Core and Guay (2002) suggest that there are two measures of option incentives: dollar change measure and percentage change measure for the firm’s value. For instance, Guay (1999), Coles et al. (2006), Burns and Kedia (2006) and Aggarwal and Samwick (2006) define option incentives or delta as the change in the modified BS (1973) model value of the CEO’s options for a 1% change in the stock price. In contrast, Demsetz and Lehn (1985), Jensen and Murphy (1990) and Yermack (1995) measure CEO option incentives as the dollar change in CEO options for a dollar change in the firm’s value. Jensen and Murphy (1990) assume that option incentives increase as a CEO’s fractional ownership of the firm increases, whereas Core and Guay (2002) assume that incentives increase with a CEO’s dollar ownership of the firm.
It is straightforward to compute a measure for shareholding incentives. For example, if share value increases by 1% for each 1% increase in the share price, then the common share delta equals 1 (Core
& Guay, 2002; Burns & Kedia, 2006). However, it is more complicated to calculate the incentives provided by options because the percentage increase in the value of an option is less than the percentage increase in the underlying share price, and depends on the parameters contained in the option contract (Core & Guay, 2002). Core and Guay (2002) obtained a sample of non-financial firms from the Execucomp database from 1992 to 1997 and find that the delta (the change in the dollar value of the CEO’s share and options for a 1% change in the share price) for a new option is approximately 0.75, which implies that the option value increases by $0.75 when the stock price increases by $1.00. Both Guay (1999) and Core and Guay (2002) estimate the total incentives from the CEO’s option portfolio as the weighted average of the deltas of each option held by the CEO multiplied by 1% of share price, and the total incentives provided by an option award as the weighted average of the deltas of each option awarded multiplied by 1% of the share price.
There are two methods to calculate delta and vega with regard to data collection. The first is the ‘full information’ (FI) method, whereby researchers use hand-collect data from as many as 10 years’ annual reports of a company that awards ten-year-maturity options to construct a CEOs’ option portfolios (e.g., Hall and Liebman, 1998; Guay, 1999). Even though the FI method process is tedious, it does not involve any assumptions of option exercise price.
Core and Guay (2002) provide an easy alternative to the FI method and term this technique the ‘one- year approximation’ (OA) method in which the data are retrieved from a single-year firm annual report and newly awarded options, prior awarded unvested (unexercisable) and vested (exercisable) options are treated as three separate awards. Core and Guay (2002) find that the OA proxies yield almost the same results as those of the FI method, but one limitation of the OA method is the underestimation of the average exercise price of the out-of-the-money options.
This current study uses the FI method for two reasons. First, the study’s research time span is from 2003 to 2012 when CEO turnover was quite high. Second, the exercise prices of the CEO’s option portfolio are readily available from the firm’s annual reports.
Vega and delta in this current study refer to the dollar value of vega and delta of a CEO’s option portfolio. The BS formula is a commonly used method to calculate vega and delta. There is a large debate about the appropriateness of the BS formula in valuing ESOPs. Lambert, Larcker and
Verrecchia (1991) argue that a market-based valuation formula such as BS does not capture the real executive incentives provided by ESOPs. More specifically, Lambert et al. (1991) suggest that measuring the magnitude of a CEO’s incentive effect to increase a performance variable such as share price is not equal to the partial derivative of the value of the CEO’s option with respect to a change in the performance variable, because of the huge differences in pay levels, degree of risk- aversion and degree of personal diversification among CEOs.
In contrast, Core and Guay (2001) argue that option grants are meant to increase incentives. Core and Guay maintain that the BS formula can be used to value option incentives delta and vega under the assumption that executives can adjust their equity portfolios when the risk level is higher than the contracted level. If this assumption holds, then option delta and vega are market value delta and vega.
This current study assumes that option grants in Australia are meant to increase CEOs’ incentives. Consistent with previous studies (Coles et al., 2006; Dong, Wang & Xie, 2010), we use the modified the BS formula (Merton, 1973) to value a CEO’s outstanding option portfolio delta and vega. We assume the time to expiry for non-vested (non-exercisable) options is equal to the term to expiry of the vested options plus two years, since the options become exercisable (vested) two years after the options were granted to the CEOs. Therefore, the fair price of the outstanding option portfolio, option portfolio delta and vega in any given year is equal to the weighted average of the fair price, deltas and vegas of recent issued vested, non-vested options, previously issued vested, and
previously issued non-vested options. Detailed construction of CEOs’ option portfolio fair price, vegas and deltas are presented in Appendix A.