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📐 '''Risk measure''' is a quantitative metric used by insurers, [[Definition:Reinsurer | reinsurers]], and regulators to express the magnitude of uncertainty or potential loss associated with a portfolio, business unit, or entire enterprise. In insurance, the choice of risk measure is far from academic — it directly determines how much [[Definition:Capital | capital]] a company must hold, how [[Definition:Premium | premiums]] are loaded for adverse deviation, and how [[Definition:Reinsurance | reinsurance]] programs are structured. Common risk measures in the industry include [[Definition:Value at risk (VaR) | Value at Risk (VaR)]], [[Definition:Tail value at risk (TVaR) | Tail Value at Risk (TVaR)]] (also called Conditional Tail Expectation), standard deviation of losses, and ruin probability, each offering a different lens on the shape and severity of the [[Definition:Loss distribution | loss distribution]].

⚙️ Different regulatory regimes have embedded different risk measures into their [[Definition:Capital requirement | capital]] frameworks, which creates meaningful variation in how insurers around the world quantify risk. [[Definition:Solvency II | Solvency II]] in Europe prescribes VaR at the 99.5% confidence level over a one-year horizon for calculating the [[Definition:Solvency capital requirement (SCR) | Solvency Capital Requirement]], while the Swiss Solvency Test uses TVaR at 99%, which captures the average severity of losses beyond the threshold rather than simply whether the threshold is breached. In the United States, the [[Definition:Risk-based capital (RBC) | RBC]] framework takes a factor-based approach that implicitly embeds risk measures within prescribed formulas, and many large U.S. insurers supplement this with internal [[Definition:Economic capital | economic capital]] models calibrated to TVaR or other coherent risk measures. [[Definition:Actuarial science | Actuaries]] generally favor TVaR because it satisfies the mathematical property of subadditivity — meaning diversification always reduces measured risk — whereas VaR can, in certain distributions, produce the counterintuitive result that combining two portfolios appears riskier than the sum of the parts.

💡 Selecting the right risk measure shapes strategic decisions well beyond regulatory compliance. When an insurer evaluates whether to enter a new [[Definition:Line of business | line of business]], the risk measure chosen for internal [[Definition:Capital allocation | capital allocation]] determines the hurdle that the new book must clear to justify the capital consumed. Similarly, when purchasing [[Definition:Reinsurance | reinsurance]], an insurer using TVaR will place greater emphasis on reducing the severity of tail events — pushing toward lower [[Definition:Attachment point | attachment points]] or broader [[Definition:Catastrophe bond | cat bond]] coverage — than one relying on VaR, which is less sensitive to the extremes beyond its threshold. As [[Definition:Climate risk | climate risk]], [[Definition:Cyber risk | cyber risk]], and other emerging perils introduce heavier tails into loss distributions, the insurance industry's ongoing debate about which risk measures best capture real-world exposure has become increasingly consequential for [[Definition:Solvency | solvency]], pricing, and long-term resilience.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Value at risk (VaR)]]
* [[Definition:Tail value at risk (TVaR)]]
* [[Definition:Economic capital]]
* [[Definition:Solvency capital requirement (SCR)]]
* [[Definition:Capital allocation]]
* [[Definition:Loss distribution]]
{{Div col end}}

Definition:Risk measure - Revision history

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