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Definition of Analytical VaR
VaR is a predictive (ex-ante) tool used to prevent portfolio managers from exceeding risk tolerances that have been developed in the portfolio policies. It can be measured at the portfolio, sector, asset class, and security level. Multiple VaR methodologies are available and each has its own benefits and drawbacks. To illustrate, suppose a $100 million portfolio has a monthly VaR of $8.3 million with a 99% confidence level. VaR simply means that there is a 1% chance for losses greater than $8.3 million in any given month of a defined holding period under normal market conditions.
It is worth noting that VaR is an estimate, not a uniquely defined value. Moreover, the trading positions under review are fixed for the period in question. Finally, VaR does not address the distribution of potential losses on those rare occasions when the VaR estimate is exceeded. We should also bear in mind these constraints when using VaR. The ease of using VaR is also its pitfall. VaR summarizes within one number the risk exposure of a portfolio. But it is valid only under a set of assumptions that should always be kept in mind when handling VaR.
VaR involves two arbitrarily chosen parameters: the holding period and the confidence level. The holding period corresponds to the horizon of the risk analysis. In other words, when computing a daily VaR, we are interested in estimating the worst expected loss that may occur by the end of the next trading day at a certain confidence level under normal market conditions. The usual holding periods are one day or one month. The holding period can depend on the fund’s investment and/or reporting horizons, and/or on the local regulatory requirements. 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. It is therefore no surprise that most regulators require a 95% or 99% confidence interval to compute VaR.
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