Fractional Exercises of Executive Stock Options

Abstract

In this paper I develop a theoretical model in which an executive exercises her option package (ESO) in fractions to diversify into other assets. I find that fractional exercises affect ESO values considerably for companies with highly volatile stock returns compared to a model with assumed full exercise (all options exercised together). Fractional exercises also make option packages provide more incentives for the executive to increase the stock price. Analyzing exercise data, I find that ESO exercises cluster at fractions of 20%, 25%, 33%, and multiples of those percentage numbers that I also use as inputs for my model. Empirical observations that the second fractional exercise occurs at a higher stock price than the first one and that fractional exercise is more likely for high return volatility of the employer firm's stock are borne out by my model. Furthermore, I find that large option packages are more likely to be exercised in fractions and owners of numerous option packages to have a preference for full exercise, which can be explained by monitoring costs.

Keywords: Executive stock options, early exercise, fractional exercise, incentives, executive compensation, ESO valuation

JEL Classification: C61, G30, M52