Financial Risk Analysis

Introduction

Financial institutions want to assess the risk levels of their portfolios or investments. In this notebook, we perform a comprehensive financial risk analysis of a portfolio using various quantitative methods. The aim is to understand the risks associated with the portfolio, evaluate how different assets interact, and assess how the portfolio might behave under different market conditions. This analysis is crucial for financial institutions to make informed decisions and develop strategies to mitigate potential risks.

Data Loading and Preprocessing

Explanation

We begin by importing the necessary libraries and loading the dataset. The dataset financial_portfolio_data.csv contains historical price data for various assets. We convert the 'Date' column to datetime format and sort the data chronologically to ensure accurate time series analysis.

Mathematical and Financial Terminologies

• DataFrame: A two-dimensional, data structure with labeled axes (rows and columns) used in pandas for data manipulation.

1  import pandas as pd
2  import numpy as np
3  import matplotlib.pyplot as plt
4  import seaborn as sns
5  %matplotlib inline
6  data = pd.read_csv(r'''/app/financial_portfolio_data.csv''')
7  data['Date'] = pd.to_datetime(data['Date'])
8  data.head()

Calculating Daily Returns

Explanation

We calculate the daily returns for each asset to analyze their performance over time. Daily return is the percentage change in the asset's price from one day to the next.

1  data['Return'] = data.groupby('Asset')['Price'].pct_change()
2  returns = data.dropna(subset=['Return'])
3  returns.head()

Exploratory Data Analysis

Understanding Asset Price Distribution

Explanation

We use a boxplot to visualize the distribution of asset prices. This helps identify the median, quartiles, and potential outliers for each asset.

Financial Terminologies

• Boxplot: A graphical representation of data that displays the dataset's minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

1  plt.figure(figsize=(12, 6))
2  sns.boxplot(x='Asset', y='Price', data=data)
3  plt.title('Price Distribution by Asset')
4  plt.xlabel('Asset')
5  plt.ylabel('Price')
6  plt.show()

Time Series of Asset Prices

Explanation

We plot the prices of each asset over time to observe trends, seasonality, or anomalies in the data.

1  plt.figure(figsize=(14, 7))
2  for asset in data['Asset'].unique():
3      asset_data = data[data['Asset'] == asset]
4      plt.plot(asset_data['Date'], asset_data['Price'], label=asset)
5  plt.title('Asset Prices Over Time')
6  plt.xlabel('Date')
7  plt.ylabel('Price')
8  plt.legend()
9  plt.show()

Correlation Analysis

Explanation

We analyze the correlation between the returns of different assets to understand how they move in relation to each other.

1  # Pivot the data to have assets as columns using pivot_table
2  pivot_data = returns.pivot_table(index='Date', columns='Asset', values='Return', aggfunc='mean')
3  # Calculate the correlation matrix
4  corr_matrix = pivot_data.corr()
5  # Visualize the correlation matrix
6  plt.figure(figsize=(8,6))
7  sns.heatmap(corr_matrix, annot=True, cmap='coolwarm')
8  plt.title('Correlation Matrix of Asset Returns')
9  plt.show()

Value at Risk (VaR) Analysis

What is Value at Risk (VaR)?

Value at Risk (VaR) is a statistical technique used to measure the risk of loss on a specific portfolio. It estimates the potential loss over a certain period for a given confidence interval.

Calculating Portfolio Returns

Explanation

We compute the portfolio returns by averaging the returns of all assets for each date, assuming equal weighting.

1  # Compute portfolio returns by averaging asset returns
2  portfolio_returns = pivot_data.mean(axis=1)

Computing VaR at 95% Confidence Level

Explanation

We calculate the 5th percentile of the portfolio returns distribution to find the VaR at 95% confidence level.

1  var_95 = np.percentile(portfolio_returns.dropna(), 5)
2  print(f"Portfolio VaR at 95% confidence level: {var_95:.2%}")

Expected Shortfall (Conditional VaR)

What is Expected Shortfall?

Expected Shortfall (ES), also known as Conditional VaR, is the expected loss on days when there is a VaR violation (i.e., when the loss exceeds the VaR threshold). It provides information about the tail of the loss distribution.

Calculating Expected Shortfall

Explanation

We calculate the average of the portfolio returns that are less than or equal to the VaR value.

1  es_95 = portfolio_returns[portfolio_returns <= var_95].mean()
2  print(f"Expected Shortfall at 95% confidence level: {es_95:.2%}")

Asset Risk Contributions

Calculating Mean and Standard Deviation of Asset Returns

Explanation

We calculate the mean (average) return and standard deviation (a measure of volatility) for each asset.

1  asset_stats = pivot_data.agg(['mean', 'std']).transpose()
2  asset_stats

Visualizing Risk vs. Return

Explanation

We plot the standard deviation (risk) against the mean return for each asset to visualize the risk-return trade-off.

1  import plotly.express as px
2  # Prepare the data
3  asset_stats_reset = asset_stats.reset_index().rename(columns={'index': 'Asset'})
4  # Create an interactive scatter plot
5  fig = px.scatter(
6      asset_stats_reset,
7      x='std',
8      y='mean',
9      text='Asset',
10      color='mean',
11      color_continuous_scale=px.colors.sequential.Plasma,
12      labels={
13          'std': 'Standard Deviation (Risk)',
14          'mean': 'Mean Return'
15      },
16      title='Risk vs Return for Assets'
17  )
18  # Customize the marker size and opacity
19  fig.update_traces(marker=dict(size=15, opacity=0.8),
20                    textposition='top center')
21  # Update the layout for better aesthetics
22  fig.update_layout(
23      font=dict(size=14),
24      title_font=dict(size=20, family='Helvetica'),
25      xaxis=dict(showgrid=True, gridcolor='lightgray'),
26      yaxis=dict(showgrid=True, gridcolor='lightgray'),
27      plot_bgcolor='white'
28  )
29  # Show the figure
30  fig.show()

1  # Calculate daily returns
2  data.sort_values('Date', inplace=True)
3  data['Return'] = data.groupby('Asset')['Price'].pct_change()
4  # Compute VaR at 95% confidence level
5  var_95 = data['Return'].quantile(0.05)
6  print(f"Value at Risk (95% confidence): {var_95:.2%}")

Stress Testing in Financial Risk Analysis

Stress testing is a crucial risk management technique used to evaluate how a financial portfolio or institution might perform under extreme market conditions. It involves simulating adverse scenarios to assess potential vulnerabilities and ensure preparedness for unexpected events.

Purpose of Stress Testing:

• Risk Identification: Detects weaknesses in portfolios that may not be apparent during normal market fluctuations.
• Capital Adequacy Assessment: Ensures that the institution holds sufficient capital reserves to withstand financial shocks.
• Regulatory Compliance: Meets regulatory requirements imposed by financial authorities, promoting stability in the financial system.
• Strategic Planning: Informs decision-making regarding risk mitigation strategies and contingency planning.

Key Concepts:

• Stress Scenarios: Hypothetical or historical situations representing extreme market conditions, such as a sudden economic downturn, market crash, or interest rate spike.
• Shock Factors: Variables that are stressed, including asset prices, interest rates, exchange rates, or credit spreads.
• Stressed Metrics: Financial indicators recalculated under stress scenarios, like Value at Risk (VaR), portfolio returns, or liquidity ratios.

1  # Define stress scenarios
2  stress_factors = [0.9, 0.8, 0.7]  # Corresponds to 10%, 20%, 30% market drops
3  for factor in stress_factors:
4      stressed_prices = data['Price'] * factor
5      plt.figure(figsize=(10, 4))
6      sns.histplot(stressed_prices, bins=30, kde=True, color='red')
7      plt.title(f'Stress Test with Market Drop of {int((1 - factor) * 100)}%')
8      plt.xlabel('Stressed Asset Prices')
9      plt.show()

Scenario Analysis

What is Scenario Analysis?

Scenario analysis assesses the potential impact of different hypothetical events or market conditions on the portfolio's performance.

Defining Market Scenarios

Explanation

We define three market scenarios to simulate how the portfolio might perform under different conditions.

• Bull Market: Prices increase by 10% (optimistic scenario).
• Bear Market: Prices decrease by 15% (pessimistic scenario).
• Stagnant Market: No price change (neutral scenario).

1  # Define scenarios: Bull Market, Bear Market, and Stagnant Market
2  scenarios = {
3      'Bull Market': 1.10,    # Prices increase by 10%
4      'Bear Market': 0.85,    # Prices decrease by 15%
5      'Stagnant Market': 1.00 # No change in prices
6  }
7  # Analyze each scenario
8  for scenario, factor in scenarios.items():
9      # Apply the scenario factor to prices
10      scenario_prices = data.copy()
11      scenario_prices['Scenario Price'] = scenario_prices['Price'] * factor
12      # Calculate the scenario returns
13      scenario_prices['Scenario Return'] = scenario_prices.groupby('Asset')['Scenario Price'].pct_change()
14      # Drop NaN values
15      scenario_returns = scenario_prices.dropna(subset=['Scenario Return'])
16      # Use pivot_table to handle duplicate entries
17      scenario_pivot = scenario_returns.pivot_table(
18          index='Date', columns='Asset', values='Scenario Return', aggfunc='mean'
19      )
20      # Compute portfolio returns
21      scenario_portfolio_returns = scenario_pivot.mean(axis=1)
22      # Calculate VaR for the scenario
23      scenario_var_95 = np.percentile(scenario_portfolio_returns.dropna(), 5)
24      print(f"{scenario} - Portfolio VaR at 95% confidence level: {scenario_var_95:.2%}")

Visualizing Scenario Portfolio Returns

Explanation

We plot the portfolio returns under each scenario to compare their performance visually.

1  # Plotting the Scenario Portfolio Returns
2  plt.figure(figsize=(12,6))
3  for scenario, factor in scenarios.items():
4      # (Previous steps remain the same)
5      # ...
6      plt.plot(
7          scenario_portfolio_returns.index,
8          scenario_portfolio_returns.values,
9          label=scenario
10      )
11  plt.xlabel('Date')
12  plt.ylabel('Portfolio Return')
13  plt.title('Portfolio Returns Under Different Market Scenarios')
14  plt.legend()
15  plt.show()

Conclusion

In this notebook, we have conducted an extensive financial risk analysis, including:

• Data Preprocessing: Loaded and prepared data for analysis.
• Calculating Daily Returns: Analyzed asset performance over time.
• Exploratory Data Analysis: Visualized asset price distributions and trends.
• Correlation Analysis: Assessed relationships between asset returns.
• Value at Risk (VaR) and Expected Shortfall: Quantified potential losses and tail risks.
• Asset Risk Contributions: Evaluated individual asset risk-return profiles.
• Scenario Analysis: Simulated portfolio performance under different market conditions.

This comprehensive analysis provides valuable insights for financial institutions to manage risks effectively and make informed investment decisions.