7) COVARIANCE AND CORRELATION COEFFICIENT. What is covariance?
How is covariance and correlation coefficients linked? How does the
concept of covariance link to the Timura depiction of an efficient
frontier oriented “silver bullet” In addition, draw a graphic that
explains your thinking using real estate, international, private
equity, venture capital, etc.
Explain the importance of covariance and correlation between
assets and understanding the expected value, variance, and standard
deviation of a random variable and of returns on a portfolio.
6. Measures of linear relationship - Covariance and
coefficient of correlation
Consider a data set consisting of observations for three
variables: x, y, and z. Their sample means, variances, and standard
deviations are shown in Table 1.
Table 1
Sample Mean
x̄ x̄ = 4
ȳ ȳ = 5
z̄ z̄ = 5
Sample Variance
sx2sx2 = 4
sy2sy2 = 3
sz2sz2 = 9
Sample Standard Deviation
sxsx = 2
sysy = 1.732
szsz = 3
Table 2 shows the...
Calculate the covariance and correlation coefficients by
completing the below table, assuming sample data. Show all
workings. (Note: You can calculate the mean and standard deviation
of X & Y with Excel or your calculator; no working for their
calculation is required.)
X
Y
(X - X bar)
(Y - Y bar)
(X - X bar)(Y - Y bar)
5
5
2
3
5
4
8
7
6
9
(b) Comment on the
direction and strength of the association between X...
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
Determine the value of c and the covariance and
correlation for the joint probability mass function
f(x, y) = c(x +
y) for x = 1, 2, 3 and y = 1, 2, 3.