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5. There are three risky assets with rates of return $r_1$, $r_2$, and $r_3$, respectively. The covariance matrix and the expected rates of return are $\Sigma = \begin{bmatrix} 0.4 & 0.2 & 0\\ 0.2 & 0.4 & 0.2\\ 0 & 0.2 & 0.4 \end{bmatrix}$, $\bar{r} = \begin{bmatrix} 0.04\\ 0.08\\ 0.06 \end{bmatrix}$. (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 $r_f = 0.03$. (c) Find the tangent portfolio.

          5. There are three risky assets with rates of return $r_1$, $r_2$, and $r_3$, respectively. The covariance matrix and the expected rates of return are
$\Sigma = \begin{bmatrix} 0.4 & 0.2 & 0\\ 0.2 & 0.4 & 0.2\\ 0 & 0.2 & 0.4 \end{bmatrix}$, $\bar{r} = \begin{bmatrix} 0.04\\ 0.08\\ 0.06 \end{bmatrix}$.
(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 $r_f = 0.03$.
(c) Find the tangent portfolio.

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5. There are three risky assets with rates of return r1, r2, and r3, respectively. The covariance matrix and the expected rates of return are
Σ =
< b m a t r i x >, r̅ =
< b m a t r i x >.
(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.

Added by Philip W.

Horngren’s Cost Accounting

Srikant M. Datar, Madhav V. Rajan 16th Edition

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Solved by Expert Sri K

01/16/2023

Step 1

To find the global minimum-variance portfolio, we need to calculate the weights of the risky assets that minimize the portfolio variance. Let w1, w2, and w3 be the weights of the risky assets r1, r2, and r3, respectively. The portfolio variance can be Show more…

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Please make sure your answer is correct! Please do not copy other wrong answers 5. There are three risky assets with rates of return r1, r2, and r3, respectively. The covariance matrix and the expected rates of return are 0.40.2 0 >= 0.20.40.2 0 0.2 0.4 [0.04] r= 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 Tf = 0.03. (c) Find the tangent portfolio.

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