Value at Risk (VaR) Calculator: Parametric VaR and Expected Shortfall

Enter Values

Portfolio Value

Total portfolio market value

Daily Volatility (σ)

Daily standard deviation of returns

Confidence Level

Higher confidence = larger VaR estimate

Time Horizon

trading days

1 day (trading), 10 days (Basel), 252 days (1 year)

Include Expected Return (μ)

VaR Formula

VaR = V × z_α × σ × √T

V = Portfolio value | z_α = z-score | σ = Daily vol | T = Days

Calculator by Ryan O'Connell, CFA

Risk Metrics

Value at Risk (VaR) $24,675.00 Moderate Risk

Expected Shortfall (CVaR) $30,939.00 Moderate Risk

VaR % 2.47%

ES % 3.09%

z-Score 1.645

Annual Vol 23.81%

Formula Breakdown

VaR = V × z_α × σ × √T

ES = V × σ × √T × φ(z) / (1 − α)

Risk Level Guide

VaR % of Portfolio	Risk Level	Description
< 2%	Low Risk	Conservative risk exposure
2% – 5%	Moderate Risk	Typical risk level
5% – 10%	Elevated Risk	Above-average risk exposure
> 10%	High Risk	Significant portfolio risk

Heuristic thresholds for educational purposes. Actual risk tolerance varies by investor and asset class.

Model Assumptions

Assumes normally distributed returns (parametric/variance-covariance method)
Single-asset portfolio (or portfolio treated as single position with given volatility)
Constant volatility over the time horizon
Square root of time scaling (assumes independent, identically distributed returns)
No leverage or non-linear positions (linear model)

For educational purposes. Not financial advice. Market conventions simplified.

Understanding Value at Risk and Expected Shortfall

Video Explanation

Video: Value at Risk Explained

What is Value at Risk?

Value at Risk (VaR) is a statistical measure that estimates the maximum potential loss of a portfolio over a specified time period at a given confidence level. It answers the question: "How bad can things get under normal market conditions?"

For example, a 95% one-day VaR of $100,000 means there is a 5% chance of losing more than $100,000 in a single trading day. VaR is a quantile of the loss distribution — it is not the maximum possible loss.

Parametric VaR Formula

VaR = V × z_α × σ × √T
V = portfolio value, z = z-score, σ = daily volatility, T = days

VaR vs Expected Shortfall

Value at Risk

Threshold measure
"How bad can things get?" Gives the loss level that will not be exceeded with probability α.

Expected Shortfall

Tail average
"If things do get bad, how much do we lose?" Average loss in the worst (1−α) scenarios.

The Three VaR Methods

Parametric (this calculator): Assumes normal distribution. Fast, closed-form solution using z-scores and standard deviation.
Historical Simulation: Uses actual past returns. No distributional assumptions, but limited by available data. See Hull Chapter 22.
Monte Carlo Simulation: Generates thousands of random scenarios. Flexible but computationally intensive.

Regulatory Context

Bank regulators historically used 99% 10-day VaR for market risk capital (Basel I–III). Basel IV (FRTB) switched to 97.5% Expected Shortfall, recognizing that ES is a coherent risk measure that better captures tail risk and respects diversification benefits.

Learn more: Read our articles on Value at Risk, Expected Shortfall (CVaR), and Standard Deviation in Finance.

Frequently Asked Questions

Value at Risk (VaR) is a quantile-based risk measure that estimates the maximum potential loss of a portfolio over a specified time period at a given confidence level. For example, a 95% one-day VaR of $1 million means there is a 5% probability that the portfolio will lose more than $1 million in a single trading day. Importantly, VaR is not the maximum possible loss — it is a threshold that losses are unlikely to exceed under normal market conditions.

VaR tells you the loss threshold at a given confidence level, while Expected Shortfall (ES), also called Conditional VaR (CVaR), tells you the average loss when that threshold is exceeded. ES is considered a superior risk measure because it is "coherent" — it satisfies subadditivity, meaning diversification never increases risk under ES. VaR can violate this property, which is why Basel IV (FRTB) switched to 97.5% ES for market risk capital requirements.

A 95% VaR of $500,000 means you are 95% confident that portfolio losses will not exceed $500,000 over the specified time horizon. Equivalently, there is a 5% chance of losing more than $500,000. This does not tell you how much you could lose in that worst 5% — for that information, you need Expected Shortfall, which measures the average loss in those tail scenarios.

The three main VaR calculation methods are: (1) Parametric (variance-covariance) — assumes returns are normally distributed and uses standard deviation and z-scores for a closed-form solution; (2) Historical simulation — uses actual past returns to build the loss distribution without assuming any particular distribution; (3) Monte Carlo simulation — generates thousands of random scenarios using assumed return distributions to estimate the loss distribution. This calculator uses the parametric method.

Regulators prefer Expected Shortfall because it is a "coherent" risk measure that satisfies subadditivity — the ES of a combined portfolio is never greater than the sum of the individual portfolio ES values. VaR can violate this property, potentially penalizing diversification. ES also captures the severity of tail losses, not just whether they exceed a threshold. The Basel IV Fundamental Review of the Trading Book (FRTB) switched from 99% VaR to 97.5% ES for calculating market risk capital.

The square root of time rule scales one-day VaR to multi-day VaR by multiplying by √N (the number of days). For example, 10-day VaR is approximately 3.16 times the one-day VaR. This rule assumes returns are independent, identically distributed (i.i.d.) with zero mean. The rule breaks down when returns exhibit autocorrelation, volatility clustering, or mean reversion — which is common in practice over longer horizons.

Disclaimer

This calculator is for educational purposes only and uses the parametric (normal distribution) method. Actual portfolio risk involves additional factors including fat tails, volatility clustering, correlation breakdowns during crises, and non-linear exposures. For professional risk management, use historical simulation or Monte Carlo methods with validated models. This tool should not be used for trading or capital allocation decisions.

Value at Risk (VaR) Calculator

Enter Values

VaR Formula

Risk Metrics

Formula Breakdown

Risk Level Guide

Model Assumptions

Understanding Value at Risk and Expected Shortfall

Video Explanation

What is Value at Risk?

VaR vs Expected Shortfall

Value at Risk

Expected Shortfall

The Three VaR Methods

Regulatory Context

Frequently Asked Questions

What is Value at Risk (VaR)?

What is the difference between VaR and Expected Shortfall (CVaR)?

How do you interpret a 95% VaR?

What are the three main methods for calculating VaR?

Why do regulators prefer Expected Shortfall over VaR?

What is the square root of time rule in VaR?

Disclaimer

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