Options Backdating: The Statistics of Luck

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by Renzo Comolli, Branko Jovanovic, Patrick Conroy & Erik Stettler

Allegations of backdating typically involve a claim of practice by which companies look back to past stock prices and record option grants on a date prior to the actual date of the grants – a date at which the stock price was low. According to these allegations, companies were motivated by two goals. The first was to report granting options with a strike price equal to the stock price on the day of the grant – a goal motivated by accounting and taxation rules. The second goal was to grant options to provide remuneration to the employees who receive them. One way to increase the value of the options is to grant them with a strike price lower than the stock price on the day in which the grant is issued.¹ In finance parlance, according to the allegation, these companies granted options that were “at the money” on paper, while, in fact, the options were “in the money.”

What the academics are saying about stock price patterns around grant dates

Aggregate Patterns

The academic literature so far has focused on aggregate patterns across publicly traded companies, not on individual companies. The academic literature on backdating is designed to detect whether the aggregate pattern of stock price movement close to grant dates is inconsistent with an assumed benchmark, not whether an individual company has engaged in backdating. The benchmark that the academic literature has assumed, sometimes explicitly, sometimes implicitly, is that grants were made on a random day. This benchmark is analogous to saying that the grant date is determined by a process similar to that used to select the winning number in the Powerball lottery or to toss a coin. That is, the company randomly picks from trading days when selecting the day of the option grant, regardless of past prices or expectation of future prices.

Different authors have indeed investigated option grant timing and have found varying results. Lie (2005) finds that, in the aggregate, stock prices tend to decline prior to grant dates and increase immediately after grant dates. Lie speculates that the explanation for this price pattern lies in backdating. Other authors who have investigated stock price movements around option grants find results that in part correspond to, and are in part at odds with, Lie’s findings. These other works propose a different explanation for their findings: insiders manipulate information releases around the grant dates, a practice sometimes referred to as spring loading. The academic articles do not, and could not, given the methodologies that they use, find proof of backdating, spring loading or similar practices; they find, or claim to find, aggregate price patterns that are consistent with those practices being adopted by at least some companies.

Currently available academic literature on option timing does not disentangle legal from illegal practices

Current academic literature uses methodologies that are not designed to determine whether an individual company has engaged in backdating. They are designed to detect aggregate patterns, but do not directly analyze specific companies. To our knowledge, no published academic study has addressed the likelihood of grants of specific companies.

The probability of grants

What is the benchmark to determine whether a grant is likely or unlikely?

The assumption made by academic articles and popular press that, in the absence of backdating, a company would randomly grant options throughout the year (according to the Powerball method) is problematic. Rather than randomly granting options, companies may be more likely to grant options on days when they perceive their stock to be undervalued. This could lead to a pattern where the price increases after grants would be better than random even in the absence of backdating. Similarly, one would expect to find a price pattern different from random in cases where a company offers employees a bonus paid in option grants if certain production deadlines are reached and announced to the public.

Some patterns of options grants that may appear very unlikely are actually very likely

On March 18, 2006, the Wall Street Journal published an article entitled “The Perfect Payday” singling out seven companies that, according to the Journal, exhibited “wildly improbable option-grant patterns.” Yet some grant patterns that may appear extremely unlikely at first are actually very likely and should be expected.

To illustrate the tricky issues associated with identifying backdating in individual companies, we will set aside for the moment the fact that some companies may issue option grants when they perceive their own stock to be undervalued (that is, we set aside the issue of the appropriate benchmark). Rather, we adopt the assumption that companies are equally likely to grant on any trading day within a year and show that even under this (the Powerball) assumption some grants that may appear unlikely are actually very likely. Probability theory indicates that if companies were granting options using the Powerball method, we would observe grants on days when the stock price is at a relative low, on days that the stock price is at a relative high, and on days that it is in between.

Probability theory also implies that, if the companies granted options using the Powerball method for each grant, by chance, some companies would grant on a day with a relatively low strike price for most or all of their grants. This can be counterintuitive. However, statistical theory states that when many companies select grant dates at random, this will be the case.

The Wall Street Journal did not account for the fact that there are a large number of directors and officers (D&O) in the United States who receive grants. With such a large number of D&O, it was practically certain that some of them would receive most of their grants on days when the stock price was particularly low, even just by chance.

In the same way in which there are companies that granted on very favorable days, there are companies that granted on very unfavorable days

As mentioned above, probability theory implies that some companies would grant on days that are consistently good and others on days that are consistently bad, even with the Powerball method. We performed our own analysis that confirmed this to be true for U.S. companies. We analyzed grant patterns for U.S. companies that granted options from 1995 through August 2002.² We focused on at-themoney grants.³

Following the Wall Street Journal’s approach, we calculated the 20-day stock price return after each trading day in the year and ranked them. For a year with 252 trading days, if a grant fell on the day followed by the highest 20-day return, it would have a probability of one in 252 of occurring by chance. Likewise, the chance of the grant occurring on the day of the year ranked eighth or higher would be eight in 252. For each company, we then averaged the ranks associated with each grant. Exhibit 1 shows all companies and the average rank of their grants.

For example, the exhibit shows that there are companies with an average rank between 6 and 12. Informally, people would say that these companies have been very lucky. The exhibit also shows that some companies have an average rank between 240 and 246 (that is, their grants rank on average between the 6th and 12th worst day of the year). Informally, people would say that these companies have been very unlucky.

Speculation has been rampant about companies that have been very lucky, yet nobody has been paying any attention to companies that have been very unlucky. Probability theory tells us that chance alone can produce both very lucky and very unlucky companies, and indeed we see that there are some of both types. Consistent with some of the academic findings, exhibit 1 also shows that the aggregate pattern of returns for U.S. companies is more favorable than what granting based on the Powerball method would suggest. Specifically, there are more companies that do better than 50% (ranked about 126) than there are companies that on average do worse than 50%.

This brings us back to the fact that some companies presumably issue grants when they perceived their stock to be undervalued, while some companies have admitted to engaging in backdating. Thus our finding, very much like the academic literature, does not disentangle legal from illegal practices.

Factors disregarded in published probability calculations that may be important

On what alternative dates could the grant have been issued?

When assessing the probability of a particular grant, the grant date is compared to other days. The Wall Street Journal, for instance, compares grant dates against all other trading dates in the year in which the grant was issued. This, however, may overstate the number of “available comparison” dates. Even before Sarbanes-Oxley, a very large number of grants were reported to the Securities and Exchange Commission in Form 4, which required that a grant be reported, not within one year, but within 10 days after the end of the month of the grant.

Scheduled grants

Scheduled grants cannot be backdated. Some academic authors have taken this specifically into account and noted that grants that are always filed on the same date can hardly be prone to backdating. One needs to consider that scheduled grants may not necessarily always fall on the same calendar day. For instance, a scheduled grant may always fall on the first Monday of the fiscal quarter.

Grants for events that are good news for the company Another potential factor that (to the best of our knowledge) has not been taken into consideration is that grants may be issued to employees for the accomplishment of corporate milestones that the market interprets as good news. Investors may buy after the news of the grant reaches the market if, in fact, companies are more likely to issue grants when they perceive their stock to be undervalued. Investors may take the news of a grant as a signal to purchase the stock, thereby causing the price increase. Therefore, a high return following a grant may be a result of an increase in demand for the stock of the issuing company by investors. Thus, it may be appropriate to disentangle the price movement after a grant from the price movement after the news of a grant is on the market.

What’s next?

A lot of misconceptions have been circulating about options backdating and in particular about the statistical calculations that have been used in connection with it. On the one hand, the academic literature studying aggregate price pattern following option grants is comparatively recent and no methodology to disentangle illicit practices from legitimate ones has consolidated yet. On the other hand, we have discussed and presented corrections for some conceptual errors regarding the probability calculations concerning specific companies or specific insiders. Each new case may present some specific characteristic that challenge economists to rethink their method to arrive to the correct conclusion.

A more detailed exposition of the content in this article is available at http://www.nera.com/publication.asp?p_ID=3076

¹ The increase in value is an increase only in the potential value of the option and might not ultimately translate into any increase in value if the option is not exercised.  

² In August 2002, the passage of Sarbanes-Oxley drastically reduced the time period in which grants must be reported to the SEC.

³ Like the academic studies, we analyzed those grants that we could match to stock prices.