This article provides a detailed exploration of three different approaches for calculating Value at Risk (VaR) – Historical, Variance-Covariance, and Monte Carlo Simulation. The analysis is based on Nifty data spanning from January 1, 2021, to August 14, 2023, and the confidence level chosen is 99%. Here are the results:
- Historical VaR: 2.64%
- Variance-Covariance VaR: 2.17%
- Monte Carlo VaR: 2.18%
The study offers insights into how these approaches are applied and compares their outcomes in assessing risk.
# Importing libraries
import numpy as np
import pandas as pd
import yfinance as yf
import warnings
warnings.filterwarnings("ignore")
# Getting Historical data of Nifty from Yahoo Finance
df = yf.download('^NSEI', '2021-01-01', '2023-08-14')
df = df[['Close']]
df['returns'] = df.Close.pct_change()
# Calculating Historical VaR
Historical_VaR_99 = df['returns'].quantile(0.01)
print(Historical_VaR_99)
# Calculating Variance - Covariance VaR
mean = np.mean(df['returns'])
std_dev = np.std(df['returns'])
VarianceCovariance_VaR_99 = norm.ppf(0.01, mean, std_dev)
print(VarianceCovariance_VaR_99)
# Calculating Montecarlo Simulation VaR
np.random.seed(42)
n_sims = 1000000
simulated_returns = np.random.normal(mean, std_dev,n_sims)
Simulated_VaR_99 = np.percentile(simulated_returns,1)
print(Simulated_VaR_99)
Output of the above code
