Portfolio selection under strict uncertainty: A multi-criteria methodology and its application to the Frankfurt and Vienna Stock Exchanges

Abstract

In modern portfolio theory, it is common practice to first compute the risk-reward efficient frontier and then to support an individual investor in selecting a portfolio that meets his/her preferences for profitability and risk. Potential flaws include (a) the assumption that past data provide sufficient evidence for predicting the future performances of the securities under consideration and (b) the necessity to mathematically determine or approximate the investor’s utility function. In this paper, we propose a methodology whose initial phase filters portfolios that are inefficient from a historical perspective. While this is consistent with traditional approaches, the second phase differs from the standard approach as it uses a decision table constructed by considering multiple scenarios assuming strict uncertainty. The table cells measure consequences by a multi-criteria linear performance index of simulated future returns, which avoids difficulties with performance ratios. The real world applicability is illustrated through two studies based on data from the stock exchanges in Frankfurt and Vienna.