Value at risk, or VaR, is the loss a portfolio can expect to suffer over a set horizon at a chosen confidence level, before the outcome goes worse. Enter a 100,000 portfolio, a 0.05 daily return, 1.5% daily volatility, 95% confidence and a 1 day horizon in the Value at Risk (VaR) Calculator, and the calculator answers with 2,417.50 of VaR, 3,043.32 of CVaR and 26,570.35 of annual VaR, plus a comparison table for the 99 and 99.5 percent levels.
The parametric formula and its three inputs
The tool uses the parametric, or variance-covariance, family of VaR: the expected loss equals the z score times volatility times the square root of the horizon, minus the daily return times the horizon. Three inputs drive it: the portfolio value scales the answer linearly, the daily volatility sets the size of the swings, and the daily return, the drift, moves the center. That is the whole model, which is why the result appears instantly. The price is the assumption that returns are roughly bell-shaped, and the Monte Carlo guide covers the simulation family that drops that assumption by drawing thousands of random paths instead.
The z score table: 1.645, 2.326 and 2.576
The confidence level is a lookup, not a calculation: 95% maps to 1.645, 99% to 2.326 and 99.5% to 2.576, the points where the normal distribution keeps that much of the tail behind it. With 1.5% daily volatility and zero drift the three figures read 2,467.50, 3,489.00 and 3,864.00; the tool subtracts the drift before printing, so 95% shows 2,417.50 at 2.42%, 99% shows 3,439.00 at 3.44% and 99.5% shows 3,814.00 at 3.81%. The volatility itself usually comes from data, and the implied volatility guide shows how the market implied number is solved out of option prices.
CVaR: the average loss beyond the line
CVaR, also called expected shortfall, answers a harsher question: on the worst days, how much is lost on average? For a normal distribution it equals the portfolio times volatility times the square root of the horizon times the bell curve height at the z point, divided by the tail probability, minus the drift. At 95% that is 3,043.32, clearly above the 2,417.50 VaR line, because it averages every loss past the cutoff instead of marking the cutoff itself. The max drawdown guide looks at the same tail from the other side: not the modeled worst day, but the worst streak the portfolio actually recorded.
Why the horizon scales with the square root
Risk accumulates with the square root of time while drift accumulates linearly, so stretching the horizon widens the loss window faster than it raises the expected return. The tool makes the jump visible: one day is 2.42%, five days 5.27% at 5,267.50, twenty-one days 10.26% at 10,257.51, and the annual figure 26,570.35 comes from multiplying the daily volatility by the square root of 252, about 15.87. The Compound Interest Calculator shows the mirror image on the return side, where time compounds instead of spreading.
The drift term and the Sharpe connection
The daily return enters with a minus sign: 0.05% a day takes 50.00 off the one day loss, which is why the drift free 95% figure of 2,467.50 prints as 2,417.50. Set the return to zero and the VaR climbs back to 2,467.50; make it large and positive and the VaR shrinks, which is exactly the number to distrust, because a high drift estimate is doing all the work. The same two inputs, drift and volatility, are the numerator and denominator of the Sharpe Ratio Calculator: earning a lot per unit of risk is precisely what keeps the drift term large relative to the volatility term.
Where VaR sits in a risk pipeline
In practice the output is a budget, not a verdict. If the one day loss budget is 2,500, the 2,417.50 result fits inside it; halving the portfolio to 50,000 halves the VaR to 1,208.75, because the formula is linear in the portfolio value. The Position Sizing Calculator performs the same scaling from the other direction, starting from the account size and a per trade risk percentage. For a single trade rather than the whole book, the risk reward guide measures the same discipline at position level.