VaR = 98% 2): Value of portfolio is $120 million today. A Bank invests inæ1 amount in asset with return N(0:1; 0:1), x2 amount in asset with returnN(0:12; 0:2), x3 amount in asset with return N(0:13; 0:3),Covariance matrix ofthe portfolio ;[0.10.0S = | 00.2 0-0.0 0- 0.3i) Determine x1 , 2zand x3 such that Vport [x] becomes minimum. a)Eport=? , b) V port=? ,Calculate VaR for 9R%, and c) 4 days d) 8 days d)5 weeks time horizons

Given a portfolio which consists of two assets. The returns of the assets are normally distributed…

Answered: 2): Value of portfolio is $120 million…

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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= data instances given by x₁ = (20,5), x₂ - (8, -2) and xy = (6₁4) Compute the covariance matrix dataset. 1] A dataset has four > x3 = (-6, -3) of this 1
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.
Define Covariance matrix.
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.
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Let A € Rmxn, B € Rmxp be any matrix. Solve the following problem _min_ ||AX – B||2/17. XERnxp Hint: Write X = [X₁,..., Xp] and B = [b₁,..., bp]. Then AX – B = [Ax₁ – b₁,..., Axp – bp]. Use this to reduce the prob- lem accordingly.
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Construct a model of population flow between metropolitan and nonmetropolitan areas of the United States, given that their respective populations in 2012 were 255 million and 52 million. The probabilities are given by the matrix (from) (to) metro nonmetro [0.99 [0.01 0.02] metro 0.98 nonmetro Predict the population distributions of metropolitan and nonmetropolitan areas for the years 2013 through 2015 (in millions, to four decimal places). If a person was living in a metropolitan area in 2012, what is the probability that the person will still be living in a metropolitan area in 2015?
2. We have two random variables representing returns on two assets: X₁ and X₂. They have the following covariance matrix: Ex = 0.01 -0.01 -0.01 0.04 Now we create three new portfolios with the following returns: Y₁ = 0.25X₁ +0.75X₂ Y₂ = 0.5X₁ +0.5X₂ Y3 = aX₁ + (1 − a) X₂ a. 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. If you do that, include your code in the solution.
4. A real estate agent has the data on the housing prices (X₁, in millions of pesos), the number of bedrooms in the house (X₂), and the size of the house (X3, in thousands of square feet) of the 88 properties he sold. Suppose that X~N3(µ,Σ), and the mean [1.5] vector and covariance matrix are μ = [1.3 2.1 4.01 and Σ = |2.1 5.0 2.3, respectively. L4.0 2.3 2.0] 12.4 Suppose that he is interested in 0.002X₂ + 0.123X3, determine the distribution of this linear combination.
Can you show that Q is an intensity matrix?

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