The Value of Being Lucky: Option Backdating and Non-Diversifiable Risk

Abstract

Empirical evidence shows that backdating of executive stock option grants was prevalent, particularly at firms with highly volatile stock prices. Yet extant Black-Scholes style models used for empirical estimates of gains to executives from backdating suggest that this benefit is not only modest but is greatest for low volatility firms. In this paper we take the stance that, ex ante, executives who have the opportunity to backdate should take this into account in their valuation and we quantify the value to a risk averse executive of a "lucky" option grant with strike chosen to coincide with the lowest stock price of the month. This enables us to reconcile theory with empirics - we show the ex ante gain to risk averse executives is significant and increases with volatility. Our explanation hinges on valuing the embedded lookback option, and key features of risk aversion, inability to diversify and American early exercise.