Executive Stock Options: Portfolio Effects

Abstract

Since executives typically receive new grants of stock options (ESOs) each year, longerserving executives often have portfolios of ESOs with differing strikes and maturities. Valuation models for stand-alone ESO grants have shown that trading restrictions, which force executives to bear unhedgeable risk until the options are exercised, induce earlier exercise and hence a lower cost to shareholders than in a risk-neutral setting. However, since unhedgeable risk varies non-linearly with portfolio size and composition, the executive's exercise strategy and thus also the shareholder cost of an option held as part of a portfolio depend also on the remainder of the executive's ESO portfolio. We show that such portfolio effects matter -lowering both the moneyness required for exercise and the shareholder cost of most options in a portfolio. In contrast to a risk-neutral setting, both exercise thresholds and costs depend on an option's position in the optimal exercise order. An option's cost varies with the maturities and, nonlinearly, with the strike prices of other options in the executive's portfolio. The model explains several empirical findings in the literature -which options are attractive to exercise first, how exercise can be induced by a new grant, and the prevalence of early exercise.

Executive Compensation and Board Governance in US Firms

“…There has been an debate as to whether Black–Scholes is the appropriate way to measure the value of an option granted to an executive (Lambert et al ., ; Hall and Murphy, , ; Henderson et al ., ). The Black–Scholes method provides a current estimate of the expected future value of the option assuming that the underlying assumptions of the model are valid.…”

“…18 As such it represents the value the firm assigns to executive talent. and Murphy, , 2002Henderson et al, 2013). The Black-Scholes method provides a current estimate of the expected future value of the option assuming that the underlying assumptions of the model are valid.…”