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4

If $\Sigma$ is the covariance matrix of all assets and $w$ is the column vector of weightings of the asset in a certain portfolio. Then $$w^T \Sigma w = VAR$$ is the variance of the portfolio. The contribution to volatility of asset $i$ is given by $$w_i (\Sigma w)_i/\sqrt{VAR},$$ where $(\Sigma w)_i$ is the $i_{th}$ entry in the vector $\Sigma w$. Note ...

2

The concrete (general) answer to part (ii) of my question seems to be contained in Equation 8 of the following link: http://www.columbia.edu/~ks20/FE-Notes/4700-07-Notes-portfolio-I.pdf In particular, interpreting $\sigma$ as volatility, take for example $E_A=0.10,\sigma_A=0.15,E_B=0.25,\sigma_B=0.40$ and $\rho =−0.2$. I get that about 83 percent of the ...

0

Firstly, to answer your question for part (i), this part of the question makes no sense - your expected return is unbounded and is asymptotically linear with respect to risk. Let ${\bf w}\in\mathbb{R}^{2}$ denote your vector of weights, $\Omega$ denote the covariance matrix and $\iota$ denote a unit exposure vector (defined by \$\iota_{j}:=1\ \forall j, j ...

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