Improved Analytic VaR that Avoids Previous Inconsistencies

VaR_Delta-Normal fails in two counts: subadditivity and potentially producing losses larger than its portfolio value. This paper solves the second inconsistency developing formulas derived from a put option, named PVaR_Delta-Normal and Put_Expected_Shortfall, PSF_Delta-Normal; the latter also being a coherent measure. Using data of 4Q08, a Delta-Normal VaR_1%,5-Days gives losses of 88% to 98% of a financial assets portfolio value, when true PVaR_1%,5-Days losses are 50%-55%. Taking action is more urgent when considering VaR is used daily to measure capital, risk limits and liquidity of trillions of dollars. VaR_Delta-Normal large inaccuracy makes a case for policy makers to consider PVaR_Delta-Normal and PES_Delta-Normal as legitimate risk metrics