Applying the partitioned multiobjective risk method (PMRM) to portfolio selection

Area of Science:

• Quantitative Finance
• Risk Management
• Computational Finance

Background:

• Modern Portfolio Theory (MPT) relies on historical returns and volatility for portfolio analysis.
• Volatility effectively measures risk for small asset price fluctuations but is inadequate during extreme market events.
• Historical market crashes demonstrate the limitations of volatility in predicting aberrant market behavior.

Purpose of the Study:

• To address the limitations of volatility in measuring extreme portfolio risk.
• To introduce and model an extreme risk measure, f(4), using the partitioned multiobjective risk method (PMRM).
• To compare the performance of the f(4) risk measure against volatility under various market conditions.

Main Methods:

• Utilized the principles of extreme-risk-analysis via the partitioned multiobjective risk method (PMRM).
• Defined an extreme portfolio risk measure, f(4), as the conditional expectation for a lower-tail distribution of portfolio returns.
• Employed a genetic algorithm (Evolver software) to solve the multiobjective optimization problem of expected return and f(4).

Main Results:

• The proposed PMRM model yielded results compatible with volatility-based models under normal market conditions.
• Under extreme market downturns, the f(4) risk measure demonstrated superior validity compared to traditional volatility.
• The study highlights the effectiveness of f(4) in capturing risks associated with aberrant market fluctuations.

Conclusions:

• The f(4) measure, derived from PMRM, offers a more robust assessment of portfolio risk during extreme market events.
• Volatility remains a useful metric for stable markets but is insufficient for predicting catastrophic losses.
• The study advocates for the adoption of advanced risk metrics like f(4) for comprehensive portfolio risk management.