An optimization approach to resolving circular shareholding in large business groups

Circular shareholding refers to a situation where a series of capital contributions made by companies in a family business group establish a chain of shareholdings. For example, a circular shareholding is formed when company A owns stock in company B, company B owns stock in company C, and company C owns stock in company A. In Korea, the practice of circular shareholding in large family-controlled business groups may give the principal families higher control over member firms and more opportunities to pursue their own interest at the expense of other shareholders. For this reason, the government of Korea has encouraged large conglomerates to gradually eliminate their circular shareholdings. However, there has been no research as to which shareholdings out of the complicated ownership structure should be cleared in order to resolve the issue of circular shareholding. In this paper, we propose optimization models to address the problem. Of the proposed integer programming models that can eliminate circular shareholding, one maximizes the sum of cash-flow rights while another maximizes the sum of voting rights. The proposed models have been applied to Korean family-controlled business groups, and the results are included herein. To the best knowledge of the authors, this research is the first study to apply optimization theory to the problem of resolving circular shareholding.