2. We have two random variables representing returns on two assets: X₁ and X₂. They have the followingcovariance matrix:Ex=0.01 -0.01-0.01 0.04Now we create three new portfolios with the following returns:Y₁ = 0.25X₁ +0.75X₂Y₂ = 0.5X₁ +0.5X₂Y3 = aX₁ + (1 − a) X₂a. Find a such that Y₂ and Y3 are uncorrelated.b. Suppose a = 0.75. Find the correlation matrix of Y₁, Y₂ and Y3.Note: For b, you should set up the problem by hand but it is much easier to solve computationally. Ifyou do that, include your code in the solution.

Answered: Image /qna-images/answer/6ae9432a-9f8c-42e2-b5a2-50a6ed8bebce.jpg

Answered: 2. We have two random variables…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The matrix that projects onto the line y = -x is X 0.6 0.8 0.8 -0.6
Let X, Y, and Z be random variables, and let Cov(⋅,⋅) denote the covariance operator as usual. Suppose that the variance of X is 0.7, Cov(X,Y) = 0.4, Cov(X,Z) = 1.2, and Cov(Y,Z) = 0.8. Find each of the following to two decimal places. (a) Cov(3Y, 3X) (b) Cov(3Y + 3, 3X + 8Z)
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Suppose that the correlation coefficient ρ between two random variables has been found in an experiment to be zero. Which of the following is NOT TRUE?
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Find leng th of the Cardioid V-ag from e -oto0 - 1 %3D
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Sarah is conducting a correlation analysis. She creates a correlation matrix with 5 variables, using data from a sample of 37 people. What is Sarah's degrees of freedom for this test? Enter your answer as a whole number with no decimal places (i.e., 10, not 10.1, not 10.01).
2. Previously, you studied linear combinations of independent random variables. What happens if the variables are not independent? A lot of mathematics can be used to prove the following: Let x and y be random variables with means μx and μy, variances σ2x and σ2y, and population correlation coefficient ρ (the Greek letter rho). Let a and b be any constants and let w = ax + by for the following formula. μw = aμx + bμyσ2w = a2σ2x + b2σ2y + 2abσxσyρ In this formula, r is the population correlation coefficient, theoretically computed using the population of all (x, y) data pairs. The expression σxσyρ is called the covariance of x and y. If x and y are independent, then ρ = 0 and the formula for σ2w reduces to the appropriate formula for independent variables. In most real-world applications the population parameters are not known, so we use sample estimates with the understanding that our conclusions are also estimates.Do you have to be rich to invest in bonds and real estate? No, mutual…
I estimate a multiple linear regression model for portfolio using market size and value and adding as usual a constant ( to make sure that E(errors)=0 as per the GM assumptions request ). Then I wish to identify monthly effects so I generate a dummy for each month of the year , from January to December included . EViews will Select one: a. send out an error message saying : near singular matrix . This is happening because I fell into the dummy variable trap because the sum of all the dummy variables is at any point in time equal to 1 . As a consequence the OLS estimator is not identified b. send out an error message saying : near singular matrix . This is happening because I fell into the dummy variable trap because the costant (c) multiplies the regressor 1 and the sum of all the dummy variable is at any point in time equal to 1 . As a consequence the model is not identified and no estimator can estimate the betas c. send out an error message saying : near singular…
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