The Value of Being Lucky: Option Backdating and Nondiversifiable Risk

Abstract

The practice of executives influencing their option compensation by setting a grant date retrospectively is known as backdating. Since executive stock options are usually granted at-the-money, selecting an advantageous grant date to coincide with a low stock price will be valuable to an executive. Empirical evidence shows that backdating of executive stock option grants was prevalent, particularly at firms with highly volatile stock prices. Executives who have the opportunity to backdate should take this into account in their valuation. 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. We show the ex ante gain to risk averse executives from the ability to backdate increases with both risk aversion and with volatility, and is significant in magnitude. Our model involves valuing the embedded partial American lookback option in a utility indifference setting with key features of risk aversion, inability to diversify and early exercise.