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…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 47E: Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.

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Consider a set of three assets, one risk-free and two risky. The covariance matrix [0.36 0.07] for the risky assets is given by = 0.07 The risk-free rate is 0.03 0.07 0.29 and risk aversion is A = 4. Calculate the optimal portfolio for this individual.
The index model has been estimated for stocks A and B with the following results: RA = 0.03 + 0.8RM + eA. RB = 0.01 + 0.9RM + eB. σM = 0.35; σ(eA) = 0.20; σ(eB) = 0.10. The covariance between the returns on stocks A and B is A) 0384. B) 0.0406. C) 0.0882. D) 0.0772. E) 0.4000. 2) Analysts may use regression analysis to estimate the index model for a stock. When doing so, the slope of the regression line is an estimate of A) the α of the asset. B) the β of the asset. C) the σ of the asset. D) the δ of the asset. Choose correct answer with justification.
1. Generate random 100 MVN data, p=20. The covariance matrix should be positive semi- definite symmetric matrix. (1) Show the generated data matrix. (2) Plot the scatter plot to show the correlation among variables.
A person is interested in constructing a portfolio. Two stocks are being considered. Let x= percent return for an investment in stock 1 and y = percent return for an investment in stock 2. The expected return and variance for stock 1 are E[x] = 8.45% and Var[x) = 25. The expected return and variance for stock 2 are E[Y] = 3.2% and Var(y) = 1. The covariance between the returns is σXY = -3. (Hint: in this problem all numbers must be altered. Change from percentages to real numbers. So, 8.45 would be 0.0845 and Var(x) = 25 would be Var(x) = 0.25, etc.) Show Steps in Excel What is the expected percent return and standard deviation for a person who constructs a portfolio by investing 70% in stock 1 and 30% in stock 2? Compute the correlation coefficient for x and y and comment on the relationship between the returns for the two stocks.
A person is interested in constructing a portfolio. Two stocks are being considered. Let x= percent return for an investment in stock 1 and y = percent return for an investment in stock 2. The expected return and variance for stock 1 are E[x] = 8.45% and Var[x) = 25. The expected return and variance for stock 2 are E[Y] = 3.2% and Var(y) = 1. The covariance between the returns is σXY = -3. (Hint: in this problem all numbers must be altered. Change from percentages to real numbers. So, 8.45 would be 0.0845 and Var(x) = 25 would be Var(x) = 0.25, etc.) Show Steps in Excel a What is the standard deviation for the investment in stock 1 and for the investment in stock 2? Using the standard deviation as a measure of risk, which of these stocks is the riskier investment? b What is the expected return and standard deviation, in dollars, for a person who invests $500 in stock 1? c What is the expected percent return and standard deviation for a person who constructs a portfolio by investing…
Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =-0.03+2.10RM+eHD R-squared =0.7 RML =0.06+1.60RM+eML R-squared =0.6 σM =0.15 where M is S&P/TSX Comp Index and RX is the excess return of stock X. What is the covariance and the correlation coefficient between HD and ML?
Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =-0.03+2.10RM+eHD R-squared =0.7 RML =0.06+1.60RM+eML R-squared =0.6 σM =0.15 where M is S&P/TSX Comp Index and RX is the excess return of stock X. What is the covariance and the correlation coefficient between HD and ML? For portfolio P with investment proportion of 0.4 in HD and 0.6 in ML, calculate the systematic risk, non-systematic risk, and total risk of P.

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