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--- personal:portfolio:portopt [2015/02/10 13:26]
antonello [Usage]
+++ personal:portfolio:portopt [2015/03/30 14:20]
antonello [Theorical Background]
@@ Line 54: / Line 54: @@
 \end{equation}
-where $x_i$ is the share of the asset $i$, $p_i$ is its productivity and hence $\sum_i {x_i p_i}$ is the overall portfolio productivity and $\sum_i { \sum_j { x_i x_j \sigma_{i,j}}}$ its variance.
+where $x_i$ is the share of the asset $i$, $p_i$ is its productivity, $\sigma_{i,j}$ is the covariance between assets $i$ and $j$ and hence $\sum_i {x_i p_i}$ is the overall portfolio productivity and $\sum_i { \sum_j { x_i x_j \sigma_{i,j}}}$ is its variance.
 As the only quadratic term arises when $i=j$ and $\sigma_{i,j}$ being the variance is always positive, the problem is convex and hence easily numerically solved.