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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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I have not found any literature directly handling this. But you could pose the question in terms of risk management of stationary series. Here is extreme values in stationary series. You can try this Quantile Cointegrating Regression. This Sensitivity of portfolio VaR and CVaR to portfolio return characteristics is an interesting twist. Here is an another ...



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