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Next: Multivariate Context: Up: Portfolio specification Previous: Introduction:

Univariate Context:

Taking into account the long and short positions, in the univariate case we introduce notation $\mu^{\pm_{(k)}}$ to denote a generic measure, $\mu$, associated with a specific portfolio and position. Using this notation we can than construct the mean measure, $\mu_u$,in the univariate (u) context as  
 \begin{displaymath}
\mu_u = {1\over20}\left(\sum_{k=1}^{10}\mu^{+_{(k)}} +
\sum_{k=1}^{10}\mu^{-_{(k)}}\right)\end{displaymath} (1)
where each of the $\mu^{\pm_{(k)}}$ is an entirely univariate construct related to the 20 distinct univariate portfolios with respect to which loss is estimated by a candidate model.