A Multiplicative Factor for Analytic VaR to Avoid Previous Inconsistencies

VaR_Delta-Normal is derived from a Put option, named PVaR_Delta-Normal and Expected_Shortfall, PSF_Delta-Normal – the latter a coherent measure – guaranteeing VaR can never be larger than the fund value. Current standard VaR_Delta-Normal uses covariances calculated from the entire price-return histogram, while the newly proposed PVaR_Delta-Normal uses tail price-return covariance. Recognizing that fund managers have developed an expertise in using the standard VaR_Delta-Normal as well as Component and Marginal VaRs derived from it, changing to the new formula would be a costly project of global proportions, a compromise is proposed: derive a Multiplicative Factor “γ” as the ratio between tail covariance PVaR_Delta-Normal and full sample covariance VaR_Delta-Normal, such that new PVaR_Delta-Normal equals current VaR_Delta-Normal × γ. Empirical results show that under normal market conditions VaR_1%,1Day underestimates PVaR_1%,1Day by 20% to 35%; while under high volatility and assets turning illiquid it could double PVaR_1%,20Days, and the fund would lose more than it is worth (happened in 4Q08 to 1Q09). Results can be used to analyze the market-risk of emerging markets which tend to hold assets with low daily trading volumes