Portfolio Value at Risk: Calculation, Interpretation, and Limitations
Summary
The document introduces Value at Risk (VaR) as a loss threshold tied to a specified confidence level and time horizon. It presents a parametric portfolio calculation that multiplies portfolio return volatility by the relevant standard-normal quantile and portfolio value. A worked example uses a three-stock portfolio, weighted asset returns, and an annualized volatility estimate to illustrate the calculation and interpretation.
The discussion summarizes VaR’s usefulness as a compact, comparable risk measure for setting limits and reporting exposures. It also explains that VaR does not describe losses beyond its threshold and can understate risk when returns have fat tails, positions are nonlinear, liquidity is limited, or historical patterns change. The example relies on distributional and estimation assumptions, and the article recommends complementing VaR with expected shortfall, stress testing, scenario analysis, and backtesting rather than treating one VaR estimate as a complete picture of portfolio risk.
Key ideas
- VaR estimates a loss threshold for a chosen confidence level and time horizon.
- The illustrated parametric method scales portfolio volatility by a normal quantile and portfolio value.
- VaR is easy to communicate and can support risk limits and portfolio comparisons.
- VaR does not show the severity of losses beyond its threshold and can miss tail, liquidity, and nonlinear risks.
- Expected shortfall, stress tests, scenario analysis, and backtesting can supplement VaR.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.