What is Value at Risk (VaR)?

Value at Risk (VaR) is the maximum expected loss over a specified time horizon at a given confidence level. For example, a 1-day 95% VaR of $5,000 means there is a 5% probability of losing more than $5,000 on any given trading day. VaR is the most widely used risk measurement in banking and investment management, required by regulators for capital adequacy calculation under Basel III.

What is the difference between VaR and CVaR?

VaR answers: 'What is the maximum loss at a given confidence level?' CVaR (Conditional VaR, also called Expected Shortfall) answers: 'When losses DO exceed the VaR threshold, what is the average loss?' CVaR is always larger than VaR and provides more information about tail risk. For example, if 95% VaR is $5,000, the 95% CVaR might be $7,500 — meaning that on the 5% of days when the VaR is breached, the average loss is $7,500. Basel III prefers CVaR (Expected Shortfall) over VaR for this reason.

What is VaR backtesting?

VaR backtesting compares a model's predicted VaR against actual realized returns to assess whether the model is well-calibrated. A 95% VaR should be breached on approximately 5% of days. If breaches occur too frequently the model underestimates risk; too rarely and it is overly conservative. The Kupiec test is a formal statistical test for this. The Basel III traffic light system classifies models as Green (0–4 breaches in 250 days), Amber (5–9 breaches) or Red (10+ breaches, model rejected).

How does diversification reduce portfolio VaR?

When assets have less than perfect positive correlation, combining them in a portfolio produces lower VaR than the weighted sum of individual VaRs. Portfolio VaR is calculated from the full covariance matrix: σ_p² = Σᵢ Σⱼ wᵢ wⱼ σᵢ σⱼ ρᵢⱼ. Assets with low or negative correlations provide meaningful diversification — the reduction in VaR versus weighted average standalone VaR is the diversification benefit.

Is this VaR calculator free?

Yes. The Value at Risk Calculator Pro on StockToolHub is completely free with no registration, account, or subscription required. All five tabs — Parametric VaR, Historical VaR, Monte Carlo VaR, Multi-Asset VaR, and Backtesting — are fully accessible.

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Value at Risk (VaR) Calculator Pro

Q: What are the three main VaR calculation methods?

The three main methods are: Parametric VaR (assumes returns are normally distributed — uses mean and standard deviation to compute VaR analytically; fast but inaccurate for non-normal distributions), Historical VaR (uses actual historical return observations to compute empirical percentiles — no distributional assumption; captures real skewness and fat tails but limited by available history), and Monte Carlo VaR (simulates thousands of random scenarios from a specified distribution — highly flexible and can incorporate fat tails, correlations and complex instruments; computationally intensive).

Calculate the maximum expected portfolio loss across five professional methods — parametric VaR using the normal distribution, historical simulation from an actual return series, Monte Carlo simulation with thousands of scenarios, multi-asset portfolio VaR from the full covariance matrix, and VaR model backtesting against real outcomes. All methods compute both VaR and CVaR (Expected Shortfall) at multiple confidence levels.

Portfolio Parameters

Portfolio Value

Expected Daily Return

Set 0 for conservative estimate

Daily Volatility (σ)

Ann. vol ÷ √252

Holding Period

days

Ann. Volatility opt

Auto-fills daily σ

Confidence Levels

90% 95% 99% 99.5%

1-Day VaR (95% Confidence)

—

5% probability of losing more than this amount in one day

Confidence	Z-Score	VaR ($)	VaR (%)	CVaR ($)	CVaR (%)

Daily Volatility

—

1σ Daily Range

—

10-Day VaR (95%)

—

Annual VaR (95%)

—

Normal Distribution — Return Distribution & VaR Thresholds

Portfolio Value

Historical Returns (%)

Return series (comma-separated)

Enter daily percentage returns. Minimum 20 observations recommended.

Holding Period

days

Weighting

Historical VaR (95%)

—

Enter a return series of at least 20 observations

Confidence	Percentile	VaR ($)	VaR (%)	CVaR ($)	CVaR (%)

Observations

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Mean Return

—

Worst Day

—

Best Day

—

Return Distribution Histogram — Historical Percentiles

Simulation Parameters

Portfolio Value

Daily Return (μ)

Daily Volatility (σ)

Simulations

Horizon

days

Fat Tail Multiplier optional

1.0 = normal | 1.2–1.5 = heavier tails (t-distribution approximation)

Monte Carlo VaR (95%)

—

Configure parameters and click Run Simulation

Confidence	VaR ($)	VaR (%)	CVaR ($)	CVaR (%)	vs Parametric

Simulations Run

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Simulated Mean

—

Worst Scenario

—

Best Scenario

—

Monte Carlo — Simulated Return Distribution

Asset / Ticker	Weight (%)	Daily Vol (%)

Portfolio VaR

—

Enter assets, weights, volatilities and correlations

Portfolio CVaR

—

Portfolio Daily Vol

—

Weighted Avg Vol

—

Div. Benefit

—

VaR Contribution by Asset

What each tab calculates

Parametric VaR

Calculates VaR and CVaR using the normal distribution with portfolio value, daily return and daily volatility. Scales to any holding period via the square-root-of-time rule. Shows a VaR table at 90%, 95%, 99% and 99.5% confidence with a normal distribution chart and VaR threshold markers.

Historical VaR

Computes VaR directly from a user-entered return series using empirical percentiles — no distributional assumption required. Supports equal weighting and exponential decay (EWMA with λ=0.94). Shows a histogram of the actual return distribution with VaR markers.

Monte Carlo VaR

Runs up to 10,000 simulated scenarios from the input distribution parameters with an optional fat-tail multiplier for t-distribution approximation. Computes VaR and CVaR from the simulation results and compares against the equivalent parametric estimate.

Multi-Asset VaR

Calculates portfolio VaR from the full covariance matrix across up to 6 assets using individual weights, daily volatilities, and pairwise correlation coefficients. Shows diversification benefit versus the weighted average standalone VaR and a VaR contribution bar chart.

Backtesting

Tests VaR model accuracy by comparing predicted VaR against actual realized returns. Counts breaches, calculates the breach rate, and applies the Kupiec likelihood ratio test. Classifies the model under the Basel III traffic light system (Green / Amber / Red zone) with a breach timeline chart.