Value at Risk (VaR) Calculator

Value at Risk states a loss threshold: an amount that losses are expected to stay under, at a chosen confidence level, over a chosen period. On a 100,000 portfolio a 95% one-day VaR of 2,000 says that on 95% of days the loss stays under 2,000, and on the remaining one day in twenty it does not. Banks report it under the Basel market-risk framework, and it is also used by funds and trading desks for risk budgeting.

On the sample figures, a 1,000,000 portfolio with an 8% expected return and 15% volatility gives a 95% one-year VaR of 166,728. The reading is that in 95 years out of 100 the annual loss stays under about 167,000, and in the other five it does not. Moving to 99% confidence raises the figure to about 269,000. A higher confidence level always raises VaR. A longer horizon does not, because the volatility term grows with the square root of time while the expected-return offset grows in a straight line. At the sample figures VaR peaks near 599 trading days at about 190,000 and falls back to about 152,000 by the 1,260-day maximum the field accepts.

The limitations are well known. The model assumes a normal distribution, while real markets have fat tails, so extreme events arrive more often than the normal curve implies. It also says nothing about the size of the loss once the threshold is crossed: the worst 5% could be a 10% fall or a 90% one, and VaR does not distinguish them. Expected shortfall, also called conditional VaR, addresses that second gap by averaging the losses in the tail, and stress testing addresses the first. VaR sits alongside both in the Basel market-risk framework rather than standing on its own.

Quick example

With portfolio value of 1,000,000 and expected annual return of 8% (plus annual volatility of 15% and confidence level of 95%), the result is 166,728.04.

Which inputs matter most

Confidence level is much the strongest lever. Raising each input by 1% of its own value at the sample figures moves the result 9.00% for confidence, 1.48% for volatility, 1.00% for portfolio value, 0.48% downward for expected return, and 0.26% for the horizon.

Portfolio value is exactly proportional, since it multiplies the whole expression and cannot touch the percentage row. The volatility and return levers are tied to each other: because the bracket is the z-scaled volatility less the period return, their two elasticities always differ by exactly one, which is why 1.48% and 0.48% sit either side of the portfolio lever's 1.00%. Confidence dominates because it moves the z-score, which multiplies the larger of the two terms.

What's happening under the hood

The calculation is parametric VaR under a normal distribution. Annual volatility is converted to a daily figure by dividing by the square root of 252, then scaled back up by the square root of the horizon, while the annual return is divided by 252 and scaled up linearly. VaR is the portfolio value multiplied by the z-scored volatility term less that return term.