Risk Metrics in Python

Risk management is what separates professionals from gamblers. This guide covers the essential risk metrics every quant should know — with Python code for each method.

Setup: Get the Data

import yfinance as yf import numpy as np import pandas as pd import matplotlib.pyplot as plt from scipy import stats # Download stock data ticker = "AAPL" df = yf.download(ticker, start="2020-01-01", end="2024-01-01") returns = df["Close"].pct_change().dropna() portfolio_value = 100000  # $100,000 portfolio confidence = 0.95

Method 1: Historical VaR

The simplest approach. Sort all historical returns and find the 5th percentile. No assumptions about distribution needed.

# Historical VaR: just sort returns and find the percentile historical_var = np.percentile(returns, (1 - confidence) * 100) print(f"Historical VaR (95%, 1-day): {{historical_var:.4f}} ({{historical_var:.2%}})") print(f"On a ${{portfolio_value:,.0f}} portfolio: ${{abs(historical_var * portfolio_value):,.2f}} max daily loss") # Visualise plt.figure(figsize=(10, 5)) plt.hist(returns, bins=100, color="teal", alpha=0.7, edgecolor="black") plt.axvline(x=historical_var, color="red", linewidth=2, label=f"95% VaR: {{historical_var:.2%}}") plt.title(f"{{ticker}} Daily Returns Distribution with VaR") plt.xlabel("Daily Return") plt.ylabel("Frequency") plt.legend() plt.grid(True, alpha=0.3) plt.tight_layout() plt.show()

Method 2: Parametric VaR

Assumes returns follow a normal distribution. Faster to compute but less accurate (real returns have fat tails).

# Parametric (Gaussian) VaR mean_return = returns.mean() std_return = returns.std() # Z-score for 95% confidence = 1.645 z_score = stats.norm.ppf(1 - confidence) parametric_var = mean_return + z_score * std_return print(f"Parametric VaR (95%, 1-day): {{parametric_var:.4f}} ({{parametric_var:.2%}})") print(f"On a ${{portfolio_value:,.0f}} portfolio: ${{abs(parametric_var * portfolio_value):,.2f}}")

Method 3: Monte Carlo VaR

Simulate thousands of possible future returns using random sampling. The most flexible method — you can model any distribution.

# Monte Carlo VaR: simulate 10,000 possible next-day returns np.random.seed(42) num_simulations = 10000 # Simulate returns from the historical distribution simulated_returns = np.random.normal(mean_return, std_return, num_simulations) # VaR from simulated distribution mc_var = np.percentile(simulated_returns, (1 - confidence) * 100) print(f"Monte Carlo VaR (95%, 1-day): {{mc_var:.4f}} ({{mc_var:.2%}})") print(f"On a ${{portfolio_value:,.0f}} portfolio: ${{abs(mc_var * portfolio_value):,.2f}}")

Conditional VaR (Expected Shortfall)

# CVaR: average of returns beyond the VaR threshold cvar = returns[returns <= historical_var].mean() print(f"CVaR (Expected Shortfall, 95%): {{cvar:.4f}} ({{cvar:.2%}})") print(f"When things go wrong, average loss: ${{abs(cvar * portfolio_value):,.2f}}")

Maximum Drawdown

# Maximum Drawdown: largest peak-to-trough decline cumulative = (1 + returns).cumprod() rolling_max = cumulative.cummax() drawdown = (cumulative - rolling_max) / rolling_max max_dd = drawdown.min() max_dd_date = drawdown.idxmin() print(f"Maximum Drawdown: {{max_dd:.2%}}") print(f"Occurred on: {{max_dd_date.date()}}") # Plot drawdown plt.figure(figsize=(12, 4)) plt.fill_between(drawdown.index, drawdown, 0, color="red", alpha=0.3) plt.plot(drawdown.index, drawdown, color="red", linewidth=0.5) plt.title(f"{{ticker}} Drawdown Over Time") plt.xlabel("Date") plt.ylabel("Drawdown") plt.grid(True, alpha=0.3) plt.tight_layout() plt.show()

Summary of All Risk Metrics

# All risk metrics in one place print(f"=== Risk Report for {{ticker}} ===") print(f"Portfolio value:     ${{portfolio_value:,.0f}}") print(f"Historical VaR 95%: {{historical_var:.2%}} (${{abs(historical_var * portfolio_value):,.0f}})") print(f"Parametric VaR 95%: {{parametric_var:.2%}} (${{abs(parametric_var * portfolio_value):,.0f}})") print(f"Monte Carlo VaR 95%:{{mc_var:.2%}} (${{abs(mc_var * portfolio_value):,.0f}})") print(f"CVaR (Exp. Short.): {{cvar:.2%}} (${{abs(cvar * portfolio_value):,.0f}})") print(f"Max Drawdown:       {{max_dd:.2%}}") print(f"Annual Volatility:  {{std_return * np.sqrt(252):.2%}}")