Active Portfolio
Overview
An active portfolio is a portfolio that has assets weights that differ from a given benchmark. Such portfolios
are typically measured with respect to the benchmark portfolio.
Active Weights
{% \vec{w} = \vec{b} + \vec{a} %}
portfolio weights are equal to the benchmark weights plus a set of active weights,
where we require the active weights to sum to zero.
if we are given a set of return forecasts {% \vec{f} %}, then the expected active return
(the return relative to the benchmark) is
{% \vec{a}^T \vec{f} %}
and the active risk is then
{% \omega = \frac{1}{2} \vec{a}^T \Sigma \vec{a} %}
