Does a simple, observable indicator exist that reveals whether a firmís corporate governance structure can be improved? To clear this question, a procedure for testing the U-shaped relationship of shareholding ratios and financial performance is employed. From two hypotheses concerning the relationship between financial performance and ownership structure, the convergence-of-interest hypothesis (Jensen and Meckling, 1976; Jensen, 1993) and the entrenchment hypothesis (Jensen and Ruback, 1983; Jensen, 2005), the extreme point of the nonlinear relationship clarifies sense about the two hypotheses of corporate governance. The lower extreme point of shareholding, the easier it is for the convergence-of-interest hypothesis is accepted. To examine the influence of board composition on financial performance, the test for U-shaped relationship of Lind and Mehlum (2010) is utilized to find the optimal shareholding structures in Chinese and Taiwanese markets. The results are consistent with the hypothesis that corporate performance is a U-shaped function of the shareholding ratios. This study observes the sensitivity of the related variables about corporate governance, such as education level, board seats, leverage, and firm size, affecting the movement of extreme value in U-shaped relationship. As the results show, the education level of directors and supervisors, board size, firm size, and leverage are negatively correlated with the quantity of the extreme points. Increasing the education level of directors can lower the extreme value of the shareholding ratio of the directors, the empirical shareholding ratio is more likely to be in a range in which the convergence-of-interest applies.