Daily VaR Calculator

Why daily VaR matters for routine oversight

Daily Value at Risk translates market uncertainty into a single, comparable loss threshold for a chosen confidence level. For example, a 99% one‑day VaR of 18,500 implies that only 1 day out of 100 is expected to lose more than 18,500, under the model assumptions. This makes VaR useful for setting trading limits, prioritizing hedges, and aligning risk appetite across desks.

Interpreting confidence and horizon correctly

Confidence controls the tail probability, while the horizon controls the time scale. A 95% VaR is less conservative than a 99% VaR because it tolerates more tail events. Multi‑day horizons commonly scale by the square root of time when returns are assumed independent and identically distributed. If volatility clusters, an EWMA estimate can adapt faster than a fixed input and may better reflect current conditions.

Choosing between parametric, historical, and simulation

Parametric VaR is fast and transparent, relying on mean and volatility plus a distribution quantile. Historical simulation uses the empirical return distribution and can capture skew and fat tails present in the data, but it depends heavily on the lookback window. Monte Carlo adds flexibility: you can simulate many scenarios and stress the distribution choice, which helps when portfolios include non‑linear exposures or when you want stable tail estimates.

Expected Shortfall adds depth beyond VaR

VaR answers “how bad is bad,” but it does not describe the average severity once that threshold is crossed. Expected Shortfall (ES), also called Conditional VaR, estimates the mean loss in the worst tail fraction. In practice, ES supports capital planning and contingency sizing because it is sensitive to extreme outcomes. Reporting VaR and ES together improves decision quality during regime shifts.

Data quality checks that improve reliability

Reliable VaR starts with clean inputs. Ensure returns are in decimals, prices are strictly positive, and the sample size is sufficient for the selected method. A 250‑day window is common for liquid assets, while shorter windows react faster but can be noisy. Review outliers, corporate actions, and missing values. Finally, backtest exceedances: if breaches occur more frequently than expected, recalibrate assumptions and controls. Document assumptions, repeat monthly, and align limits with liquidity conditions.

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FAQs

1) What does a negative VaR return mean?

VaR return is shown as a positive loss threshold after sign conversion. If your intermediate quantile is negative, the final VaR return is reported as a positive magnitude of loss.

2) Can I paste percentage returns like 1.2?

Yes. If the tool detects typical magnitudes consistent with percent points, it converts values to decimals automatically, so 1.2 becomes 0.012 for calculation.

3) How many observations should I use for historical VaR?

Use at least 250 observations for stable daily estimates when markets are liquid. Shorter windows respond faster to shocks but can produce volatile results and inconsistent tail behavior.

4) When should I prefer Student‑t over Normal?

Choose Student‑t when returns show fat tails or frequent outliers. It typically produces larger tail losses at the same confidence, improving conservatism during stressed periods.

5) Why does multi‑day VaR use square‑root scaling?

Square‑root scaling assumes independent daily returns with constant volatility, so variance grows linearly with time. If volatility clusters, consider EWMA or a simulation approach for multi‑day horizons.

6) What should I do if backtesting shows too many breaches?

Increase data quality checks, adjust the lookback, update volatility estimation, or move to a heavier‑tailed distribution. Also review position mapping and ensure the portfolio value reflects current exposure.