5. (30 points) A financial market consisting of 4 risky assets and a risk-free asset satisfies...

 

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5. (30 points) A financial market consisting of 4 risky assets and a risk-free asset satisfies the CAPM exactly. The expected rates of return and the covariance matrix of the risky assets are given respectively by T = 1 1 0 0 1 3 1 and = 0 2 1 0 1 1 4 (1) A fund seeks the minimum-variance portfolio that consists only of assets 2 and 3. Find the range of values of a for which this portfolio does not require short-selling. It is given further that -1 = 35/3 and -e = (2/3, 1/3,2/3,0). (2) Find the exact value of a. (3) An economist seeks the minimum-variance portfolio whose weight vector wis of the form (B, B, Y, B). Find the exact values of and Y. (4) Find the equation of the minimum-variance frontier of risky assets, giving your answer in the form o = A(zzg)+02, where A is a constant, (, z) is any point on the frontier and (g; g) is the point corresponding to the global minimum-variance portfolio of risky assets. (5) The equation of the Capital Market Line is given by z = /52/50 + 1/5. Write down the value of risk-free rate r and find the mean rate of return of the tangent portfolio. 5. (30 points) A financial market consisting of 4 risky assets and a risk-free asset satisfies the CAPM exactly. The expected rates of return and the covariance matrix of the risky assets are given respectively by T = 1 1 0 0 1 3 1 and = 0 2 1 0 1 1 4 (1) A fund seeks the minimum-variance portfolio that consists only of assets 2 and 3. Find the range of values of a for which this portfolio does not require short-selling. It is given further that -1 = 35/3 and -e = (2/3, 1/3,2/3,0). (2) Find the exact value of a. (3) An economist seeks the minimum-variance portfolio whose weight vector wis of the form (B, B, Y, B). Find the exact values of and Y. (4) Find the equation of the minimum-variance frontier of risky assets, giving your answer in the form o = A(zzg)+02, where A is a constant, (, z) is any point on the frontier and (g; g) is the point corresponding to the global minimum-variance portfolio of risky assets. (5) The equation of the Capital Market Line is given by z = /52/50 + 1/5. Write down the value of risk-free rate r and find the mean rate of return of the tangent portfolio.