Value at Risk (VaR) formula: 95% / 99% Parametric VaR & √T horizon scaling

Why Value at Risk uses ONE-TAILED Z-scores (1.6449 for 95%, NOT 1.96!) and √T scaling

This educational model assumes normally distributed, independent daily returns with constant variance, zero mean return, a fixed portfolio exposure and a linear relationship between return and profit/loss. The positive one-tailed normal quantiles used here are rounded: 1.6449 for 95% and 2.3263 for 99%.

With a $1,000,000 portfolio and 1.5% daily volatility, the rounded 95% estimate is $24,673.50 for one day. Under the model, the probability of a larger loss is 5%; this is not a loss cap, a guarantee of future performance, or an estimate of loss severity beyond that threshold.

Square-root scaling gives $78,024.46 for ten days under the stated assumptions. Correlated returns, volatility changes, nonlinear positions and heavy tails can invalidate this scaling. This simple spreadsheet is not a regulatory capital or Basel-compliance model.

1-Day and Multi-Day √T Parametric Dollar Value at Risk formulas

Zero drift is an explicit simplifying assumption in this exercise. Use decimal volatility: 0.015 means 1.5%.

=IF(OR(COUNT(A2:C2)<>3,A2<0,B2<0,C2<=0),"Invalid inputs",ROUND(A2*B2*C2,2))

Multi-day horizon VaR scaled by the Square-Root-of-Time rule SQRT(D2)

Under independent daily returns, variance scales linearly with T, so volatility and VaR scale with SQRT(T).

=IF(OR(OR(COUNT(A2:C2)<>3,A2<0,B2<0,C2<=0),NOT(ISNUMBER(D2)),D2<1,D2<>INT(D2)),"Invalid inputs",ROUND(A2*B2*C2*SQRT(D2),2))

Further reading

• Microsoft Support — SQRT function
• Brummelhuis and Kaufmann — Value-at-Risk time scaling for long-term risk estimation