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Estimation of Employee Stock Option Exercise Rates and Firm Cost⇤

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Estimation of Employee Stock Option Exercise Rates and Firm Cost⇤ Estimation of Employee Stock Option Exercise Rates and Firm Cost⇤ Jennifer N. Carpenter Richard Stanton Nancy Wallace New York University U.C. Berkeley U.C. Berkeley December 1, 2017 Abstract We develop the first empirical model of employee-stock-option exercise that is suitable for valu- ation and allows for behavioral channels in the determination of employee option cost. We estimate exercise rates as functions of option, stock and employee characteristics in a sample of all employee exercises at 89 firms. Increasing vesting date frequency from annual to monthly reduces option value by 10-16%. Men exercise faster than women, reducing option value by 2-4%. Top employees exercise more slowly than lower-ranked, increasing value by 2-10%. Finally, we develop an analytic valuation approximation that is much more accurate than methods used in practice. ⇤Financial support from the Fisher Center for Real Estate and Urban Economics and the Society of Actuaries is gratefully acknowledged. For helpful comments and suggestions, we thank Daniel Abrams, Terry Adamson, Xavier Gabaix, Wenxuan Hou, James Lecher, Kai Li, Ulrike Malmendier, Kevin Mur- phy, Terry Odean, Nicholas Reitter, Jun Yang, David Yermack, and seminar participants at Cheung Kong Graduate School of Business, Erasmus University, Federal Reserve Bank of New York, Fudan University, Lancaster University, McGill University, New York University, The Ohio State University, Oxford Univer- sity, Peking University, Rice University, Securities and Exchange Commission, Shanghai Advanced Institute of Finance, Temple University, Tilburg University, Tsinghua University, and the 2017 Western Finance As- sociation meetings. We thank Terry Adamson at AON Consulting for providing some of the data used in this study. We also thank Xing Huang for valuable research assistance. Please direct correspondence to [email protected], [email protected], or [email protected]. 1 Introduction Employee stock options (ESOs) are a major component of corporate compensation and a material cost to firms. Murphy (2013) reports that options represented 21% of CEO pay in 2011, and the 2010 General Social Survey of the National Opinion Research Center found that 9.3 million employees hold options. As a fraction of outstanding shares of common stock, the median number of shares underlying outstanding options at S&P 1500 firms was 4.4% in 2010, with almost 1% of outstanding shares allocated to new option grants annually, according to Equilar (2011). At the same time, accounting valuation methods for ESOs significantly a↵ect corporate decisions about compensation structure and allocation, and thus a↵ect both employee incentives and firm cost. For example, the 2005 change in accounting valuation precipitated a decline in the granting of options from previous levels and an increase in the allocation to top managers.1 Valuation methods for employee stock options are therefore an important issue for investors. ESO valuation remains a challenge in practice, as illustrated by the recent controversy over the value of options granted to the CEO of IBM, in which Institutional Shareholder Services valued the options at more than twice the company’s valuation (see Melin, 2017). The valuation of these long-maturity American options is very sensitive to assumptions about how they will be exercised, and because employees face hedging constraints, standard option- exercise theory does not apply. For example, employees systematically exercise options on non-dividend-paying stocks well before expiration2 and this substantially reduces their cost to firms. The modifications to Black Scholes used to address this in practice are inadequate because they ignore key features of employee exercise patterns. At the same time, existing empirical descriptions of option-exercise behavior based on OLS or hazard rate models, such as Heath, Huddart, and Lang (1999), Armstrong, Jagolinzer, and Larcker (2007), and Klein and Maug (2011), are not appropriate as an input for option valuation. In this paper we develop the first empirical model of employee option exercise suitable for valuation and apply it in a sample of all employee exercises at 89 publicly traded firms from 1981 to 2009 to show empirically how employee exercise patterns a↵ect option cost to firms. We develop a GMM-based methodology that is robust to both heteroskedasticity and correlation across option exercises to estimate the rate of voluntary exercise as a function 1For example, Equilar (2011) reports that the median number of shares underlying outstanding options at S&P 1500 firms fell from 6.1% in 2006 to 4.4% in 2010, while the fraction of options allocated to CEOs and named executives rose from 21% to 26%. Murphy (2013) finds that as a fraction of total CEO pay, option compensation of 21% in 2011 is down from 53% in 2001. Other estimates of the fraction of CEO pay in the form of options include 33% in 1991 from Yermack (1995) and 25% in 2008 from Frydman and Jenter (2010). 2See, for example, Huddart and Lang (1996); Bettis, Bizjak, and Lemmon (2005). 1 of the stock price path and of firm, contract, and option-holder characteristics. We show that these characteristics significantly a↵ect exercise behavior, in a manner consistent with both portfolio theory and results from the behavioral literature, such as those in Barber and Odean (2001). We then value options using the the estimated exercise function and show how sensitive option values are to the exercise factors. For example, the passage of vesting dates triggers exercises, so vesting structure has a large impact on option value: Increasing vesting-date frequency from annual to monthly reduces option value by as much as 16% for typical option holders. In addition, men exercise options significantly faster than women, resulting in a 2-4% lower option value. Consistent with both standard option theory and utility-maximizing theory, the rate of voluntary option exercise is positively related to the level of the stock price and the imminence of a dividend. However, the exercise rate is also higher when the stock price is in the 90th percentile of its distribution over the past year, which may reflect behavioral e↵ects. We also proxy for employee portfolio e↵ects using the employee’s Black-Scholes option wealth and option risk, and we find that, consistent with theory, employees with greater wealth tend to exercise more slowly, and employees with greater risk tend to exercise faster. In contrast to the existing academic literature, our proprietary dataset contains all em- ployee exercises at a large number of firms.3 Since estimation of exercise behavior requires a large sample of stock price paths, and thus a large number of firms, our paper can investigate di↵erential option-exercise patterns and option cost across top and lower-ranked employees. We define top-ranked employees as those among the top ten option holders at a given firm. To the extent that options are granted where their performance incentives have greatest benefit, the top option holders within a firm are likely to be the key decision makers. Con- sistent with Bettis et al. (2005), Armstrong et al. (2007) and Klein and Maug (2011), we find that top-ten option holders exercise slower than lower-ranked holders within a given firm. Similarly, in a subsample with data on employee titles, senior executives tend to exercise at slower rates than lower-ranked employees. We then show that this pattern implies that the options of top employees are typically worth 2-10% more than those of lower-ranked employees. These results may stem from greater wealth among top employees, although we do try to control for this. Finally, our methodology permits us to test for di↵erential exercise factor e↵ects across top and lower-ranked employees. We find that top employees are less responsive to the passage of vesting dates and the passage of the stock price to a new high, but the gender e↵ect is more pronounced among top employees than among the lower-ranked. 3For example, the samples of Heath et al. (1999) and Armstrong et al. (2007) contain only seven and ten firms, respectively, while the sample of Klein and Maug (2011) contains only top executives. 2 We compare option values calculated using the empirically estimated exercise function with option valuations based on methods used in practice. While FAS 123R outlines a range of potentially acceptable methods, the vast majority of firms use one of two Black- Scholes-based approximations with a downward adjustment to the option’s expiration date to account for early exercise. The SEC’s Sta↵Accounting Bulletin (SAB) 110 permits firms with limited exercise data to use the Black-Scholes formula with the stated expiration date replaced by the average of the vesting date and stated expiration date. This adjustment is simple to make, and does much better than the traditional Black-Scholes formula, but it takes no account of the stock return and employee characteristics that a↵ect exercise patterns and the approximation errors can be quite large. The modified Black-Scholes method permitted by FAS 123R replaces the option’s stated expiration date with the option’s expected term. Unfortunately, this expected term must be estimated from historical firm data on option outcomes, and can entail significant error, since option outcomes depend on a firm’s stock price path and a given firm has option data based only on its own realized stock price path. We show, moreover, that even in the hypothetical ideal case where the option’s expected term is estimated perfectly, this method creates systematic biases. In particular, we calculate the option’s expected term exactly from the estimated exercise function to get the Modified Black Scholes value and show that the approximation error still varies widely and systematically with firm characteristics. Finally, recognizing the practical appeal of a Black-Scholes-based approximation, we develop an analytic approximation of the implied Black-Scholes maturity, which, when used as the expiration date in the Black-Scholes formula, delivers option values that much more closely approximate the correct option value than the existing methods.
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