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The Actuary The magazine of the Institute & Faculty of Actuaries
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Actuaries, share schemes, and options

Most readers of The Actuary will be aware that share options can form a major element of an executive’s remuneration package. As a result of the reports of the Greenbury and Cadbury Committees on corporate governance and the chancellor’s recent announcements, option schemes have received high media exposure, and institutional investors are demanding increasingly challenging performance conditions on the exercise of options. Although mainly the province of lawyers and accountants, share scheme work can provide actuaries with an opportunity to make an important contribution by applying their expertise in finance and probability.

Types of arrangement
The two main types of share schemes are:

An executive share option scheme (ESOS)
Options are granted to the executive with an exercise price equal to the share price at grant. If specified performance conditions are met, the options may be exercised.

A long-term incentive plan (LTIP)
Free shares are earmarked for the executive, usually via the purchase of existing shares by a discretionary trust. At the end of the performance period, the proportion of shares actually awarded to the executive will usually depend on the company’s performance against some comparator group. For example, if the performance measure is total shareholder return (TSR), the schedule in table 1 is typical.
Table 2 illustrates popular performance measures for LTIPs and ESOSs in the top 350 UK companies. Note that for an LTIP there is usually only one performance period, reflecting the fact that the award of free shares is more generous than the growth in share price available under an ESOS.

Role of the actuary
Actuaries can assist in valuation of a share incentive package. Typical situations are:

The introduction of a new share incentive package
The valuation enables the board to demonstrate to shareholders that the value of the recommended package is in line with market practice.
Furthermore, the Association of British Insurers’ statement of principles for share incentive schemes (July 1999) recommends that ‘the expected value of the award at the outset [be disclosed”, bearing in mind the probability of achieving the stipulated performance criteria’.
The replacement of one arrangement by another
Ensure that the values of the two arrangements are comparable.
Each case must be considered on its own, and close attention must be paid to the particular performance conditions imposed.

Valuation of options
To value options, the BlackScholes equation is normally used as a starting point, treating a LTIP as an option with a zero exercise price. The algebra is then modified to take account of the scheme’s performance conditions and the fact that the options are quasi-American they can be exercised over a period of time rather than on just one day. The following can all have an effect on the value of an option.
Window of exercise
This applies to an ESOS and is usually between three and ten years from the date of grant. A longer window of exercise normally increases an option’s value.

Length and type of performance period
(one-off, rolling or increasing)
A longer performance period reduces the value of an option.

Executive remaining in service
An option is usually only exercisable while an executive remains employed by the company. As with all situations involving decrements, the estimation of the probability of leaving service will be highly dependent on the particular circumstances. For example, an additional golden handcuff arrangement may just have expired, thus increasing the likelihood of the executive leaving the company.

Market realignment of company (change in
future dividend yields)
In many situations it is reasonable to assume that the future dividend yield will be constant and to use the yield over the past year as an estimate. However, if the current yield is very low, one cannot necessarily assume it will remain so. Investor expectations of improved future profitability of the company may be fulfilled, resulting in a significant rise in dividend yield and a slowdown in share price growth. Correspondingly, a high dividend yield may be an indication of expected dividend cuts in the future.

A pitfall to be avoided
If the exercise price of an option is very low, the time value of the option will be minimal. This means that the option should be exercised immediately, as the resulting dividends are greater than the deposit rate one would otherwise earn on the exercise price. However, the situation may be complicated by the fact that income tax is payable on the value of the shares awarded. A future reduction in tax rates may mean it is advisable to delay exercise, contradicting the mathematical theory.

In the spotlight
Share scheme work, like all areas of actuarial work, requires familiarisation with its own lore and terminology. Of particular note is the challenge involved in explaining to a non-mathematician the significance of expected value, where the underlying outcome has a very high volatility. As executive remuneration remains in the spotlight in the UK and institutional shareholders expect to see greater disclosure of the potential value of share incentive schemes, the role of the actuary will become more important.

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