5.7 Given two random variables x and y: Probability of State of Nature State of Nature Variable x Variable y 22222 I 18 0 II 5 -3 III 12 15 IV 4 12 V 6 1 (a) Calculate the mean and variance of each of these variables, and the covariance between them. (b) Suppose x and y represent the returns from two assets. Calculate the mean and variance for the following portfolios: % in x 125 % in y -25 100 75 50 25 0 -25 0 25 50 75 100 125 (c) Find the portfolio that has the minimum variance. (d) Let portfolio A have 75% in x and portfolio B have 25% in x. Calculate the covariance between the two portfolios. (e) Calculate the covariance between the minimum variance portfolio and portfolio A, and the covariance between the minimum variance portfolio and portfolio B.
5.7 Given two random variables x and y: Probability of State of Nature State of Nature Variable x Variable y 22222 I 18 0 II 5 -3 III 12 15 IV 4 12 V 6 1 (a) Calculate the mean and variance of each of these variables, and the covariance between them. (b) Suppose x and y represent the returns from two assets. Calculate the mean and variance for the following portfolios: % in x 125 % in y -25 100 75 50 25 0 -25 0 25 50 75 100 125 (c) Find the portfolio that has the minimum variance. (d) Let portfolio A have 75% in x and portfolio B have 25% in x. Calculate the covariance between the two portfolios. (e) Calculate the covariance between the minimum variance portfolio and portfolio A, and the covariance between the minimum variance portfolio and portfolio B.
Chapter2: Mathematics For Microeconomics
Section: Chapter Questions
Problem 2.16P
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Strictly Note ->( Provide solution for the last two parts [d and e])
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Transcribed Image Text:5.7 Given two random variables x and y:
Probability of State
of Nature
State of
Nature Variable x Variable y
22222
I
18
0
II
5
-3
III
12
15
IV
4
12
V
6
1
(a) Calculate the mean and variance of each of these variables, and the covariance between
them.
(b) Suppose x and y represent the returns from two assets. Calculate the mean and variance
for the following portfolios:
% in x
125
% in y
-25
100 75 50 25 0 -25
0 25 50 75 100 125
(c) Find the portfolio that has the minimum variance.
(d) Let portfolio A have 75% in x and portfolio B have 25% in x. Calculate the covariance
between the two portfolios.
(e) Calculate the covariance between the minimum variance portfolio and portfolio A, and
the covariance between the minimum variance portfolio and portfolio B.
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