 answers one simple but powerful question:

“What is the maximum loss I can expect over a given time horizon, with a given confidence level?”

There is a 95% probability that my loss tomorrow will not exceed ₹25,000.

If rp is the ((1-alpha)  percentile of returns:

import yfinance as yf
import numpy as np

# Download data
data = yf.download("AAPL", start="2022-01-01", end="2024-01-01")
prices = data['Close']

# Log returns
returns = np.log(prices / prices.shift(1)).dropna()

# Historical VaR (95%)
confidence_level = 0.95
VaR_hist = -np.percentile(returns, (1 - confidence_level) * 100)

print("Historical VaR (95%):", VaR_hist)


There is a 95% chance daily loss will not exceed 

🔹 Method 2: Parametric (Variance-Covariance) VaR

from scipy.stats import norm

mu = returns.mean()
sigma = returns.std()

confidence_level = 0.95
z = norm.ppf(1 - confidence_level)

VaR_parametric = -(mu + z * sigma)

print("Parametric VaR (95%):", VaR_parametric)


“Let’s simulate thousands of possible futures.”

num_simulations = 100000

# Simulated returns
simulated_returns = np.random.normal(mu, sigma, num_simulations)

# Monte Carlo VaR
VaR_mc = -np.percentile(simulated_returns, (1 - confidence_level) * 100)

print("Monte Carlo VaR (95%):", VaR_mc)
