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📉 '''Value at Risk (VaR)''' is a statistical measure widely used in the insurance and financial services industries to quantify the maximum expected loss on a portfolio — whether of invested assets, [[Definition:Underwriting|underwriting]] exposures, or an entire balance sheet — over a specified time horizon and at a given [[Definition:Confidence level|confidence level]]. In insurance, VaR has particular prominence as the foundational metric underpinning the [[Definition:Solvency capital requirement (SCR)|solvency capital requirement]] under [[Definition:Solvency II|Solvency II]], which defines the SCR as a one-year VaR calibrated to a 99.5% confidence level — meaning that an insurer's own funds should be sufficient to absorb losses in all but the worst one-in-two-hundred-year scenarios. While VaR originated in banking and trading-desk risk management during the 1990s, its adoption by insurance regulators and [[Definition:Enterprise risk management (ERM)|enterprise risk management]] frameworks has made it one of the most consequential risk metrics in the sector globally.

⚙️ Calculating VaR for an insurance enterprise involves modeling the probability distribution of potential gains and losses across all material risk categories — including [[Definition:Insurance risk|insurance risk]] (such as [[Definition:Catastrophe risk|catastrophe]], [[Definition:Reserving risk|reserving]], and [[Definition:Premium risk|premium risk]]), [[Definition:Market risk|market risk]], [[Definition:Credit risk|credit risk]], and [[Definition:Operational risk|operational risk]] — and then identifying the loss threshold at the chosen confidence level. Insurers may compute VaR using the Solvency II [[Definition:Standard formula|standard formula]], which applies prescribed stress factors and correlation matrices, or through an [[Definition:Internal model|internal model]] approved by the relevant supervisor, which allows firms to capture their own risk profile with greater granularity. In the United States, the [[Definition:Risk-based capital (RBC)|risk-based capital]] framework administered by the [[Definition:National Association of Insurance Commissioners (NAIC)|NAIC]] uses a related but structurally different approach to capital adequacy, while regimes such as China's [[Definition:C-ROSS|C-ROSS]], Japan's solvency margin framework, and Singapore's [[Definition:Risk-based capital (RBC)|RBC]] requirements each incorporate their own variants of quantile-based risk measurement. Beyond regulatory compliance, insurers and reinsurers deploy VaR in [[Definition:Asset-liability management (ALM)|asset-liability management]], investment portfolio construction, and [[Definition:Reinsurance|reinsurance]] purchasing decisions, using it to benchmark risk exposures and allocate [[Definition:Economic capital|economic capital]] across business units.

🔍 Despite its ubiquity, VaR has well-known limitations that insurance professionals must navigate carefully. The measure captures a single point on the loss distribution — the threshold at the chosen percentile — but says nothing about the severity of losses beyond that point, a shortcoming that is especially relevant for insurers exposed to heavy-tailed risks such as [[Definition:Natural catastrophe|natural catastrophes]] or [[Definition:Liability insurance|long-tail casualty]] liabilities. This weakness has led many firms and some regulators to supplement VaR with [[Definition:Tail Value at Risk (TVaR)|Tail Value at Risk]] (also known as Conditional VaR or Expected Shortfall), which averages losses in the tail beyond the VaR threshold and provides a more complete picture of extreme downside exposure. Model risk is another persistent concern: the accuracy of VaR estimates depends heavily on the quality of underlying data, the assumed statistical distributions, and the correlation assumptions used to aggregate risks — all of which can break down precisely when they matter most, during severe market dislocations or unprecedented [[Definition:Loss event|loss events]]. For insurers, robust [[Definition:Stress testing|stress testing]] and [[Definition:Scenario analysis|scenario analysis]] remain essential complements to VaR, ensuring that capital adequacy assessments are not anchored exclusively to a single statistical output.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Solvency capital requirement (SCR)]]
* [[Definition:Tail Value at Risk (TVaR)]]
* [[Definition:Economic capital]]
* [[Definition:Internal model]]
* [[Definition:Stress testing]]
* [[Definition:Enterprise risk management (ERM)]]
{{Div col end}}

Definition:Value at Risk (VaR) - Revision history

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