There are three risky assets with rates of return r, 72, and r3, respectively. The covariance...

 

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There are three risky assets with rates of return r₁, 72, and r3, respectively. The covariance matrix and the expected rates of return are Σ= 0.4 0.2 0 0.2 0.4 0.2 0 0.2 0.4 2 r = [0.04] 0.08 0.06 (a) Find the global minimum-variance portfolio. (b) For the required return z = 0.075, find (the weight of) the optimal portfolio with risky assets. For (c) and (d) only, assume there is an additional risk-free asset with return rf = 0.03. (c) Find the tangent portfolio. (d) For the required returi z = 0.075, find the optimal rtfolio with both risk-free and risky assets. [Hint: Recall that to calculate x = -¹r, one can either calculate -¹ and do the matrix multiplication, or solve the linear system Ex = = r.] There are three risky assets with rates of return r₁, 72, and r3, respectively. The covariance matrix and the expected rates of return are Σ= 0.4 0.2 0 0.2 0.4 0.2 0 0.2 0.4 2 r = [0.04] 0.08 0.06 (a) Find the global minimum-variance portfolio. (b) For the required return z = 0.075, find (the weight of) the optimal portfolio with risky assets. For (c) and (d) only, assume there is an additional risk-free asset with return rf = 0.03. (c) Find the tangent portfolio. (d) For the required returi z = 0.075, find the optimal rtfolio with both risk-free and risky assets. [Hint: Recall that to calculate x = -¹r, one can either calculate -¹ and do the matrix multiplication, or solve the linear system Ex = = r.]

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To solve the given portfolio optimization problem we can follow these steps Step 1 Calculate the global minimumvariance portfolio Step 2 Calculate the tangent portfolio Step 3 Calculate the optimal po... View the full answer