Value at risk is the displayed upper loss quantile for a specified horizon and confidence level. It is distinct from a two-sided confidence interval for a model parameter and does not by itself describe the severity of losses exceeding that quantile.
Let annual losses be with independent of identically distributed nonnegative loss given default amounts of mean and variance . Conditional expectation and variance give and . A many-event normal approximation yields the displayed quantile; the actual loss distribution has a zero atom and depends on the entire severity law. For rare events or extreme tails, the moment-based normal approximation need not be accurate.
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Value at Risk (VaR) is a financial metric used to assess the potential loss in value of an asset or portfolio over a defined period for a given confidence interval. It is commonly employed in the fields of risk management, investment analysis, and regulatory compliance. VaR provides a way to quantify the level of financial risk within a firm or portfolio over a specific time frame.