Question
In: Finance
state of the economy probability of occurrence expected return on stock A expected return on stock...
| state of the economy | probability of occurrence | expected return on stock A | expected return on stock B |
| High growth | 0.1 | 60% | 5% |
| Moderate growth | 0.2 | 20% | 20% |
| No growth | 0.5 | 10% | 5% |
| Recession | 0.2 | -25% | 0% |
1)Calculate the weighted average of the standard deviation
of individual stocks A and B ; and show that each portfolio
standard deviation is less than this weighted average except the
portfolio standard deviation with correlation of 1.
2) Given correlation of -1, what portfolio weights will reduce the portfolio standard deviation to zero? Show calculations to support your answer.
Solutions
jeff jeffy answered 2 years agoRelated Solutions
State of Economy Probability of State of Economy Return of Stock A if State Occurs Return...
State of Economy
Probability of State of Economy
Return of Stock A if State Occurs
Return of Stock B if State Occurs
Recession
0.30
-0.20
0.10
Normal
?
0.30
0.20
Boom
0.15
0.40
0.30
What is the expected return for Stock A?
What is the standard deviation for Stock A?
Suppose you have $50,000 total. If you put $20,000 in Stock A
and the remainder in Stock B, what are the portfolio returns in
each state?
Suppose you have $50,000...
State of Economy Probability of State of Economy Return of Stock A if State Occurs Return...
State of Economy
Probability of State of Economy
Return of Stock A if State Occurs
Return of Stock B if State Occurs
Recession
0.20
-0.20
0.05
Normal
?
0.20
0.22
Boom
0.25
0.30
0.25
What is the expected return for Stock A?
What is the standard deviation for Stock A?
Suppose you have $50,000 total. If you put $10,000 in Stock A
and the remainder in Stock B, what are the portfolio returns in
each state?
Suppose you have $50,000...
State of Economy Probability of State of Economy Return on Stock J Return on stock K...
State of Economy
Probability of State of Economy
Return on Stock J
Return on stock K
Bear
.23
-.013
.041
Normal
.58
.145
.069
Bull
.19
.225
.099
What is the Convariance and Correlation between
the returns of the 2 stocks?
Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A...
Rate of Return if State Occurs State of Economy Probability of
State of Economy Stock A Stock B Recession .25 .03 −.15 Normal .55
.13 .13 Boom .20 .16 .33 a. Calculate the expected return for the
two stocks. (Do not round intermediate calculations. Enter your
answers as a percent rounded to 2 decimal places.) b. Calculate the
standard deviation for the two stocks. (Do not round your
intermediate calculations. Enter your answers as a percent rounded
to 2 decimal...
Rate of return if state occurs State of economy Probability of state of economy Stock A...
Rate of return if state occurs
State of economy
Probability of state of economy
Stock A
Stock B
Stock C
Boom
0.3
0.35
0.45
0.38
Good
0.3
0.15
0.20
0.12
Poor
0.3
0.05
–0.10
–0.05
Bust
0.1
0.00
–0.30
–0.10
5. Consider the
following information on three stocks in four possible future
states of the economy:
Your portfolio is invested 30% in A, 50% in B, and 20% in C.
What is the expected return of your portfolio?
What...
Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A...
Rate of Return if State Occurs
State of Economy
Probability of
State of Economy
Stock A
Stock B
Stock C
Boom
0.70
0.25
0.19
0.09
Bust
0.30
0.09
0.09
0.03
a. What is the expected return on an equally
weighted portfolio of these three stocks?
b. What is the variance of a portfolio invested
30 percent each in A and B and 40 percent in C?
Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A...
Rate of Return If State Occurs
State of
Probability of
Economy
State of Economy
Stock A
Stock B
Stock C
Boom
.15
.39
.49
.29
Good
.55
.15
.20
.08
Poor
.25
−.01
−.09
−.07
Bust
.05
−.20
−.24
−.10
a.
Your portfolio is invested 24 percent each in A and C, and 52
percent in B. What is the expected return of the portfolio?
(Do not round intermediate calculations and enter your
answer as a percent rounded to...
Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A...
Rate of Return if State Occurs
State of Economy
Probability of State of Economy
Stock A
Stock B
Stock C
Boom
.25
.19
.35
.28
Good
.30
.14
.13
.14
Poor
.10
.00
−.10
−.05
Bust
.35
−.20
−.28
−.13
a. Your portfolio is invested 35 percent each
in Stocks A and C and 30 percent in Stock B. What is the expected
return of the portfolio? (Do not round intermediate
calculations. Enter your answer as a percent rounded to...
Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A...
Rate of Return If State Occurs
State of
Probability of
Economy
State of Economy
Stock A
Stock B
Stock C
Boom
.25
.21
.33
.55
Normal
.60
.17
.11
.09
Bust
.15
.00
−
.21
−
.45
a-1.
If your portfolio is invested 40 percent each in A and B and 20
percent in C, what is the portfolio expected return? (Do
not round intermediate calculations and enter your answer as a
percent rounded to 2 decimal places, e.g.,...
Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A...
Rate of Return if State Occurs
State of Economy
Probability of
State of Economy
Stock A
Stock B
Stock C
Boom
0.76
0.29
0.33
0.31
Bust
0.24
0.15
0.11
0.09
Requirement 1:
What is the expected return on an equally weighted portfolio of
these three stocks? (Do not round your intermediate
calculations.)
26.36%
28.86%
38.39%
41.16%
20.63%
Requirement 2:
What is the variance of a portfolio invested 20 percent each in
A and B and 60 percent in...
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