Applying Partitioned Multiobjective Risk Method to Portfolio Selection.* J. R. Santos and Y. Y. Haimes, University of Virginia
The analysis of the risk-return trade-offs and their practical applications to portfolio analysis paved way for the Modern Portfolio Theory, which won Harry Markowitz a 1992 Nobel Prize in Economics. A typical approach in measuring the portfolio expected return is based on the historical returns of the assets included in the portfolio. On the other hand, portfolio risk is usually measured using the volatility, which is derived from the historical variance-covariance relationships among the portfolio assets. The paper focuses on the assessment of portfolio risk, with emphasis on extreme risks. Volatility is justified for stable market performance but its weakness in addressing portfolio risk under aberrant market fluctuations warrants the need for a more robust metric of risk. To date, volatility is still a major measure of risk owing to its simplicity and validity for relatively small asset price fluctuations. Extreme market crashes such as the October 19, 1987 ("Black Monday") and catastrophic events such as the four-day suspension of NYSE trading in the aftermath of the September 11, 2001 attacks are a few examples where measuring risk via volatility can lead to inaccurate predictions. By invoking the principles of the extreme-risk-analysis method, Partitioned Multiobjective Risk Method (PMRM), the paper contributes to the modeling of extreme risks in portfolio performance. A measure of an extreme portfolio risk, denoted by f4, is defined as the "conditional expectation" at a lower tail region of the distribution of the possible portfolio returns. Under business-as-usual market scenarios, the results of the proposed PMRM portfolio selection model are found to be compatible with that of volatility-based model. However, under extremely unfavorable market conditions, results indicate that f4 is a more valid measure of risk than volatility. The paper discusses a process of measuring portfolio f4 using extreme value theory, time-series analysis, and heuristic methods.
*Best Paper Finalist.
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