VALUE AT RISK
VaR is a predictive (ex-ante) tool used to prevent portfolio managers from exceeding risk tolerances that have been developed in the portfolio policies at a certain confidence level under normal market conditions. The usual holding periods are one day or one month. The confidence level is intuitively a reliability measure that expresses the accuracy of the result. The higher the confidence level, the more likely we expect VaR to approach its true value or to be within a pre-specified interval.
Analytical VaR is also called Parametric VaR because one of its fundamental assumptions is that the return distribution belongs to a family of parametric distributions such as the normal or the lognormal distributions. Analytical VaR can simply be expressed as: | | where: * VaRα is the estimated VaR at the confidence level 100 × (1 - α)%. * xα is the left-tail α percentile of a normal distribution . xα is described in the expression where R is the expected return. In order for VaR to be meaningful, we generally choose a confidence level of 95% or 99%. xα is generally negative. * P is the marked-to-market value of the portfolio.

Objectives of VaR measurement * It facilitate risk reporting and control decisions. * The simplicity of VAR measurement greatly facilitated dealers’ reporting of risks to senior managers and directors. * VAR also proves useful in dealers’ risk control efforts. * Commercial banks, use VAR measures to quantify current trading exposures and compare them to established counterparty risk limits. * VAR provided traders with information useful in formulating hedging policies and evaluating the effects of particular transactions on net portfolio risk. * For managers, VAR is popular as a means of analysing the performance of traders for compensation purposes and for allocating reserves or capital