Value at Risk (VaR) Calculator

Value at Risk (VaR) is a standard risk management metric used to estimate the maximum potential loss a portfolio could suffer over a given time frame with a specific degree of confidence.

The Danger of Parametric VaR

The calculator above uses the Parametric (or Variance-Covariance) method. It is computationally elegant but harbors a dangerous assumption: it assumes financial returns are normally distributed.

As explored in our Monte Carlo and Black-Scholes sections, financial markets exhibit "fat tails" (kurtosis). Black swan events—like the 1987 crash or the 2020 pandemic—occur far more frequently than a normal distribution predicts.

During the 2007-2008 financial crisis, institutions discovered that their 99% VaR models vastly underestimated true risk because the models failed to account for extreme correlation breakdowns and non-linear derivatives.

Alternatives to Parametric VaR

To avoid the normality assumption, quants use:

1. Historical VaR: Directly sorts historical daily returns and finds the 1st percentile worst day. This doesn't assume a normal distribution, but it does assume the future will look like the past—a flaw when market regimes shift.
2. Monte Carlo VaR: Uses stochastic processes (often with jump-diffusion to model fat tails) to simulate millions of paths and calculate the VaR from the resulting distribution.
3. Conditional VaR (Expected Shortfall): VaR only tells you the threshold of pain. CVaR answers a more important question: If we breach the VaR threshold, how much will we actually lose?

Risk models are only as good as their inputs. A machine learning model that suffers from overfitting will produce artificially low volatility estimates, which feeds into VaR, leading to gross over-allocation. This is why aggressive strategies must be tempered by sizing frameworks like the Kelly Criterion.