Introduction to Portfolio Value-at-Risk

Gianluca Fusai and Laura Ballotta

The aim of this second chapter is to introduce the main tools for assessing the relevant risk measures, as VaR and ES, at portfolio level. The main issue is how to specify the joint distribution of the log-returns of the portfolio components. In addition, the inclusion of nonlinear derivative positions in the portfolio makes it difficult to obtain the portfolio distribution. In this case, Monte Carlo simulation is of great help. Concrete examples from energy markets are also considered.


As we move from exposure at a single asset level to exposure at portfolio level, non-trivial issues arise because we need to be able to capture the dependence structure among the portfolio components. A possible solution is the so-called top-down approach, ie, the porfolio P&L distribution is assigned without reference to the portfolio constituents. Then the computation of the portfolio VaR can be done by referring to the approaches previously presented, treating the portfolio return series as a univariate series. The limit of this approach is that it does not allow us to identify the assets contribution to the portfolio exposure: a large loss can occur at portfolio

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