M&A Portfolio Selection of Targets Valued by Probabilistic and Possibilistic Real Options Methods

In this paper we present a two-component portfolio selection problem under two types of uncertainties, i.e., probabilistic risk and possibilistic risk. We study the portfolio selection problem in mergers and acquisitions, M&As, and show the usability of the presented mixed model in portfolio selection of corporate acquisition targets. We view the total M&A value consisting of a stand-alone of a target value plus a synergistic strategic (real options) value. We illustrate, through a numerical example, how the portfolio model can be applied to M&As from an acquirer’s perspective, in the case, where some targets are valued probabilistically using DatarMathews real options approach (Datar and Mathews, 2004) to value the strategic part and other targets possibilistically using the fuzzy real options approach to value the strategic part as presented by Kinnunen (2010) in the 14th Annual International Conference on Real Options and the Japan Association of Real Options and Strategy’s journal paper of Collan and Kinnunen (2011). The portfolio problem corresponds to a situation in which some return rates on M&A investments are described by random variables, while others by fuzzy numbers. We discuss the setup of an acquirer facing a situation in which some acquisition targets are reasonable to be valued probabilistically and others possibilistically. Markowitz probabilistic model and a possibilistic portfolio selection model are unified resulting in the optimal solution of the mixed portfolio problem with the minimum of the unified portfolio risk.