Value at Risk (VaR) Calculator — Parametric Method
Enter portfolio size, daily return volatility, confidence level, and holding period to calculate the parametric Value at Risk (VaR) — the maximum loss not exceeded with a given probability — plus the Expected Shortfall (CVaR) for the tail beyond VaR.
%
Επίπεδο εμπιστοσύνης
trading days
Parametric VaR at 95 % confidence over 1 trading day(s)
- 1
Daily volatility (decimal)
σ = 1,5% ÷ 100 = 0,015 - 2
Horizon scaling factor
√1 trading days = 1 - 3
Value at Risk
1.000.000 × 0,015 × 1,645 × 1 = 24.675z = 1.645 corresponds to the 95% confidence level.
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Parametric VaR = Portfolio × σ_daily × z × √t, where σ_daily is the daily return volatility and z is the confidence-level z-score (1.645 at 95 %, 2.326 at 99 %). It estimates the worst expected loss at the chosen confidence over t trading days, assuming normally distributed returns.
Τύπος
How this is calculated
The parametric (variance-covariance) VaR method assumes that daily portfolio returns are normally distributed with mean zero and standard deviation σ_daily. Under that assumption, the probability-weighted worst loss over a holding period of t trading days is VaR = P × σ_daily × z × √t, where z is the standard normal quantile for the chosen confidence level (z = 1.645 for 95 %, 2.326 for 99 %) and the √t scaling converts daily volatility to the t-day horizon (assuming i.i.d. returns).
The Expected Shortfall (CVaR) is the average loss given that the loss exceeds VaR: CVaR = P × σ_daily × φ(z) / (1 − CL) × √t, where φ is the standard normal PDF. CVaR is a coherent risk measure and is preferred in Fundamental Review of the Trading Book (FRTB) regulation.
Important limitations: parametric VaR underestimates risk when returns have fat tails (kurtosis > 3), are skewed, or are non-stationary. It ignores liquidity risk, event risk, and correlation changes under stress. Use it as a first-order estimate; complement it with historical simulation, Monte Carlo, or stress testing for production risk systems.
Συχνές ερωτήσεις
A 95 % VaR of $50 000 means there is a 5 % probability that the portfolio will lose more than $50 000 over the specified holding period, assuming the return distribution is correct. On average, losses will exceed this threshold roughly 1 in 20 trading days.
Basel II and the original Basel III market-risk framework used 99 % VaR over a 10-day horizon. The Fundamental Review of the Trading Book (FRTB, 2019) replaced VaR with Expected Shortfall at 97.5 % confidence, which better captures tail risk.
Under the square-root-of-time rule, volatility and therefore VaR scale with √t. A 10-day VaR is about √10 ≈ 3.16 times the 1-day VaR. This scaling is exact only when daily returns are independent and identically distributed (i.i.d.), which is an approximation in practice.
TG we-Calculate Editorial Team. (2026). Value at Risk (VaR) Calculator — Parametric Method [Online calculator]. TG we-Calculate. https://we-calculate.com/el/calculator/var-calculator
TG we-Calculate Editorial Team. "Value at Risk (VaR) Calculator — Parametric Method." TG we-Calculate. 2026. https://we-calculate.com/el/calculator/var-calculator.
TG we-Calculate Editorial Team, "Value at Risk (VaR) Calculator — Parametric Method," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/el/calculator/var-calculator
@misc{wecalculate_var_calculator, title = {Value at Risk (VaR) Calculator — Parametric Method}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/el/calculator/var-calculator}}, year = {2026}, note = {TG we-Calculate} }
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