Quick definition Value at Risk (VaR) is a number that answers: "What is my worst-case loss at a 95 percent confidence level (or other level) over the next day?" A portfolio with 1 million dollar VaR at 95 percent has a 1 in 20 chance of losing more than 1 million in the next day. What it is VaR is calculated from historical returns and volatility. It assumes prices move roughly normally (a simplification). VaR is not a maximum loss; it is a threshold. Losses can exceed VaR, but with low probability. Time horizon VaR is reported for different time horizons: 1 day, 10 days, etc. A 10-day VaR accounts for more volatility than a 1-day VaR. Traders and regulators use 1-day VaR. Longer horizons (10 days) are used for capital calculations. Confidence level VaR is reported at different confidence levels: 95 percent, 99 percent, etc. A 99 percent VaR is larger than a 95 percent VaR (higher confidence means larger loss threshold). Limitations VaR has significant limitations: - Assumes normal distribution (markets are not normal; extreme events are more common) - Only looks at one percentile (ignores tail risk) - Based on history (historical VaR may not predict future risk) - Can underestimate risk in stressed markets VaR is a useful metric but should not be the only risk measure. Practical example Your portfolio has a 1-day VaR of 500,000 dollars at the 95 percent level. This means there is a 1 in 20 chance you will lose more than 500,000 dollars tomorrow. The other 19 in 20 days, you will lose less than 500,000 dollars. Alternative measures Expected shortfall (CVaR) measures average loss beyond VaR, avoiding VaR's limitations. See also - Risk Measurement - Expected Shortfall - Stress Testing - Portfolio Risk
