Value at Risk (VaR)
Value at Risk answers a simple, crucial question: "What is my worst-case scenario over a given time horizon, at a certain confidence level?"
For example, if a portfolio has a one-day 95% VaR of $1 million, it means there is a 95% confidence that the portfolio will not lose more than $1 million in a single trading day.
Calculation Methodologies
Institutions typically employ three primary methods to calculate VaR, each with distinct assumptions regarding market behavior.
1. Historical Simulation
Assumes that history will repeat itself. Applies actual historical returns of the assets in the portfolio over a defined period (e.g., the last 1,000 trading days) to the current portfolio weights to create a distribution of simulated past returns, then finds the percentile corresponding to the confidence level.
2. Variance-Covariance (Parametric)
Assumes asset returns are normally distributed. Requires estimation of expected returns, standard deviations (volatility), and the covariance matrix of the assets. Computationally fast but struggles with fat-tailed distributions (kurtosis).
3. Monte Carlo Simulation
Develops a model for future stock price returns based on stochastic processes and runs thousands of hypothetical trials. Highly flexible and can account for non-linear instruments like options, but computationally intensive.
Limitations (The "Fat Tail" Problem)
VaR models, particularly Parametric ones, often assume normal distributions. However, financial markets frequently exhibit "fat tails"—extreme events (black swans) occur more frequently than a normal bell curve predicts.
Furthermore, VaR tells you the threshold of loss, but not the magnitude of loss beyond that threshold. For this reason, institutions pair VaR with Conditional VaR (CVaR) or Expected Shortfall, which calculates the average loss in the worst-case scenarios.