Definition
Value at risk is a summary risk measure that states the loss a portfolio would not exceed over a specified time horizon at a specified confidence level, typically expressed as a dollar amount or a percentage of portfolio value.
Why it matters
Value at risk is the most widely used single-number risk statistic in financial reporting and regulatory capital work. It answers a specific question, "over the next N days, at C percent confidence, how large could my loss be," in a form that is easy to communicate and compare across portfolios. Its limitations are equally well known: it says nothing about how bad the tail beyond the confidence level actually is.
How it works
Value at risk is defined by three parameters: a portfolio, a time horizon, and a confidence level. A one-day ninety-five percent value at risk of one million dollars means that, based on the chosen statistical model, there is a ninety-five percent probability that the portfolio will not lose more than one million dollars over a one-day horizon. Value at risk can be computed under different methodologies: historical simulation using observed past returns, parametric methods assuming a specific return distribution, or Monte Carlo simulation drawing from a specified stochastic model. Each methodology produces a different value at risk figure from the same underlying data. The measure has two important limitations: it is a threshold, not an expected loss, so it does not describe how severe losses can be beyond the confidence level, and it is highly sensitive to the modeling assumptions used to generate it, especially the assumed shape of the tail. Worked example: a diversified retirement portfolio worth one million dollars, evaluated at a one-year ninety-five percent value at risk of two hundred thousand dollars, has a five percent probability of losing more than two hundred thousand dollars over the next year based on the underlying model. This is a threshold statement about the boundary of ordinary bad outcomes, not a description of what happens in the tail beyond that boundary.
In practice
For an individual evaluating investment options for retirement savings, value at risk is unlikely to appear on retail fact sheets but is embedded in the risk management underlying institutional products, default investment options, and carrier capital regulation. A professional working with retirement portfolios uses value at risk as one of several risk summaries, generally alongside expected shortfall (the expected loss conditional on being in the tail beyond the value at risk threshold) and drawdown analysis. Plan fiduciaries reviewing default investment options should recognize that value at risk is a threshold statistic and that portfolios with the same value at risk can differ substantially in what happens in the tail beyond it, a distinction that matters particularly for the concentrated tail conditions in which participants near or in retirement are most exposed.
Related terms
- Standard deviation
- Drawdown
- Maximum drawdown
- Monte Carlo simulation
- Stress testing
- Sequence of returns risk
- Risk-based capital
- Tail risk