Value at Risk (VaR) Calculator & Simulator

simulator intermediate ~10 min
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VaR ≈ $6,554 at 95% confidence over 10 days

A $100,000 portfolio with 20% annual volatility has a 95% parametric VaR of approximately $6,554 over 10 trading days. There is a 5% chance of losing more than this amount.

Formula

Parametric VaR = V · σ · z_α · √(T/252)
z_95% ≈ 1.645, z_99% ≈ 2.326
Expected Shortfall = E[Loss | Loss > VaR]

Quantifying the Downside

Value at Risk answers a deceptively simple question: how much could I lose? Specifically, VaR estimates the maximum portfolio loss over a defined period at a given confidence level. A 1-day 95% VaR of $50,000 means that on 19 out of 20 trading days, your losses should not exceed $50,000. It became the standard risk metric after JP Morgan published its RiskMetrics methodology in 1994, and regulators embedded it in the Basel capital framework.

Three Methods of Calculation

Parametric VaR assumes normally distributed returns and uses a formula involving portfolio volatility and the normal distribution's z-score. Historical VaR simply looks at past returns and picks the appropriate percentile. Monte Carlo VaR simulates thousands of future scenarios using random sampling. Each method has trade-offs: parametric is fast but assumes normality, historical captures real fat tails but requires extensive data, and Monte Carlo is flexible but computationally expensive.

Expected Shortfall: Beyond VaR

VaR has a critical blind spot: it tells you the threshold of the worst 5% (or 1%) of outcomes, but nothing about what happens beyond that threshold. Expected Shortfall (also called Conditional VaR) addresses this by averaging all losses that exceed the VaR level. After the 2008 financial crisis revealed that VaR underestimated catastrophic tail risks, the Basel Committee mandated Expected Shortfall as a supplementary measure for bank capital requirements.

Limitations and Lessons

The 2008 crisis exposed VaR's deepest flaw: it is only as good as its assumptions. Normal distribution assumptions miss extreme events. Correlation structures break down in crises — assets that seem independent suddenly crash together. VaR gives a false sense of precision in calm markets and fails precisely when you need it most. Modern risk management uses VaR alongside stress testing, scenario analysis, and Expected Shortfall to build a more complete picture of portfolio risk.

FAQ

What is Value at Risk (VaR)?

Value at Risk estimates the maximum loss a portfolio could suffer over a given time period at a specified confidence level. For example, a 1-day 95% VaR of $10,000 means there is a 5% chance of losing more than $10,000 in a single day. It is the most widely used risk metric in banking and portfolio management.

What is the difference between parametric and Monte Carlo VaR?

Parametric VaR assumes returns are normally distributed and uses a simple formula: VaR = V × σ × z × √T. Monte Carlo VaR simulates thousands of possible future scenarios without assuming normality, capturing fat tails and nonlinear exposures. Monte Carlo is more flexible but computationally intensive.

What is Expected Shortfall (CVaR)?

Expected Shortfall, also called Conditional VaR, measures the average loss in scenarios worse than the VaR threshold. Unlike VaR, which only tells you the boundary of the worst-case, Expected Shortfall answers 'how bad is it when things go wrong?' It is considered a more coherent risk measure.

Why do regulators require VaR?

The Basel Accords require banks to calculate VaR to determine minimum capital reserves. VaR provides a standardized, comparable risk measure across institutions and asset classes. After the 2008 crisis, regulators added Expected Shortfall requirements to better capture tail risks that VaR alone misses.

Sources

Embed

<iframe src="https://homo-deus.com/lab/finance/portfolio-var/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub