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Stress Test Strategy

Rigorously stress test trading strategies against historical worst-case cryptocurrency market scenarios including the COVID-19 crash, China mining ban, FTX exchange collapse, LUNA and UST depeg event, and Three Arrows Capital contagion to fully assess extreme downside robustness.

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Stress Test Strategy on Crisis Periods

Introduction: Understanding Stress Test Strategy on Crisis Periods

Stress testing is a critical risk management technique used to evaluate the resilience of a financial institution or portfolio under extreme yet plausible adverse scenarios. When applied to crisis periods, stress testing becomes even more vital as it helps identify vulnerabilities and potential losses that might not be apparent during normal market conditions.

Definition

A stress test strategy on crisis periods involves designing and executing analytical simulations to assess the impact of severe, low-probability events (crises) on financial systems, portfolios, or individual assets. The goal is to quantify potential losses, evaluate capital adequacy, and inform risk mitigation strategies.

Purpose

Identify Vulnerabilities: Uncover weaknesses in portfolios, business models, or risk management frameworks that could be exposed during a severe market downturn or economic shock.
Quantify Potential Losses: Estimate the magnitude of financial losses under various crisis scenarios.
Assess Capital Adequacy: Determine if an entity has sufficient capital reserves to absorb losses during a crisis and remain solvent.
Inform Strategic Decisions: Provide insights for capital planning, risk limits setting, business continuity, and hedging strategies.
Regulatory Compliance: Meet regulatory requirements for stress testing (e.g., Dodd-Frank Act stress tests, EBA stress tests).

This section introduces the fundamental concept of stress testing, particularly its application during financial crisis periods. It defines what stress testing entails, outlines its core objectives—such as identifying vulnerabilities, quantifying potential losses, and assessing capital adequacy—and explains its critical role in risk management for financial institutions. The purpose is to lay the groundwork for understanding why and how stress tests are conducted, providing a foundational context for the subsequent practical demonstrations.

What Constitutes a Crisis Period?

A crisis period, in the context of financial stress testing, refers to a period characterized by significant adverse economic or market conditions. These can include:

Financial Crises: E.g., 2008 Global Financial Crisis, 1997 Asian Financial Crisis.
Economic Recessions/Depressions: Periods of sustained economic contraction, high unemployment, and reduced consumer spending.
Market Shocks: Sudden, sharp declines in asset prices (equities, bonds, commodities), increased volatility, and liquidity freezes.
Geopolitical Events: Wars, political instability, or major policy shifts that disrupt global markets.
Health Crises: Pandemics (e.g., COVID-19) that lead to widespread economic shutdowns and supply chain disruptions.

These periods are typically marked by:

High Volatility: Rapid and unpredictable price swings.
Reduced Liquidity: Difficulty in buying or selling assets without significantly impacting prices.
Correlation Shifts: Assets that usually diversify a portfolio may become highly correlated, failing to provide protection.
Credit Contraction: Banks become less willing to lend, tightening credit conditions.

This section delves into the definition and characteristics of what constitutes a 'crisis period' within the financial context of stress testing. It categorizes various types of crises, including financial crises, economic recessions, market shocks, and geopolitical and health crises. By detailing the typical features of these periods—such as high volatility, reduced liquidity, and correlation shifts—it establishes the adverse environments that stress test scenarios aim to replicate. Understanding these conditions is crucial for designing relevant and impactful stress tests.

Components of a Stress Test Strategy

A robust stress test strategy involves several key components:

Scenario Definition: Developing plausible but severe hypothetical situations.
Impact Assessment: Quantifying the financial effects of these scenarios.
Mitigation Planning: Formulating strategies to address identified vulnerabilities.
Validation and Governance: Ensuring the models and processes are sound and regularly reviewed.

This section provides an architectural overview of a comprehensive stress test strategy. It breaks down the process into four key components: Scenario Definition, Impact Assessment, Mitigation Planning, and Validation & Governance. Each component represents a distinct phase in the stress testing lifecycle, from creating hypothetical adverse situations to ensuring the integrity of the process. This structural outline is important as it sets the framework for the detailed discussions and practical implementations presented in the subsequent sections of the notebook.

1. Scenario Definition

Scenario definition is the cornerstone of any stress test. It involves creating hypothetical situations that represent extreme market movements, economic downturns, or specific idiosyncratic events. These scenarios should be:

Plausible: Based on historical events or expert judgment.
Severe: Designed to push the limits of an institution's resilience.
Consistent: Internally coherent across different risk factors.
Quantifiable: Allowing for the calibration of relevant market and economic variables.

How it works: Scenarios often involve defining shocks to various risk factors over a specific time horizon. For example:

Market Risk: Equity index drops by 30%, credit spreads widen by 200 bps.
Credit Risk: Default rates double, recovery rates halve.
Interest Rate Risk: Yield curve shifts dramatically.
Liquidity Risk: Funding markets freeze, inability to roll over short-term debt.

[1]

# Import necessary libraries
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# Set a random seed for reproducibility
np.random.seed(42)

def generate_portfolio_value(initial_value: float = 1000000, num_days: int = 252, annual_volatility: float = 0.20, annual_return: float = 0.05) -> pd.Series:
    """
    Generates a mock portfolio value series over a specified number of days.

    Args:
        initial_value (float): The starting value of the portfolio.
        num_days (int): The number of days to simulate (e.g., 252 for a trading year).
        annual_volatility (float): The annualized volatility of the portfolio's returns.
        annual_return (float): The annualized expected return of the portfolio.

    Returns:
        pd.Series: A pandas Series representing the portfolio's value over time.
    """
    daily_volatility = annual_volatility / np.sqrt(num_days)
    daily_return = annual_return / num_days

    # Generate daily returns using a normal distribution
    returns = np.random.normal(daily_return, daily_volatility, num_days)

    # Calculate cumulative returns and portfolio value
    cumulative_returns = (1 + returns).cumprod()
    portfolio_value = initial_value * np.insert(cumulative_returns, 0, 1)[:-1] # Start with initial value

    dates = pd.date_range(start='2022-01-01', periods=num_days)
    return pd.Series(portfolio_value, index=dates)

# Generate a normal portfolio value series
normal_portfolio = generate_portfolio_value()
display(normal_portfolio.head())

	0
2022-01-01	1.000000e+06
2022-01-02	1.006456e+06
2022-01-03	1.004903e+06
2022-01-04	1.013302e+06
2022-01-05	1.032947e+06

dtype: float64

[2]

def simulate_crisis(portfolio_series: pd.Series, crisis_start_index: int, crisis_duration: int, stress_factor: float = 0.50) -> pd.Series:
    """
    Simulates a crisis event on a portfolio value series by applying a stress factor.

    Args:
        portfolio_series (pd.Series): The original portfolio value series.
        crisis_start_index (int): The index (day) where the crisis begins.
        crisis_duration (int): The number of days the crisis affects the portfolio.
        stress_factor (float): The percentage reduction applied to the portfolio value
                               during the crisis period (e.g., 0.50 for a 50% drop).

    Returns:
        pd.Series: A new pandas Series representing the portfolio's value under stress.
    """
    stressed_portfolio = portfolio_series.copy()

    # Calculate the percentage drop per day during the crisis
    daily_stress_impact = (1 - stress_factor) ** (1 / crisis_duration)

    for i in range(crisis_duration):
        if crisis_start_index + i < len(stressed_portfolio):
            # Apply a cumulative reduction starting from the crisis start
            stressed_portfolio.iloc[crisis_start_index + i] = \
                stressed_portfolio.iloc[crisis_start_index + i] * (daily_stress_impact ** (i + 1))

    # After the crisis, the portfolio might recover or stabilize, for simplicity we keep it at the stressed level
    # For more complex scenarios, one could model a recovery phase

    return stressed_portfolio

# Define crisis parameters
crisis_start_day = 100
crisis_duration_days = 20
crisis_magnitude = 0.30 # A 30% drop over the crisis duration

# Simulate the stressed portfolio
stressed_portfolio = simulate_crisis(normal_portfolio, crisis_start_day, crisis_duration_days, crisis_magnitude)
display(stressed_portfolio.head())

	0
2022-01-01	1.000000e+06
2022-01-02	1.006456e+06
2022-01-03	1.004903e+06
2022-01-04	1.013302e+06
2022-01-05	1.032947e+06

dtype: float64

2. Impact Assessment

Once scenarios are defined and applied, the next step is to quantify the impact. This involves calculating key risk metrics under both normal and stressed conditions to understand the potential losses and vulnerabilities. Common metrics include:

Maximum Drawdown (MDD): The largest peak-to-trough decline in a portfolio's value during a specific period.
Value at Risk (VaR): An estimate of the maximum potential loss over a given time horizon at a specific confidence level.
Expected Shortfall (ES): Also known as Conditional VaR, it measures the expected loss given that the loss exceeds the VaR level. This is often considered a more robust measure than VaR as it accounts for tail risk.
Capital Ratios: Measures like Common Equity Tier 1 (CET1) capital ratio for banks, indicating ability to absorb losses.

How it works: Mathematical models are used to re-price assets and re-evaluate portfolios under the stressed market conditions specified by the scenarios. The outputs are then aggregated to derive the impact on key performance and risk indicators.

[3]

def calculate_max_drawdown(series: pd.Series) -> float:
    """
    Calculates the maximum drawdown of a financial series.

    Args:
        series (pd.Series): A series of financial values (e.g., portfolio value).

    Returns:
        float: The maximum drawdown as a percentage (e.g., 0.10 for 10% drawdown).
    """
    if series.empty:
        return 0.0
    peak = series.expanding(min_periods=1).max()
    drawdown = (series - peak) / peak
    return drawdown.min()

def calculate_value_at_risk(returns: pd.Series, confidence_level: float = 0.95) -> float:
    """
    Calculates the historical Value at Risk (VaR) for a series of returns.

    Args:
        returns (pd.Series): A series of daily returns.
        confidence_level (float): The confidence level for VaR (e.g., 0.95 for 95% VaR).

    Returns:
        float: The VaR as a percentage (e.g., 0.02 for 2% VaR).
    """
    if returns.empty:
        return 0.0
    return returns.quantile(1 - confidence_level)

# Calculate daily returns for VaR calculation
normal_returns = normal_portfolio.pct_change().dropna()
stressed_returns = stressed_portfolio.pct_change().dropna()

# Calculate metrics for normal scenario
mdd_normal = calculate_max_drawdown(normal_portfolio)
var_normal = calculate_value_at_risk(normal_returns)

# Calculate metrics for stressed scenario
mdd_stressed = calculate_max_drawdown(stressed_portfolio)
var_stressed = calculate_value_at_risk(stressed_returns)

print(f"Normal Scenario - Max Drawdown: {mdd_normal:.2%}, VaR (95%): {var_normal:.2%}")
print(f"Stressed Scenario - Max Drawdown: {mdd_stressed:.2%}, VaR (95%): {var_stressed:.2%}")

Normal Scenario - Max Drawdown: -19.29%, VaR (95%): -1.87%
Stressed Scenario - Max Drawdown: -41.03%, VaR (95%): -2.16%

Visualization 1: Portfolio Value Under Normal vs. Stressed Conditions

This visualization shows how the portfolio's value evolves over time under both normal market conditions and a simulated crisis scenario. It highlights the direct impact of the stress event on the portfolio's trajectory.

[4]

plt.figure(figsize=(12, 6))
plt.plot(normal_portfolio.index, normal_portfolio.values, label='Normal Portfolio Value', color='blue')
plt.plot(stressed_portfolio.index, stressed_portfolio.values, label='Stressed Portfolio Value', color='red', linestyle='--')

# Highlight the crisis period
crisis_start_date = normal_portfolio.index[crisis_start_day]
crisis_end_date = normal_portfolio.index[min(len(normal_portfolio) - 1, crisis_start_day + crisis_duration_days - 1)]
plt.axvspan(crisis_start_date, crisis_end_date, color='orange', alpha=0.2, label='Crisis Period')

plt.title('Portfolio Value: Normal vs. Stressed Scenario')
plt.xlabel('Date')
plt.ylabel('Portfolio Value')
plt.legend()
plt.grid(True)
plt.tight_layout()
plt.show()

# Interpretation
print("Interpretation: The plot clearly shows the divergence of the stressed portfolio from the normal portfolio during the crisis period. The red dashed line (stressed portfolio) demonstrates a significant drop in value, while the blue line (normal portfolio) continues its upward trend (or experiences normal fluctuations). The orange shaded area visually marks the defined crisis duration, making it easy to see the immediate and sustained impact of the stress event.")

Interpretation: The plot clearly shows the divergence of the stressed portfolio from the normal portfolio during the crisis period. The red dashed line (stressed portfolio) demonstrates a significant drop in value, while the blue line (normal portfolio) continues its upward trend (or experiences normal fluctuations). The orange shaded area visually marks the defined crisis duration, making it easy to see the immediate and sustained impact of the stress event.

Visualization 2: Comparison of Key Risk Metrics

This visualization compares key risk metrics, such as Maximum Drawdown and Value at Risk, between the normal and stressed scenarios. It quantifies the increase in risk exposure during a crisis, making the impact more tangible.

[5]

metrics_data = {
    'Metric': ['Max Drawdown', 'VaR (95%)'],
    'Normal Scenario': [abs(mdd_normal), abs(var_normal)], # Use absolute values for easier comparison on bar chart
    'Stressed Scenario': [abs(mdd_stressed), abs(var_stressed)]
}

df_metrics = pd.DataFrame(metrics_data)
df_metrics = df_metrics.set_index('Metric')

fig, ax = plt.subplots(figsize=(10, 6))
df_metrics.plot(kind='bar', ax=ax, colormap='viridis')

ax.set_title('Comparison of Risk Metrics: Normal vs. Stressed Scenarios')
ax.set_ylabel('Percentage (Absolute Value)')
ax.set_xticklabels(df_metrics.index, rotation=0)
ax.yaxis.set_major_formatter(plt.FuncFormatter(lambda y, _: '{:.0%}'.format(y))) # Format y-axis as percentage
plt.grid(axis='y', linestyle='--', alpha=0.7)
plt.tight_layout()
plt.show()

# Interpretation
print("Interpretation: This bar chart quantitatively illustrates the heightened risk during a crisis. Both Maximum Drawdown and VaR are significantly larger in the 'Stressed Scenario' compared to the 'Normal Scenario'. For instance, the Max Drawdown in the stressed scenario shows a much deeper potential loss. This visual comparison provides clear evidence of the increased risk exposure and potential capital at risk during adverse conditions, underscoring the importance of stress testing.")

Interpretation: This bar chart quantitatively illustrates the heightened risk during a crisis. Both Maximum Drawdown and VaR are significantly larger in the 'Stressed Scenario' compared to the 'Normal Scenario'. For instance, the Max Drawdown in the stressed scenario shows a much deeper potential loss. This visual comparison provides clear evidence of the increased risk exposure and potential capital at risk during adverse conditions, underscoring the importance of stress testing.

3. Mitigation Planning

The results from stress tests are not just for understanding risk; they are crucial for developing actionable mitigation strategies. Based on the identified vulnerabilities and potential losses, institutions can:

Adjust Capital Allocation: Increase capital buffers to absorb higher potential losses.
Revise Risk Limits: Tighten limits on exposure to certain assets, sectors, or counterparties.
Implement Hedging Strategies: Introduce or adjust hedges to protect against specific market movements identified in scenarios.
Diversify Portfolios: Reduce concentration risk in assets or funding sources.
Enhance Liquidity Management: Ensure sufficient liquid assets are available to meet obligations during market freezes.
Develop Contingency Plans: Create strategies for business continuity, emergency funding, and communication during a crisis.

Conclusion

A well-defined and executed stress test strategy is indispensable for navigating crisis periods in finance. By proactively simulating extreme scenarios, quantifying potential impacts, and developing robust mitigation plans, financial institutions and investors can enhance their resilience, protect capital, and make more informed decisions during times of market turmoil. The educational goal of this notebook was to provide a foundational understanding of what stress testing entails during crisis periods, why it is important, and how it can be practically demonstrated using basic simulations and risk metrics.