Question
In: Finance
Given the returns and probabilities for the three possiblestates listed here, calculate the covariance between...
Given the returns and probabilities for the three possible states listed here, calculate the covariance between the returns of Stock A and Stock B. For convenience, assume that the expected returns of Stock A and Stock B are 0.12 and 0.15, respectively. (Round your answer to 4 decimal places. For example .1244) Probability Return(A) Return(B) Good 0.35 0.30 0.50 OK 0.50 0.10 0.10 Poor 0.15 -0.25 -0.30
Solutions
Expert Solution
Covariance :
Covariance is a statistical tool that is used to determine the relationship between the movement of two assets/ Stocks.
If Past data is given:
Assume stock A = X
stock B = Y
Covariance = Sum [ prob * (X-Avg X)(Y-Avg Y) ]
Expected Ret:
| Scenario | Prob | Ret (X) | Prob* Ret(X) | Ret (Y) | Prob* Ret(Y) |
| Good | 0.3500 | 30.00% | 10.50% | 50% | 17.50% |
| OK | 0.5000 | 10.00% | 5.00% | 10% | 5.00% |
| Poor | 0.1500 | -25.00% | -3.75% | -30% | -4.50% |
| Expected Ret | 11.75% | 18.00% |
Covaraince:
| Scenario | Prob | Ret (X) | (X-AvgX) | Ret (Y) | (Y-AvgY) | (X-AVgX)(Y-AvgY) | Prob* (X-AVgX)(Y-AvgY) |
| Good | 0.3500 | 30.00% | 18.25% | 50.00% | 32.00% | 0.0584 | 0.02044 |
| OK | 0.5000 | 10.00% | -1.75% | 10.00% | -8.00% | 0.0014 | 0.00070 |
| Poor | 0.1500 | -25.00% | -36.75% | -30.00% | -48.00% | 0.1764 | 0.02646 |
| Covariance = Sum [Prob * (X-AvgX)(Y-AvgY) ] | 0.04760 |
jeff jeffy answered 2 years agoRelated Solutions
Given the returns and probabilities for the three possible states listed here, calculate the covariance between...
Given the returns and probabilities for the three possible
states listed here, calculate the covariance between the returns of
Stock A and Stock B. For convenience, assume that the expected
returns of Stock A and Stock B are 0.11 and 0.15, respectively.
(Round your answer to 4 decimal places. For example .1244)
Probability
Return(A)
Return(B)
Good
0.35
0.30
0.50
OK
0.50
0.10
0.10
Poor
0.15
-0.25
-0.30
Given the returns and probabilities for the three possible states listed here, calculate the covariance between...
Given the returns and probabilities for the three possible
states listed here, calculate the covariance between the returns of
Stock A and Stock B. For convenience, assume that the expected
returns of Stock A and Stock B are 0.09 and 0.16, respectively.
(Round your answer to 4 decimal places. For example .1244)
Probability
Return(A)
Return(B)
Good
0.35
0.30
0.50
OK
0.50
0.10
0.10
Poor
0.15
-0.25
-0.30
Given the returns and probabilities for the three possible states listed below, calculate the covariance between...
Given the returns and probabilities for the three possible
states listed below, calculate the covariance between the returns
of Stock A and Stock B. For convenience, assume that the expected
returns of Stock A and Stock B are 11.75 percent and 18 percent,
respectively. Probability Return on Stock A Return on Stock B Good
0.35 0.30 0.50 OK 0.50 0.10 0.10 Poor 0.15 −0.25 −0.30
Given the returns and probabilities for the three possible states listed below, calculate the covariance between...
Given the returns and probabilities for the three possible
states listed below, calculate the covariance between the returns
of Stock A and Stock B. For convenience, assume that the expected
returns of Stock A and Stock B are 10.00 percent and 16.00 percent,
respectively. (Round answer to 4 decimal places, e.g. 0.0768.)
Probability Return on Stock A Return on Stock B Good 0.35 0.30 0.50
OK 0.45 0.10 0.10 Poor 0.20 -0.25 -0.30 Covariance
Consider three scenarios with the probabilities given below. Let the returns on two different stocks in...
Consider three scenarios with the probabilities given below. Let
the returns on two different stocks in these scenarios be as
follows: Scenario Probability return K1 return K2 ω1 0.2 −10% −30%
ω2 0.5 0% 20% ω3 0.3 10% 50% If a portfolio has 60% of funds
invested in stock 1 and 40% of funds invested in stock 2, find the
risk σV for this portfolio. (Need explanation not just
spreadsheet)
Explain Key Statistical Relationships between Covariance and Correlation of Returns
Explain Key Statistical Relationships between Covariance and
Correlation of Returns
2. Two stocks A and B have expected returns, and a variance-covariance matrix of returns given...
2. Two stocks A and B have expected returns, and a
variance-covariance matrix of returns given in Table 1.
Table 1 Stock A
Stock B
E(R)
0.14
0.08
Variance-covariance matrix:
Stock A
Stock B
Stock A
0.04
0.012
Stock B
0.012
0.0225
a) What is the correlation coefficient between the returns on
stock A and stock B?
b) What is the expected return and standard deviation of
portfolio S which is invested 80% in stock A and 20% in
stock...
Based on the following information determine the covariance and correlation between the returns of the two...
Based on the following information determine the covariance and
correlation between the returns of the two stocks.
State of Economy
Probability of State of Economy
Return of X
Return of Y
Bear
0.10
-0.02
0.034
Normal
0.65
0.138
0.062
Bull
0.25
0.218
0.092
1. Calculate the covariance between profits and market capitalization and what does the covariance indicate about...
1. Calculate the covariance between profits and market
capitalization and what does the covariance indicate about the
relationship between profits and market capitalization? (positive
or negative).
2. Calculate the correlation coefficient between profits and
market capitalization and what does this indicate about the
relationship between profits and market capitalization?
(strong/weak/non-linear relationship) .
Company
Profits ($ millions)
Market Capitalization ($ millions)
Alliant Techsystems
313.20
1891.90
Amazon.com
631.00
81458.60
AmerisourceBergen
706.60
10087.60
Avis Budget Group
-29.00
1175.80
Boeing
4018.00
55188.80
Cardinal Health...
Calculate the covariance between variables X and Y. Is it a positive or negative relationship between...
Calculate the covariance between variables X and Y. Is it a
positive or negative relationship between the two variables?
b. Calculate correlation coefficient between X and Y. Is it a
positive or negative relationship? Is it a strong linear, weak
linear or nonlinear relationship between X and Y?
c. Use the Y data to calculate mean, range, standard deviation
and variance.
d. Use the first Y value to calculate the Z-score. Is it an
outlier?
e. Calculate the 60th percentile...
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