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📐 '''Value at risk''' (VaR) is a statistical measure widely used across the insurance industry to estimate the maximum potential loss on a portfolio of risks — whether [[Definition:Investment portfolio|investment assets]], [[Definition:Underwriting|underwriting]] exposures, or an entire enterprise — over a specified time horizon and at a given [[Definition:Confidence level|confidence level]]. In insurance, VaR serves as a foundational building block for [[Definition:Regulatory capital|regulatory capital]] frameworks, [[Definition:Internal model|internal models]], and [[Definition:Enterprise risk management|enterprise risk management]] programs: for example, the [[Definition:Solvency II|Solvency II]] [[Definition:Solvency capital requirement|Solvency Capital Requirement (SCR)]] is defined as the VaR of basic own funds at a 99.5% confidence level over a one-year horizon, meaning regulators expect insurers to hold enough capital to survive all but the worst one-in-200-year loss scenarios.

⚙️ Insurers calculate VaR using several methodologies depending on the risk type, data availability, and regulatory requirements. Parametric (variance-covariance) approaches assume a known distribution and work well for market risk on liquid investment portfolios. [[Definition:Monte Carlo simulation|Monte Carlo simulation]] is more common for insurance-specific risks — particularly [[Definition:Catastrophe risk|catastrophe risk]] and [[Definition:Reserving risk|reserving risk]] — where loss distributions are skewed and fat-tailed. Historical simulation draws on past loss experience but can underestimate [[Definition:Tail risk|tail risk]] if the observation window lacks extreme events. Under Solvency II, insurers may use the [[Definition:Standard formula|standard formula]] or apply for approval of a full or partial internal model to calculate SCR; either way, VaR at 99.5% is the target metric. In contrast, [[Definition:C-ROSS|China's C-ROSS]] framework and the [[Definition:Risk-based capital|RBC]] system used in the United States and parts of Asia employ factor-based approaches that implicitly embed VaR-like concepts but do not always express the capital requirement as a single VaR figure. On the investment side, insurers managing multi-billion-dollar bond, equity, and [[Definition:Alternative investment|alternative investment]] portfolios rely on daily or weekly VaR reports to monitor [[Definition:Market risk|market risk]] exposure and ensure compliance with board-approved [[Definition:Risk appetite|risk appetite]] limits.

🎯 Despite its ubiquity, VaR has well-known limitations that insurance professionals must account for. It tells you the threshold of loss at a given confidence level but says nothing about the severity of losses beyond that threshold — a shortcoming that has led many insurers and regulators to supplement VaR with [[Definition:Tail value at risk|Tail VaR (TVaR)]], also known as [[Definition:Conditional tail expectation|Conditional Tail Expectation]], which averages losses in the tail beyond the VaR point. The Swiss [[Definition:Swiss Solvency Test|Solvency Test (SST)]], for instance, uses TVaR at 99% rather than VaR. VaR can also give a false sense of precision when applied to highly non-normal distributions typical of [[Definition:Natural catastrophe|natural catastrophe]] or [[Definition:Liability insurance|liability]] risks, where a single extreme event can dwarf the modeled estimate. Nonetheless, as a common language for quantifying and communicating risk, VaR remains indispensable — enabling insurers, [[Definition:Reinsurance|reinsurers]], regulators, and [[Definition:Rating agency|rating agencies]] to compare risk profiles across companies, lines of business, and geographies on a broadly consistent basis.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Tail value at risk]]
* [[Definition:Solvency capital requirement]]
* [[Definition:Enterprise risk management]]
* [[Definition:Internal model]]
* [[Definition:Catastrophe risk]]
* [[Definition:Risk appetite]]
{{Div col end}}

Definition:Value at risk - Revision history

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