What is Expected Shortfall and how is it calculated under FRTB?

Expected Shortfall (ES) — also known as Conditional Value at Risk (CVaR) — is a coherent risk measure that captures the average loss beyond the VaR threshold. Under the Fundamental Review of the Trading Book (FRTB), the 97.5% ES replaces the previous 99% VaR as the standard for market risk capital requirements. The reason: VaR completely ignores the severity of tail losses. It does not distinguish between barely exceeding the threshold and a catastrophic loss. Expected Shortfall captures all losses in the tail and weights them by their actual magnitude. This makes ES sub-additive — diversification is correctly reflected, which VaR cannot guarantee.

The FRTB Expected Shortfall calculation is based on a 250-day stress period that the bank selects as a period of particularly high market stress. ES is calculated across five different liquidity horizons: 10, 20, 60, 120, and 250 days — depending on the risk factor class. The formula aggregates ES values across different risk factor categories with restricted diversification. Additionally, a distinction is made between modellable and non-modellable risk factors (NMRF). For modellable factors, the internal ES approach is used; for NMRF, a separate stress test surcharge applies. The final capital requirement combines both components.

VaR only provides a threshold: the maximum loss that will not be exceeded with a given probability. It says nothing about how large losses are when that threshold is breached. Expected Shortfall calculates the average of all losses beyond that threshold. Mathematically, ES is a coherent risk measure — it satisfies sub-additivity, meaning ES(Portfolio A + B) is less than or equal to ES(A) + ES(B). VaR does not satisfy this property, which can lead to paradoxical results where diversification apparently increases measured risk.

FRTB defines five liquidity horizons for ES calculation, graduated by risk factor class: 10 days for large equity indices and major interest rates, 20 days for small-cap equities and investment-grade credit spreads, 60 days for commodities and emerging market interest rates, 120 days for high-yield credit spreads and volatilities, 250 days for illiquid securitizations and correlation trading. These staggered horizons replace the uniform 10-day VaR and reflect that different positions require different timeframes for market liquidation.

The 97.5% Expected Shortfall and the 99% VaR are approximately equivalent under a normal distribution — they produce comparable capital requirements. The Basel Committee deliberately chose the 97.5% level for ES to maintain calibration consistency with the previous 99% VaR. The decisive difference lies not in the confidence level but in the methodology: while VaR examines only a single quantile value, ES averages all losses above that quantile. For distributions with heavy tails — typical for financial markets — ES captures significantly more risk than VaR.

Backtesting under FRTB continues to validate internal models based on VaR, not directly on Expected Shortfall — because ES backtesting is statistically more difficult and requires considerably more data. The traffic light approach compares daily trading P&L against the 99% and 97.5% VaR over 250 days. Additionally, FRTB requires the P&L Attribution Test (PLAT), which checks whether the model's risk factors explain the actual trading desk P&L. If a desk fails backtesting or PLAT, it must switch from the internal model to the standardized approach.

ADVISORI guides banks and financial institutions through the complete implementation of FRTB Expected Shortfall requirements: from gap analysis of existing VaR models through development of new ES calculation methods to validation and regulatory approval. Our consultants have direct project experience with FRTB implementation at German and European institutions. Key focus areas include stress period calibration, classification of modellable and non-modellable risk factors, establishment of the P&L Attribution Test, and integration of ES calculation into existing risk infrastructure.