Parametric Expected Shortfall (CVaR)
Computes the Expected Shortfall (ES), also known as CVaR, by the parametric Gaussian method. While VaR answers what the minimum loss is in the worst cases, ES goes further and answers what the average loss is when the worst happens, summing what lies in the tail beyond the VaR. The formula is −μ + σ·φ(Φ⁻¹(c))/(1−c), with Φ⁻¹ the inverse normal. It's a coherent risk measure, required under Basel, precisely because it captures the severity of extreme losses. Enter the mean return, the standard deviation of returns and the confidence level.
Resultado
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Parametric Expected Shortfall (CVaR)
Computes the Expected Shortfall (ES), also known as CVaR, by the parametric Gaussian method. While VaR answers what the minimum loss is in the worst cases, ES goes further and answers what the average loss is when the worst happens, summing what lies in the tail beyond the VaR. The formula is −μ + σ·φ(Φ⁻¹(c))/(1−c), with Φ⁻¹ the inverse normal. It's a coherent risk measure, required under Basel, precisely because it captures the severity of extreme losses. Enter the mean return, the standard deviation of returns and the confidence level.
The question VaR doesn't answer
Value at Risk became the market standard, but it has a well-known hole: it tells you the loss that won't be exceeded in, say, 95% of cases, and stays silent about the other 5%. And it's precisely in the tail that disaster lives. Expected Shortfall, or CVaR, fills that hole by answering the next question: when the worst happens, how bad is it, on average?
This version uses the parametric Gaussian method, which assumes normally distributed returns and solves the calculation in closed form: −μ + σ·φ(Φ⁻¹(c))/(1−c). Unlike VaR, ES is a coherent risk measure in the technical sense, which is why Basel regulation moved to it. For anyone sizing portfolio risk, it's a more honest read on how big the possible fall really is.
Enter the mean return, the standard deviation of returns and the confidence level, all in the same unit (for example, daily returns in percent). The tool returns VaR and ES side by side. Remember that the normality assumption underestimates fat tails; in crisis markets, the real ES tends to be worse than the Gaussian one.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.