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Applying the Partitioned Multiobjective Risk Method (PMRM) to Portfolio Selection

The analysis of risk‐return tradeoffs and their practical applications to portfolio analysis paved the way for Modern Portfolio Theory (MPT), which won Harry Markowitz a 1992 Nobel Prize in Economics. A typical approach in measuring a portfolio's expected return is based on the historical returns of the assets included in a portfolio. On the other hand, portfolio risk is usually measured using volatility, which is derived from the historical variance‐covariance relationships among the portfolio assets. This article focuses on assessing portfolio risk, with emphasis on extreme risks. To date, volatility is a major measure of risk owing to its simplicity and validity for relatively small asset price fluctuations. Volatility is a justified measure for stable market performance, but it is weak in addressing portfolio risk under aberrant market fluctuations. Extreme market crashes such as that on October 19, 1987 (“Black Monday”) and catastrophic events such as the terrorist attack of September 11, 2001 that led to a four‐day suspension of trading on the New York Stock Exchange (NYSE) are a few examples where measuring risk via volatility can lead to inaccurate predictions. Thus, there is a need for a more robust metric of risk. By invoking the principles of the extreme‐risk‐analysis method through the partitioned multiobjective risk method (PMRM), this article 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 for a lower‐tail region of the distribution of the possible portfolio returns. This article presents a multiobjective problem formulation consisting of optimizing expected return and f4, whose solution is determined using Evolver—a software that implements a genetic algorithm. Under business‐as‐usual market scenarios, the results of the proposed PMRM portfolio selection model are found to be compatible with those of the volatility‐based model. However, under extremely unfavorable market conditions, results indicate that f4 can be a more valid measure of risk than volatility.