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

Joost Reyes Santos1, Yacov Y Haimes

  • 1Department of Systems and Information Engineering, University of Virginia, USA. jrs8e@virginia.edu

Risk Analysis : an Official Publication of the Society for Risk Analysis
|June 24, 2004
PubMed
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This study introduces a new extreme risk measure, f(4), for portfolio analysis. The partitioned multiobjective risk method (PMRM) shows f(4) is more accurate than volatility during market crashes.

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).

Related Experiment Videos

  • 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.