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📉 '''Tail value-at-risk (TVaR)''' is a risk measure that quantifies the expected loss in the worst-case tail of a loss distribution, calculated as the average of all losses exceeding a specified [[Definition:Value-at-risk (VaR) | value-at-risk]] threshold. In insurance, TVaR — also known as conditional tail expectation (CTE) or expected shortfall — has become a preferred metric for evaluating [[Definition:Catastrophe risk | catastrophe exposure]], setting [[Definition:Regulatory capital | regulatory capital]] requirements, and stress-testing [[Definition:Reinsurance program | reinsurance programs]], because it captures the severity of extreme outcomes rather than merely the probability of breaching a single loss level. While VaR answers the question "what is the loss we won't exceed with X% confidence," TVaR answers the more consequential question for an insurer: "given that we do exceed that level, how bad could it actually get?"

⚙️ To compute TVaR at a given confidence level — say, 99.5% — an [[Definition:Actuary | actuary]] identifies the VaR at that threshold and then averages all simulated or modeled losses that fall beyond it. This makes TVaR sensitive to the shape of the distribution's tail, which is precisely where insurance losses concentrate their most damaging potential: a portfolio might have the same VaR at the 99th percentile as another, yet dramatically different TVaR figures if one is exposed to events with much heavier tail severity. [[Definition:Catastrophe model | Catastrophe models]] generate the [[Definition:Stochastic event set | stochastic event sets]] and loss distributions from which TVaR is derived, and the measure feeds directly into decisions about how much [[Definition:Reinsurance | reinsurance]] to purchase, where to set [[Definition:Attachment point | attachment points]], and how to allocate capital across lines of business.

📊 Several major regulatory and rating frameworks have adopted TVaR as a standard. The [[Definition:Swiss Solvency Test (SST) | Swiss Solvency Test]] uses TVaR at the 99% confidence level as its core capital adequacy metric, in contrast to [[Definition:Solvency II | Solvency II's]] reliance on VaR at 99.5%. Canadian insurance regulation under [[Definition:Office of the Superintendent of Financial Institutions (OSFI) | OSFI]] similarly employs CTE-based measures for life insurance capital and reserving. The preference for TVaR in these regimes reflects a philosophical commitment to understanding — and capitalizing for — the full magnitude of tail events, not just their likelihood. For insurance practitioners, TVaR provides a more coherent basis for comparing risks, optimizing [[Definition:Risk transfer | risk transfer]] strategies, and communicating with [[Definition:Rating agency | rating agencies]] and investors who increasingly demand transparency about extreme scenario exposure.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Value-at-risk (VaR)]]
* [[Definition:Solvency capital requirement (SCR)]]
* [[Definition:Catastrophe model]]
* [[Definition:Swiss Solvency Test (SST)]]
* [[Definition:Risk measure]]
* [[Definition:Exceedance probability curve]]
{{Div col end}}

Definition:Tail value-at-risk (TVaR) - Revision history

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