Systematic Risk Aggregation Model

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The “Systematic Risk Aggregation Model” is a quantitative trading strategy implemented in Pine Script™ designed to assess and visualize market risk by aggregating multiple financial risk factors. This model uses a multi-dimensional scoring approach to quantify systemic risk, incorporating volatility, drawdowns, put/call ratios, tail risk, volume spikes, and the Sharpe ratio. It derives a composite risk score, which is dynamically smoothed and plotted alongside adaptive Bollinger Bands to identify trading opportunities. The strategy’s theoretical framework aligns with modern portfolio theory and risk management literature (Markowitz, 1952; Taleb, 2007).

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Key Components of the Model

1. Volatility as a Risk Proxy

The model calculates the standard deviation of the closing price over a specified period (volatility_length) to quantify market uncertainty. Volatility is normalized to a score between 0 and 100, using its historical minimum and maximum values.

Reference: Volatility has long been regarded as a critical measure of financial risk and uncertainty in capital markets (Hull, 2008).

2. Drawdown Assessment

The drawdown metric captures the relative distance of the current price from the highest price over the specified period (drawdown_length). This is converted into a normalized score to reflect the magnitude of recent losses.

Reference: Drawdown is a key metric in risk management, often used to measure potential downside risk in portfolios (Maginn et al., 2007).

3. Put/Call Ratio as a Sentiment Indicator

The strategy integrates the put/call ratio, sourced from an external symbol, to assess market sentiment. High values often indicate bearish sentiment, while low values suggest bullish sentiment (Whaley, 2000). The score is normalized similarly to other metrics.

4. Tail Risk via Modified Z-Score

Tail risk is approximated using the modified Z-score, which measures the deviation of the closing price from its moving average relative to its standard deviation. This approach captures extreme price movements and potential “black swan” events.

Reference: Taleb (2007) discusses the importance of considering tail risks in financial systems.

5. Volume Spikes as a Proxy for Market Activity

A volume spike is defined as the ratio of current volume to its moving average. This ratio is normalized into a score, reflecting unusual trading activity, which may signal market turning points.

Reference: Volume analysis is a foundational tool in technical analysis and is often linked to price momentum (Murphy, 1999).

6. Sharpe Ratio for Risk-Adjusted Returns

The Sharpe ratio measures the risk-adjusted return of the asset, using the mean log return divided by its standard deviation over the same period. This ratio is transformed into a score, reflecting the attractiveness of returns relative to risk.

Reference: Sharpe (1966) introduced the Sharpe ratio as a standard measure of portfolio performance.

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Composite Risk Score

The composite risk score is calculated as a weighted average of the individual risk factors:

• Volatility: 30%
• Drawdown: 20%
• Put/Call Ratio: 20%
• Tail Risk (Z-Score): 15%
• Volume Spike: 10%
• Sharpe Ratio: 5%

This aggregation captures the multi-dimensional nature of systemic risk and provides a unified measure of market conditions.

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Dynamic Bands with Bollinger Bands

The composite risk score is smoothed using a moving average and bounded by Bollinger Bands (basis ± 2 standard deviations). These bands provide dynamic thresholds for identifying overbought and oversold market conditions:

• Upper Band: Signals overbought conditions, where risk is elevated.
• Lower Band: Indicates oversold conditions, where risk subsides.

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Trading Strategy

The strategy operates on the following rules:

1. Entry Condition: Enter a long position when the risk score crosses above the upper Bollinger Band, indicating elevated market activity.

2. Exit Condition: Close the long position when the risk score drops below the lower Bollinger Band, signaling a reduction in risk.

These conditions are consistent with momentum-based strategies and adaptive risk control.

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Conclusion

This script exemplifies a systematic approach to risk aggregation, leveraging multiple dimensions of financial risk to create a robust trading strategy. By incorporating well-established risk metrics and sentiment indicators, the model offers a comprehensive view of market dynamics. Its adaptive framework makes it versatile for various market conditions, aligning with contemporary advancements in quantitative finance.

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References

1. Hull, J. C. (2008). Options, Futures, and Other Derivatives. Pearson Education.

2. Maginn, J. L., Tuttle, D. L., McLeavey, D. W., & Pinto, J. E. (2007). Managing Investment Portfolios: A Dynamic Process. Wiley.

3. Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77–91.

4. Murphy, J. J. (1999). Technical Analysis of the Financial Markets. New York Institute of Finance.

5. Sharpe, W. F. (1966). Mutual Fund Performance. The Journal of Business, 39(1), 119–138.

6. Taleb, N. N. (2007). The Black Swan: The Impact of the Highly Improbable. Random House.

7. Whaley, R. E. (2000). The Investor Fear Gauge. The Journal of Portfolio Management, 26(3), 12–17.

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The optimized script introduces several key improvements and adjustments compared to the original:

1. Weighting of Components
The optimized script allows for dynamic weighting of components like volatility, drawdown, put/call ratio, etc., through user inputs. In the original script, these weights were fixed and could not be adjusted.

2. Length Adjustments
Default values for the calculation lengths, such as volatility and drawdown periods, have been tuned in the optimized version to potentially improve responsiveness to market changes.

3. Bollinger Band Multipliers
In the optimized script, the multipliers for the upper and lower bands can be set independently, allowing for more granular control. The original script used a fixed multiplier for both bands.

4. Modular Design
The optimized script has improved readability and organization, with clearer naming for inputs and variables, making it easier to understand and modify.

5. Improved Risk Score Calculation
The risk score formula in the optimized script incorporates the dynamic weights, providing more customization and adaptability to user preferences, unlike the static formula in the original.

6. Overlay and Visualization
The original script plotted the risk scores and bands directly on the price chart, while the optimized script uses a separate pane for better clarity and avoids cluttering the price chart.

7. Enhanced Inputs
The optimized script introduces additional input fields, such as those for band multipliers and individual component weights, providing users with greater control.

8. Trading Logic
The trading rules remain the same in both versions, ensuring consistency in the strategy’s core logic.

9. Background Highlighting
Both scripts highlight the background when a position is active, but the optimized script improves customization and visualization.

The optimized script offers greater flexibility, better visualization, and improved user control, making it more adaptable and potentially effective in various market scenarios.