Value at Risk (VaR) & Expected Shortfall Calculator (Parametric)

How it works

σ_h = σ_daily × √h (σ_daily = σ_annual ÷ √252) · VaR = V × (z_c × σ_h − μ_h), z₉₅ = 1.645, z₉₉ = 2.326 · ES (CVaR) = V × σ_h × φ(z_c) ÷ (1 − c) − V μ_h · Student-t VaR = V × t_c(ν) × σ_h × √((ν − 2) ÷ ν)

Value at risk compresses a return distribution into one number: the loss that will be exceeded only a chosen small fraction of the time over a stated horizon. In its parametric form it takes the position's volatility, scales it to the horizon by the square root of time, and multiplies by the normal quantile for the confidence level; expected shortfall goes one step further and averages the losses beyond that threshold, which is why regulators moved to it — VaR says where the tail starts, not how long it is. Because real returns have fatter tails than the bell curve, a Student-t version or historical simulation is the honest companion at 99% and above.

Worked example

A $250,000 equity portfolio with 18% annual volatility has a daily σ of 1.13% and a 10-day σ of 3.59%; at 99% confidence the parametric VaR is about $20,900 (8.3%) and the expected shortfall about $23,900 (9.6%) — the average loss in the worst 1% of two-week periods. A Student-t with 4 degrees of freedom puts the 99% VaR near $23,700, about 14% higher, and such a loss should be exceeded roughly 2.5 ten-day windows a year.

Frequently asked questions