A Look at Bloomberg ’ s PVAR 1

he search for the ultimate market risk measurement tool has drawn market participants to the concept of Value-at-Risk (VaR). 2 VaR, endorsed by a var iety of regulatory groups, has gained popularity among traders and managers of trading books. Although large complex organizations have developed internal VaR models to integrate all the peculiarities of their trading books, less sophisticated institutions and some traders who want a quick, " on the spot " analysis look to vendor models to meet their needs. Bloomberg's Portfolio Value-at-Risk (PVAR) serves this function for many clients. This article discusses the mathematical foundations of Bloomberg's PVAR and its limitations. PVAR Assumptions and Limitations VaR models differ in their broad methodology, assumptions and details of implementation. 3 PVAR is based on the var iance/covar iance methodology 4 advanced by RiskMetrics. TM Central to the model is the use of a series of building blocks called " primitive assets " , onto which all asset retur ns are mapped. PVAR relies on three basic premises: • Primitive asset returns are normally distributed. • Primitive asset return volatilities and correlations are stable over time. • All asset retur ns can be reliably mapped onto the primitive assets, which adequately capture their behavior and risk. These three basic assumptions are piv-otal to the model; while not entirely free of problems, they result in considerable computational simplicity. A problem with the first assumption, that of normal distribution, is the existence of " fat tails " in the distribution of financial assets. Distributions of financial assets tend to exhibit more " mass " in the tail of the distribution , suggesting that rare events are likely to occur more frequently than the normal distribution implies. PVAR users should keep in mind that a model based on the normal approximation underestimates the proportion of outliers. 5 Relative to the second assumption, the variance/covariance matrix being stable over time, PVAR maintains the assumption for all asset returns and all markets and does not take into account possible differential behavior. In reality, data do not exhibit stability, and statistical measures based on past observations may not be a safe predictor of future distributions. PVAR attempts to compensate for this by recalculating its statistical parameters daily and by using exponential weighting. The user can either smooth observations over the whole year or, alternatively, weight recent observations more heavily through a greater decay factor. A general limitation …