New answers tagged mean-variance
2
You indeed seem to have an error in your calculation somewhere.
Let the covariance matrix be
$$\Sigma=\begin{pmatrix}0.0324&0.021016&0\\
0.021016 & 0.0256 & 0 \\
0 & 0 & 0.0256\end{pmatrix}$$
and the vector of (excess) returns are
$$
\mu-r_f=\begin{pmatrix}0.05 \\ 0.02 \\ 0.03\end{pmatrix}
$$
Ultimately, the weights are then computed ...
2
The key phrase is "adjusted by their covariances". The formula for the variance of a portfolio of two assets is
$\sigma _{p}^{2}=w_{A}^{2}\sigma _{A}^{2}+w_{B}^{2}\sigma _{B}^{2}+2w_{A}w_{B}\sigma _{A}\sigma _{B}\rho _{AB}$
, which, since $\rho _{AB} <= 1$, is always less than
$ w_{A}^{2}\sigma _{A}^{2}+w_{B}^{2}\sigma _{B}^{2}+2w_{A}w_{B}\sigma ...
0
You can handle this problem with scenario
optimization: assume a matrix $R$ of returns, in which
the rows are the scenarios and the columns are
assets. For given portfolio weights $w$, you can
compute the portfolio returns as $Rw$. You can now
evaluate an objective function such as the MAD, so your objective becomes $\min\ \mathrm{mean}(|Rw|)$. Now feed ...
2
The third approach is the correct one. In general, one
cannot aggregate partial moments of single assets into
partial moments of the portfolio, as discussed for
instance in this paper:
@ARTICLE{Grootveld1999,
author = {Henk Grootveld and Winfried Hallerbach},
title = {Variance vs downside risk: Is there really that
much ...
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