Abstract
This study investigates the determinants of the expected stock-price volatility assumption that firms use in estimating ESO values and thus option expense. We find that, consistent with the guidance of FAS 123, firms use both historical and implied volatility in deriving the expected volatility parameter. We also find, however, that the importance of each of the two variables in explaining disclosed volatility relates inversely to their values, which results in a reduction in expected volatility and thus option value. This can be interpreted as managers opportunistically use the discretion in estimating expected volatility afforded by FAS 123. Consistent with this, we find that managerial incentives or ability to understate option value play a key role in this behavior. Since discretion in estimating expected volatility is common to both FAS 123 and 123(R), our analysis has important implications for market participants as well as regulators.
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Notes
See CFO.com, Today in Finance for April 01, 2004, The Cost of Expensing Stock Options, at http://www.cfo.com/article.cfm/3012993?f=TodayInFinance040104
Estimating option lives does involve discretion, but the effect of this assumption on option fair value as well as the cross-sectional and time-series variation in expected option lives are relatively small. Moreover, there is no obvious benchmark against which this variable can be assessed.
SFAS No. 123(R), which was promulgated in December, 2004, mandates income statement recognition for employee stock option expense for fiscal years starting after June 15, 2005. However, in April 2005, the Securities Exchange Commission amended Rule S-X to delay the effective date for compliance with SFAS No. 123(R) to fiscal year starting after June 15, 2005. Based on the amended rule, most companies are required to adopt SFAS No. 123(R) on January 1, 2006.
SFAS No. 123 guides that in estimating expected volatility companies should consider historical volatility and forward-looking information. SFAS No. 123(R) is more specific in that it guides that in addition to historical volatility, implied volatility from traded options can be considered.
A necessary condition for the magnitude of volatility understatement to vary with incentives is that managers incur costs that offset the benefits of reporting understated option expense. We discuss these costs in Section 3 below.
The use of the IBES database did not lead to any loss in sample size. There were 700 observations out of 9,185 with no analyst following data on IBES, which we coded as having zero analyst following. Removing these observations does not affect the results reported in Table 7 below for either the analyst following partition or the composite measure.
Following Watson (1990), we detect multivariate outlier observations using the statistic\({\chi _{\rm i}^{2}=(\hbox{m}_{\rm i}-\bar{\hbox{m}})'S^{-1}(\hbox{m}_{\rm i}-\bar{\hbox{m}})}\), where i denotes the ith observation; bar denotes average over all sample firms; m is the 4 × 1 vector of volatilities (historical, implied, disclosed and realized); and S is the 4 × 4 sample covariance matrix of m.
It is well recognized that ESOs violate important assumptions underlying the Black–Scholes model (e.g., Black–Scholes assume a diffusion process and values European calls, whereas in reality stock prices may jump and nearly all ESOs are American calls). Moreover, academic research offers models which might be more appropriate for valuing ESOs (see, e.g., Hemmer, Matsunaga and Shevlin, 1994; Carpenter, 1998). Yet, most firms use the Black–Scholes model to value their ESOs, perhaps due to the robustness of the Black–Scholes values and the complexity of alternative models.
Indeed, our success in matching on time-to-maturity is only partial. The mean time-to-maturity of our traded options is 329.2 calendar days.
For example, if stock price is $42 and the two nearest call options have strike prices of $40 and $45 and implied volatilities of 0.34 and 0.36, respectively, we estimate the implied volatility of call options as: \({\frac{(1/2)\ast 0.34+(1/3)\ast 0.36}{(1/2)+(1/3)}=0.348}\). If all strike prices are on one side of the prevailing stock price, we use the implied volatility of the option with the nearest strike price.
For the Fama–MacBeth regressions, the t-statistics are corrected for auto-correlation using the methodology outlined by Bernard (1995).
When we use other measures for incentives and ability to manipulate, we consistently find that β4 (β5) increases (decreases) monotonically from the low incentives/ability group to the high incentives/ability group.
We also conduct three types of sensitivity tests to ensure that our results are robust. First, to verify that our methodology of extrapolating at-the-money implied volatilities does not induce significant measurement error, we rerun our tests excluding observations where the nearest strike price is more than five percent different from the prevailing stock price. Second, to control for skewness in the distribution of our volatility measures, as well as to account for potential non-linearities in the relationship between our dependent and independent variables, we rerun our analyses using: (1) rank regressions, and (2) log transformed variables. Results from all three types of sensitivity tests (not tabulated for parsimony) are similar to our basic results.
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Acknowledgements
We would like to thank the editor (Richard Sloan), two anonymous referees and helpful comments from Menachem Brenner and workshop participants at Columbia University, University of Chicago, University of Toronto’s Rotman School of Management, and the Susquehanna International Group LLP 2004 Accounting Research Conference. We appreciate excellent research assistance from Lucile Faurel, Sharon Katz, Seunghan Nam, and Ron Shalev. Special thanks to David Trainer and Kiran Akkineni of New Constructs for providing disclosed volatility and option life figures gleaned from Form 10-K’s footnotes.
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Bartov, E., Mohanram, P. & Nissim, D. Managerial discretion and the economic determinants of the disclosed volatility parameter for valuing ESOs. Rev Acc Stud 12, 155–179 (2007). https://doi.org/10.1007/s11142-006-9024-x
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DOI: https://doi.org/10.1007/s11142-006-9024-x