import numpy as np
import pandas as pd

# Assuming you have the daily returns data as an array called 'returns'
returns = [0.01, -0.02, 0.03, -0.01]  # Replace with your actual data

# Specify the confidence level (95%)
confidence_level = 0.95

# Calculate the portfolio value
portfolio_value = 100000

# Sort the returns in ascending order
sorted_returns = sorted(returns)

# Determine the index corresponding to the desired percentile
index = int((1 - confidence_level) * len(sorted_returns))

# Retrieve the historical return at the determined index
historical_return = sorted_returns[index]

# Calculate VaR using Historical VaR formula
historical_var = -portfolio_value * historical_return

# Calculate the weighted returns of each asset
weights = np.array([1 / len(returns)] * len(returns))
weighted_returns = np.multiply(returns, weights)

# Calculate the portfolio return
portfolio_return = np.sum(weighted_returns)

# Print the results
print("Historical VaR at", confidence_level * 100, "% confidence level:", historical_var)
print("Portfolio Return:", portfolio_return)

Historical VaR at 95.0 % confidence level: 2000.0
Portfolio Return: 0.002499999999999999

# Parameter VaR: example
import numpy as np
from scipy.stats import norm

def calculate_var(portfolio_value, returns, confidence_level):
    # Calculate portfolio returns' standard deviation
    returns_std = np.std(returns)

    # Determine the z-score corresponding to the desired confidence level
    z_score = norm.ppf(1 - confidence_level)

    # Calculate VaR using the Parametric VaR formula
    var = portfolio_value * z_score * returns_std

    return var

# Example usage
portfolio_value = 100000  # Total portfolio value
returns = np.array([0.01, -0.02, 0.03, -0.01])  # Sample returns data
confidence_level = 0.95  # Confidence level of 95%

par_var = - calculate_var(portfolio_value, returns, confidence_level)
print("VaR at 95% confidence level:", par_var)

VaR at 95% confidence level: 3158.5901106311394

# Monte carlo simulation using normal distribution

import numpy as np
import pandas as pd

# Example portfolio simulation using Monte Carlo
num_simulations = 10000
portfolio_value = 1000000
initial_investment = 1000000
expected_return = 0.08 # 8% return
volatility = 0.2

# Generate random returns based on normal distribution
returns = np.random.normal(expected_return, volatility, num_simulations)

# Calculate portfolio values for each simulation
portfolio_values = initial_investment * (1 + returns)

# Sort the simulated portfolio values
sorted_portfolio_values = np.sort(portfolio_values)

# Define the desired confidence level (e.g., 95%)
confidence_level = 0.95

# Calculate the VaR at the desired confidence level
percentile = 1 - confidence_level
index = int(percentile * num_simulations)
var = initial_investment - sorted_portfolio_values[index]

# Create a dataframe to store the portfolio returns
df_portfolio_returns = pd.DataFrame({'Portfolio Return': portfolio_values})

# Print the result
print("VaR at", confidence_level * 100, "% confidence level:", var)
print("Portfolio return for each simulation:\n", df_portfolio_returns)

VaR at 95.0 % confidence level: 242443.6554306997
Portfolio return for each simulation:
       Portfolio Return
0         9.818251e+05
1         1.174371e+06
2         1.006901e+06
3         1.037849e+06
4         1.167950e+06
...                ...
9995      1.129363e+06
9996      1.470854e+06
9997      1.229015e+06
9998      1.514311e+06
9999      1.223820e+06

[10000 rows x 1 columns]

import matplotlib.pyplot as plt
# Plot histogram of portfolio returns
plt.figure(figsize=(10, 6))
plt.hist(portfolio_values, bins=50, color='skyblue', edgecolor='black')
plt.axvline(var, color='red', linestyle='dashed', linewidth=2, label='VaR at 95%')
plt.xlabel('Portfolio Return')
plt.ylabel('Frequency')
plt.title('normal-Distribution of Portfolio Returns')
plt.legend()
plt.grid(True)
plt.show()

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# Example portfolio simulation using Monte Carlo
num_simulations = 10000
portfolio_value = 1000000
initial_investment = 1000000
expected_return = 0.08 # 8% return
volatility = 0.2

# Generate random returns based on t-distribution
degrees_of_freedom = 10  # Adjust the degrees of freedom as needed
returns1 = np.random.standard_t(degrees_of_freedom, num_simulations)

# Calculate portfolio values for each simulation
portfolio_values1 = initial_investment * (1 + returns1)

# Sort the simulated portfolio values
sorted_portfolio_values1 = np.sort(portfolio_values1)

# Define the desired confidence level (e.g., 95%)
confidence_level = 0.95

# Calculate the VaR at the desired confidence level
percentile = 1 - confidence_level
index = int(percentile * num_simulations)
tvar = initial_investment - sorted_portfolio_values1[index]

# Create a dataframe to store the portfolio returns
df_portfolio_returns1 = pd.DataFrame({'Portfolio Return': portfolio_values1})

# Print the result
print("VaR at", confidence_level * 100, "% confidence level:", tvar)
print("Portfolio return for each simulation:\n", df_portfolio_returns1)

# Plot histogram of portfolio returns
plt.figure(figsize=(10, 6))
plt.hist(portfolio_values1, bins=50, color='skyblue', edgecolor='black')
plt.axvline(tvar, color='red', linestyle='dashed', linewidth=2, label='t-distribution VaR at 95%')
plt.axvline(var, color='blue', linestyle=':', linewidth=2, label='normal-distribution VaR at 95%') # calculated previosuly
plt.xlabel('Portfolio Return')
plt.ylabel('Frequency')
plt.title('t-Distribution of Portfolio Returns')
plt.legend()
plt.grid(True)
plt.show()

VaR at 95.0 % confidence level: 1808807.650447472
Portfolio return for each simulation:
       Portfolio Return
0         1.610446e+06
1         2.395520e+06
2         3.708464e+04
3         5.411488e+05
4         1.569818e+06
...                ...
9995      1.827206e+06
9996     -4.927888e+05
9997      9.117096e+05
9998     -8.892813e+04
9999     -2.222589e+05

[10000 rows x 1 columns]

import numpy as np

# Define variables and assumptions
initial_investment = 10000
annual_return = 0.08
volatility = 0.15
investment_period = 10
num_simulations = 1000

# Generate random samples
random_returns = np.random.normal(annual_return, volatility, size=(num_simulations, investment_period))

# Perform simulations
investment_values = initial_investment * np.cumprod(1 + random_returns, axis=1)

# Analyze the results
mean_value = np.mean(investment_values, axis=0)
std_dev = np.std(investment_values, axis=0)
lower_bound = np.percentile(investment_values, 5, axis=0)
upper_bound = np.percentile(investment_values, 95, axis=0)

# Print the results
for year in range(investment_period):
    print(f"Year {year+1}: Mean Value = {mean_value[year]:.2f}, "
          f"Standard Deviation = {std_dev[year]:.2f}, "
          f"5th Percentile = {lower_bound[year]:.2f}, "
          f"95th Percentile = {upper_bound[year]:.2f}")

Year 1: Mean Value = 10753.88, Standard Deviation = 1507.84, 5th Percentile = 8378.93, 95th Percentile = 13330.71
Year 2: Mean Value = 11626.91, Standard Deviation = 2249.23, 5th Percentile = 8149.32, 95th Percentile = 15489.35
Year 3: Mean Value = 12484.33, Standard Deviation = 3032.10, 5th Percentile = 8062.11, 95th Percentile = 17936.62
Year 4: Mean Value = 13488.37, Standard Deviation = 3770.08, 5th Percentile = 8140.69, 95th Percentile = 20431.44
Year 5: Mean Value = 14596.07, Standard Deviation = 4675.40, 5th Percentile = 8409.10, 95th Percentile = 23031.90
Year 6: Mean Value = 15643.68, Standard Deviation = 5445.60, 5th Percentile = 8090.07, 95th Percentile = 25758.89
Year 7: Mean Value = 16890.48, Standard Deviation = 6317.47, 5th Percentile = 8202.91, 95th Percentile = 28733.80
Year 8: Mean Value = 18143.62, Standard Deviation = 7261.77, 5th Percentile = 8454.08, 95th Percentile = 32171.58
Year 9: Mean Value = 19423.36, Standard Deviation = 8092.34, 5th Percentile = 8939.32, 95th Percentile = 34924.04
Year 10: Mean Value = 21043.29, Standard Deviation = 9202.29, 5th Percentile = 9193.58, 95th Percentile = 38983.00

import numpy as np

# Define the portfolio assets and their expected returns and covariance matrix
assets = ['Asset1', 'Asset2', 'Asset3']
expected_returns = np.array([0.1, 0.15, 0.12])
cov_matrix = np.array([[0.05, 0.02, 0.01],
                       [0.02, 0.08, 0.03],
                       [0.01, 0.03, 0.06]])

# Define the number of simulations and portfolio size
num_simulations = 10000
portfolio_size = len(assets)

# Generate random portfolio weights
weights = []
for _ in range(num_simulations):
    w = np.random.random(portfolio_size)
    w /= np.sum(w)
    weights.append(w)
weights = np.array(weights)

# Calculate portfolio returns and volatility for each simulation
portfolio_returns = np.dot(weights, expected_returns)
portfolio_volatility = np.sqrt(np.dot(weights, np.dot(cov_matrix, weights.T)))

# Find the optimal portfolio with maximum Sharpe Ratio
optimal_portfolio_index = np.where(portfolio_returns / portfolio_volatility == np.max(portfolio_returns / portfolio_volatility))[0][0]

# Get the optimal portfolio weights and performance measures
optimal_weights = weights[optimal_portfolio_index]
optimal_returns = portfolio_returns[optimal_portfolio_index]
optimal_volatility = portfolio_volatility[optimal_portfolio_index]

# Print the optimal portfolio weights and performance measures
print("Optimal Portfolio Weights:")
for asset, weight in zip(assets, optimal_weights):
    print(f"{asset}: {weight:.2f}")
print("\nOptimal Portfolio Performance:")
print("Expected Return:", optimal_returns)
print("Volatility:", optimal_volatility)

Optimal Portfolio Weights:
Asset1: 0.96
Asset2: 0.03
Asset3: 0.01

Optimal Portfolio Performance:
Expected Return: 0.10172249180875181
Volatility: [0.17002804 0.16831453 0.16861898 ... 0.1902971  0.16490089 0.15897608]

Sr. No.	Product name	Details
1.	Deposit Accounts	savings accounts, current accounts, and fixed deposit accounts.
2.	Loans and Credit Facilities	personal loans, home loans, auto loans, business loans, lines of credit, and overdraft facilities.
3.	Credit Cards	Banks issue credit cards that allow individuals to make purchases on credit.
4.	Debit Cards	Debit cards are linked to customers' bank accounts and allow them to make purchases and withdraw cash from ATMs.
5.	Mortgages	Banks provide mortgage loans to help individuals purchase or refinance real estate properties. Mortgage loans typically have long repayment terms and are secured by the property being financed.
6.	Investment Products	mutual funds, fixed-income securities, stocks, and bonds.
7.	Foreign Exchange Services	Banks facilitate foreign exchange transactions, allowing customers to convert currencies for travel, international trade, or investment purposes.
8.	Payment Services	online banking, mobile banking, and bill payment facilities.
9.	Trade Finance	Banks offer trade finance services to facilitate international trade transactions. This includes issuing letters of credit, providing export/import financing, and managing trade-related risks.
10.	Wealth Management	Banks provide wealth management services to high-net-worth individuals and institutional clients. These services include investment advisory, portfolio management, estate planning, and other customized financial solutions.
11.	Insurance Products	Life insurance, health insurance, property insurance, and other types of coverage to help individuals and businesses manage risks.
12.	Treasury and Cash Management Services	Banks offer treasury and cash management services to corporate clients, assisting them in managing their cash flow, optimizing liquidity, and conducting efficient financial operations.

Application	Used for	Factors used or used for
Assessing portfolio risk	to know risk and volatility of investment protfolios	VaR, ES, CVaR
Scenario Analysis	to know the future sceanrios and hence impact on future outcomes	market conditions, interest rates, exchange rates, or macroeconomic variables
Stress Testing	to evaluate the resilience of financial institutions or portfolios under adverse conditions	vulnerabilities, evaluate worst-case scenarios, and design risk mitigation strategies
Risk Mitigation Strategies	helps in evaluating and comparing different risk mitigation strategies	diversification, hedging, or asset allocation adjustments
Credit Risk Analysis	to estimate credit-related metrics such as Probability of Default (PD), Loss Given Default (LGD), or Credit Value-at-Risk (CVaR)	it helps assess the credit risk of individual loans or credit portfolios by considering default correlations, recovery rates, or credit rating migrations

Risk analysis in Banking sector¶

Author: Arun Kumar Pandey

Content¶

Risk analysis¶

Various products of the banking sector¶

Types of risks analyzed in the financial banking sector¶

1. Credit risk¶

2. Market risk¶

3. Liquidity risk¶

4. Operational risk¶

5. Regulatory Risk¶

6. Reputational Risk¶

Financial Risk Analysis key steps¶

1. Risk Identification:¶

2. Risk Assessment:¶

3. Risk Measurement and Quantification:¶

4. Risk Monitoring and Reporting:¶

5. Risk Mitigation and Management:¶

6. Risk Communication and Governance:¶

7. Regular Review and Update¶

8. Risk reduction strategies¶

Market Risk¶

Parameters used for risk analysis¶

1. Value-at-Risk (VaR)

Example¶

Monte Carlo Simulation to calculate VaR and CVaR¶

Example on Monte Carlo Simulation¶

1. normal distribution¶

2. t-distribution for returns¶

Consulsion:¶

2. Expected Loss (EL)

3. Conditional Value-at-Risk (CVaR)

4.1. Example (Growth or decline of an investment)¶

Portfolio optimization¶

REFERENCE¶