Value at Risk (VaR) in Python

A statistical measure estimating the maximum expected loss over a given time horizon at a specified confidence level.

Definition

Value at Risk (VaR) is the most widely used risk management metric in institutional finance. It provides a probabilistic estimate of the maximum loss a portfolio is expected to suffer over a defined time period, given normal market conditions, at a specified confidence level (typically 95% or 99%). VaR does not describe the loss beyond that threshold — it only defines the floor of the tail. Three primary methods exist: Historical Simulation, Parametric (Variance-Covariance), and Monte Carlo Simulation.

Quantitative Formula

VaR_{\alpha} = -\inf\{l \in \mathbb{R} : P(L > l) \leq 1 - \alpha\}

Where $\alpha$ is the confidence level (e.g., 0.95 or 0.99), $L$ is the loss random variable, and the expression identifies the smallest loss threshold $l$ such that the probability of exceeding it is at most $1 - \alpha$ . For the parametric method: $VaR_{\alpha} = \mu + z_{\alpha} \cdot \sigma$ , where $z_{\alpha}$ is the z-score corresponding to the confidence level.

Why It Matters in Backtesting

Regulators (Basel III) require banks to compute VaR daily. In backtesting, computing Historical VaR on your simulated P&L series allows you to validate whether your strategy's actual tail losses exceeded their predicted frequency — a critical test for model validity. A well-calibrated model should breach its 99% VaR approximately 1% of trading days. Frequent breaches indicate fat-tailed return distributions that your model underestimates.

Python Implementation

import numpy as np
    import pandas as pd

    def calculate_var(returns: pd.Series, confidence_level: float = 0.95, method: str = "historical") -> dict:
        """
        Calculates Value at Risk using Historical or Parametric method.
        confidence_level: e.g. 0.95 for 95% VaR.
        method: 'historical' or 'parametric'.
        """
        if method == "historical":
            var = np.percentile(returns, (1 - confidence_level) * 100)
        elif method == "parametric":
            z_score = abs(np.percentile(np.random.standard_normal(100000), (1 - confidence_level) * 100))
            var = -(returns.mean() + z_score * returns.std())
        else:
            raise ValueError("Method must be 'historical' or 'parametric'.")
        breaches = (returns < var).sum()
        breach_rate = breaches / len(returns)
        return {
            "var": var,
            "confidence_level": confidence_level,
            "method": method,
            "expected_breach_rate": 1 - confidence_level,
            "actual_breach_rate": breach_rate,
            "model_accurate": abs(breach_rate - (1 - confidence_level)) < 0.01
        }

Test this in a live environment

Stop running Jupyter notebooks locally. Paste this Value at Risk (VaR) code directly into Valetha's Strategy Lab and run a full historical backtest in seconds.