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📉 '''Tail Value at Risk''' (also known as Conditional Value at Risk or Expected Shortfall) is a [[Definition:Risk measure|risk measure]] used extensively in insurance [[Definition:Enterprise risk management (ERM)|enterprise risk management]] and regulatory capital frameworks to quantify the expected loss in the worst-case tail of a loss distribution, beyond a specified confidence level. While [[Definition:Value at Risk (VaR)|Value at Risk]] tells an insurer the threshold loss that will not be exceeded with a given probability, Tail Value at Risk goes further by averaging all losses that exceed that threshold, capturing the severity of extreme outcomes rather than merely their frequency. This makes it particularly relevant for insurance, where [[Definition:Catastrophe loss|catastrophe events]], [[Definition:Long-tail liability|long-tail liabilities]], and correlated risks can produce losses far beyond the VaR boundary.

⚙️ Calculating Tail Value at Risk requires modeling the full probability distribution of an insurer's losses — or the losses of a specific [[Definition:Portfolio|portfolio]] or [[Definition:Line of business|line of business]] — and then computing the conditional expectation of losses in the tail region. For a [[Definition:Property catastrophe reinsurance|property catastrophe reinsurer]], this might involve running thousands of simulated hurricane or earthquake scenarios through a [[Definition:Catastrophe model|catastrophe model]] and averaging the losses that fall in the worst 1% of outcomes. Regulatory frameworks differ in their adoption of this measure: Switzerland's [[Definition:Swiss Solvency Test (SST)|Swiss Solvency Test]] explicitly uses Expected Shortfall (Tail VaR at the 99% level) as its core capital metric, while [[Definition:Solvency II|Solvency II]] employs a [[Definition:Value at Risk (VaR)|VaR]]-based approach at the 99.5% level. North American regulators and the [[Definition:National Association of Insurance Commissioners (NAIC)|NAIC]] have increasingly incorporated tail risk analysis into [[Definition:Own risk and solvency assessment (ORSA)|ORSA]] requirements, even where the formal capital standard does not mandate TVaR directly.

🎯 The appeal of Tail Value at Risk lies in its ability to discipline insurers against underestimating the cost of extreme events — a blind spot that has historically contributed to [[Definition:Insolvency|insolvencies]]. VaR, by contrast, is criticized for being indifferent to the shape of the tail: two portfolios can share the same VaR while having vastly different expected losses in a worst-case scenario. For an industry where a single [[Definition:Natural catastrophe|natural catastrophe]] or [[Definition:Pandemic|pandemic]] event can overwhelm reserves, the distinction is not academic. [[Definition:Rating agency|Rating agencies]], [[Definition:Internal model|internal model]] validators, and sophisticated [[Definition:Reinsurance|reinsurance]] buyers increasingly expect TVaR-based analysis alongside or in place of VaR, recognizing that prudent [[Definition:Capital management|capital management]] demands an honest reckoning with what happens when the tail bites.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Value at Risk (VaR)]]
* [[Definition:Enterprise risk management (ERM)]]
* [[Definition:Swiss Solvency Test (SST)]]
* [[Definition:Catastrophe model]]
* [[Definition:Solvency II]]
* [[Definition:Own risk and solvency assessment (ORSA)]]
{{Div col end}}

Definition:Tail Value at Risk - Revision history

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