stock B 's Beta = 6% - 3% = Beta x (7% -3%) | 0.75 | ||||||
| Stock C 's Beta = 9% - 3% = Beta x (7% -3%) | 1.5 | ||||||
| Stock C has the most systematic risk because it has the highest beta. | |||||||
| b) | |||||||
| Stock A has the most unsystematic risk because it has the negative Beta. |
jeff jeffy answered 8 months agoRelated Solutions
Consider the following situation: State of Economy Probability of State of Economy Returns if State Occurs...
Consider the following situation:
State of Economy
Probability of State of Economy
Returns if State Occurs
Stock A
Stock B
Stock C
Boom
20%
25%
10%
5%
Recession
80%
-30%
5%
10%
The expected return on the market
portfolio is 7% and the US Treasury bill yields 3%. The capital
market is currently in equilibrium.
Which stock has the most systematic risk? Provide all the steps
and equations.
Which stock has the most unsystematic risk? Explain why.
Provide all the...
Consider the following situation: State of Economy Probability of State of Economy Returns if State Occurs...
Consider the following situation:
State of Economy
Probability of State of Economy
Returns if State Occurs
Stock A
Stock B
Stock C
Boom
20%
25%
10%
5%
Recession
80%
-30%
5%
10%
The expected return on the market
portfolio is 7% and the US Treasury bill yields 3%. The capital
market is currently in equilibrium.
(5 points) Which stock has the most systematic risk? Provide
all the steps and equations.
(5 points) Which stock has the most unsystematic risk? Explain...
Consider the following situation: State of Economy Probability of State of Economy Returns if State Occurs...
Consider the following situation: State of Economy Probability
of State of Economy Returns if State Occurs Stock A Stock B Stock C
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on the market portfolio is 7% and the US Treasury bill yields 3%.
The capital market is currently in equilibrium.
(a) (5 points) Which stock has the most systematic risk? Provide
all the steps and equations.
(b) (5 points) Which stock has the most unsystematic...
) Consider the following situation: State of Economy Probability of State of Economy Returns if State...
) Consider the following situation:
State of Economy
Probability of State of Economy
Returns if State Occurs
Stock A
Stock B
Stock C
Boom
20%
25%
10%
5%
Recession
80%
-30%
5%
10%
The expected return on the market
portfolio is 7% and the US Treasury bill yields 3%. The capital
market is currently in equilibrium.
(5 points) Which stock has the most systematic risk? Provide
all the steps and equations.
(5 points) Which stock has the most unsystematic risk?...
Security Returns if State Occurs State of Economy Probability of State of Economy Roll Ross Bust...
Security Returns if State Occurs
State of Economy
Probability of State of Economy
Roll
Ross
Bust
0.40
−10
%
21
%
Boom
0.60
28
8
Calculate the expected return on a portfolio of 55 percent Roll
and 45 percent Ross by filling in the following table: (A
negative value should be indicated by a minus sign. Do not round
intermediate calculations. Enter your answers as a percent rounded
to 2 decimal places.)
Consider the following information: Rate of Return If State Occurs State of Probability of Economy...
Consider the following information:
Rate of Return If State Occurs
State of
Probability of
Economy
State of Economy
Stock A
Stock B
Stock C
Boom
.75
.08
.17
.24
Bust
.25
.11
−
.05
−
.08
a.
What is the expected return on an equally weighted portfolio of
these three stocks? (Do not round intermediate calculations
and enter your answer as a percent rounded to 2 decimal places,
e.g., 32.16.)
b.
What is the variance of a portfolio...
Consider the following information: Rate of Return if State Occurs State of Economy Probability of...
Consider the following information:
Rate of Return if State Occurs
State of Economy
Probability of
State of Economy
Stock A
Stock B
Stock C
Boom
0.76
0.23
0.21
0.31
Bust
0.24
0.09
0.15
0.07
a. What is the expected return on an equally
weighted portfolio of these three stocks?
b. What is the variance of a portfolio invested
10 percent each in A and B and 80 percent in C?
Consider the following information: Rate of Return if State Occurs State of Economy Probability of...
Consider the following
information:
Rate of Return if State Occurs
State of Economy
Probability
of
State of Economy
Stock A
Stock B
Stock C
Boom
0.62
0.07
0.27
0.17
Bust
0.38
0.17
0.15
0.01
Requirement
1:
What is the expected return on an equally weighted portfolio of
these three stocks? (Do not round your intermediate
calculations.)
14.72% 17.22% 26.75% 29.52% 8.99%
Requirement
2:
What is the variance of a portfolio invested 30 percent each in
A and...
Consider the following information: Rate of Return If State Occurs State of Probability of Economy...
Consider the following information:
Rate of Return If State Occurs
State of Probability of
Economy State of Economy Stock A Stock B
Recession .22 .10 ? .17
Normal .52 .13 .12
Boom .26 .18 .29
Calculate the expected return for each stock. (Do not round
intermediate calculations. Enter your answers as a percent rounded
to 2 decimal places, e.g., 32.16.)
Expected return
Stock A %
Stock B %
Calculate the standard deviation for each stock. (Do...
Consider the following information: Rate of Return If State Occurs State of Probability of Economy...
Consider the following information:
Rate of Return If State Occurs
State of Probability of
Economy State of Economy Stock A Stock B Stock C
Boom .65 .11 .19 .37
Bust .35 .12 .06 ?.05
a.
What is the expected return on an equally weighted portfolio
of these three stocks? (Do not round intermediate calculations.
Enter your answer as a percent rounded to 2 decimal places, e.g.,
32.16.)
Expected return %
b.
What is the variance of a portfolio...
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