Execute the following steps to estimate the value-at-risk using Monte Carlo.

1. Import the libraries:

import numpy as np
import pandas as pd
import yfinance as yf
import seaborn as sns

2. Define the parameters that will be used for this exercise:

RISKY_ASSETS = ['GOOG', 'FB']
SHARES = [5, 5]
START_DATE = '2018-01-01'
END_DATE = '2018-12-31'
T = 1
N_SIMS = 10 ** 5

3. Download the data from Yahoo Finance:

df = yf.download(RISKY_ASSETS, start=START_DATE, 
                 end=END_DATE, adjusted=True)

4. Calculate the daily returns:

adj_close = df['Adj Close']
returns = adj_close.pct_change().dropna()
plot_title = f'{" vs. ".join(RISKY_ASSETS)} returns: {START_DATE} - 
                                                     {END_DATE}'
returns.plot(title=plot_title)

We also plot the calculated returns and calculate the Pearson's correlation of the two series:

The correlation between the two series is 0.62.

5. Calculate the covariance matrix:

cov_mat = returns.cov()

6. Perform the Cholesky decomposition of the covariance matrix:

chol_mat = np.linalg.cholesky(cov_mat)

7. Draw the correlated random numbers from the Standard Normal distribution:

rv = np.random.normal(size=(N_SIMS, len(RISKY_ASSETS)))
correlated_rv = np.transpose(np.matmul(chol_mat, np.transpose(rv)))

8. Define the metrics that will be used for simulations:

r = np.mean(returns, axis=0).values
sigma = np.std(returns, axis=0).values
S_0 = adj_close.values[-1, :]
P_0 = np.sum(SHARES * S_0)

9. Calculate the terminal price of the considered stocks:

S_T = S_0 * np.exp((r - 0.5 * sigma ** 2) * T + 
                   sigma * np.sqrt(T) * correlated_rv)

10. Calculate the terminal portfolio value and the portfolio returns:

P_T = np.sum(SHARES * S_T, axis=1)
P_diff = P_T - P_0

11. Calculate the VaR for the selected confidence levels:

P_diff_sorted = np.sort(P_diff)
percentiles = [0.01, 0.1, 1.]
var = np.percentile(P_diff_sorted, percentiles)

for x, y in zip(percentiles, var):
    print(f'1-day VaR with {100-x}% confidence: {-y:.2f}$')

Running the preceding code results in the following output:

1-day VaR with 99.99% confidence: 8.49$
1-day VaR with 99.9% confidence: 7.23$
1-day VaR with 99.0% confidence: 5.78$

12. Present the results on a graph:

ax = sns.distplot(P_diff, kde=False)
ax.set_title('''Distribution of possible 1-day changes 
             in portfolio value 
             1-day 99% VaR''', fontsize=16)
ax.axvline(var[2], 0, 10000);

Running the code results in the following plot:

The preceding plot shows the distribution of possible 1-day ahead portfolio values. We present the value-at-risk with the vertical line.