Optimal Trading by a 'Large Shareholder'

Abstract

A large shareholder who undertakes costly effort to improve a firm’s dividends faces a tradeoff. Selling shares will likely lower the share price (as the market anticipates a reduction in effort), while holding the shares implies a less diversified investment portfolio. Moreover, in a dynamic setting a time -consistency problem emerges: once some shares are sold, the incentive to sell additional shares may increase since the large shareholder is less exposed to the resultant price declines. We analyze a multi -period model for the optimal trading strategy of a large shareholder. We consider the case in which the large shareholder can commit to a trading strategy, and the case in which such commitment is impossible. Absent commitment, the problem is similar to durable goods monopoly: the share price today depends on the shares expected to be sold in the future. We demonstrate that an analog of the “Coase conjecture” holds in the sense that shareholdings ultimately converge to the competitive outcome of efficient diversification. Unlike the standard monopoly setting, however, this outcome is suboptimal in that there is inefficient monitoring. We provide conditions for which convergence to this outcome is gradual, and when it occurs immediately. In the continuous trading approximation, our results produce a simple formula for the equilibrium share price in this setting: the trading strategy of the large shareholder can be ignored, and today’s share price is simply the present value of dividends given constant holdings by the large shareholder, but adjusted by a risk premium that reflects the large shareholder’s (rather than investors’) risk aversion. We demonstrate that our model provides a rational for both IPO underpricing and the use of lockup provisions. Finally, we generalize our results outside the moral hazard framework.