After considering all available information, a company may decide to exclusively rely on its historical volatility, because it believes that its historical volatility provides the most reliable indication of future volatility. According to SAB Topic 14 (section D.1, question 4), a company may rely exclusively on historical volatility when the following factors are present, so long as the methodology is consistently applied:
- A company has no reason to believe that its future volatility over the expected or contractual term, as applicable, is likely to differ from its past;
- The computation of historical volatility uses a simple average calculation method;
- A sequential period of historical data at least equal to the expected or contractual term of the share option, as applicable, is used; and
- A reasonably sufficient number of price observations are used, measured at a consistent point throughout the applicable historical period.
The following sections address adjustments that a company may need to consider when developing its historical volatility assumption, which may lead the company to conclude that exclusive reliance on historical volatility over the most recent period of time equal to the expected term is not appropriate.
Frequency of historical volatility measurement
The frequency of stock price measurement can significantly affect the expected volatility assumption. For example, volatility estimates vary depending on whether stock prices are measured on a daily, weekly, or monthly basis. While differences in annualized volatility estimates due to measurement frequency differences may be small, this is not always the case.
A high frequency of measurement (e.g., daily stock prices) provides the largest possible sample size, as discussed in ASC 718-10-55-37(d)
. According to that paragraph, a public company "would likely use daily price observations." On the other hand, it also may be appropriate to use lower frequency data (e.g., monthly), provided there is an adequate sample size.
does not provide detailed guidance on adequate sample sizes for computing historical volatility. SAB Topic 14, footnote 56, indicates that monthly data should not be used for periods shorter than three years due to insufficient data, indicating that more than 36 data points should be used to estimate historical volatility when using monthly data. Footnote 64 of SAB Topic 14 suggests that two years of daily (approximately 500 measurements) or weekly (approximately 100 measurements) data could provide a reasonable sample, though daily data may be more appropriate when there is an expected term shorter than two years.
When volatilities calculated based upon different measurement intervals (e.g., daily, weekly and/or monthly) differ significantly, a company may consider averaging the annualized volatility estimates from the different measurement intervals. When an option's expected term is much shorter than the available history or when there is less history available, generally it would be more appropriate to use an estimate based on daily or weekly data in order to assure an adequate sample, assuming daily or weekly prices are available and that sufficient trading occurs on each day to make these quotes reliable market indicators. Regardless of which measurement frequency is selected, it should be used consistently for all awards.
Insufficient historical stock price data
Some companies do not have historical stock prices that can be reliably determined for a period that is at least equal to the expected term of their options or do not believe that their recent historical volatility fairly reflects future expectations (e.g., a company that has been public for only three years and has estimated the expected term of its options to be five years). In such cases, it may be appropriate to blend the company's own volatility data with that of a peer group of public companies. Companies in the peer group should (1) be of similar size, (2) have similar histories and relatively comparable financial leverage, and (3) be in similar businesses (industry and geographical markets).
To compute peer-group volatility, a company should use data from one or more relatively recent historical periods that are at least as long as its expected term. Though various weightings are possible, volatility data from the peer group companies are usually averaged, with each company given equal weight.
If a company that grants options with a five-year expected term is looking to use peer-group data to supplement its own last three years of historical data, it would be appropriate to obtain peer-group data for the two years preceding the past three years. In this way, the historical period would equal the five years of the expected term. The company could give the peer-group's average volatility for the two earliest years a two-fifths weighting and its own historical volatility three-fifths. In other fact patterns, other weightings of peer company and company-specific volatilities may be appropriate. A company generally should avoid using overlapping periods of data in this type of analysis (e.g., averaging the peer-group data over the full five-year window with the company's three-year historical data), because that approach would unevenly weight certain periods (see the section below on Mean-reversion and term structure of volatility).
Newly public companies
SAB Topic 14 also allows newly public companies (i.e., those that recently filed for an IPO, whether or not the IPO has yet occurred) to base their estimates of expected volatility on the historical, expected, or implied volatility of similar companies whose stock or option prices are publicly available, after considering the industry, stage of life-cycle, size, and financial leverage of the other companies.
A newly public company can develop peer-group volatility using some of the companies listed in an industry sector index (e.g., a computer vendor may look to a NASDAQ Computer Index, if there is one). However, the company may not use the volatility of the index itself as a substitute. The newly public companies should use the companies selected from the industry sector index consistently, unless circumstances change, or until it has either a sufficient amount of historical information regarding the volatility of its own stock price or other traded financial instruments become available to derive an implied volatility to support an estimate of its expected volatility.
SAB Topic 14 and ASC 718
cite other instances when it may be appropriate to adjust historical volatility for past events that a marketplace participant would likely discount, such as a discrete event that is not expected to recur (e.g., failed takeover bid or major business restructuring). Historical data demonstrably affected by such events (e.g., the abnormally high volatility observed in the six-month period leading up to or following a significant transaction) might be reasonably excluded from the historical volatility calculation, provided the event is specific to the reporting company, under management's control, and not expected to recur during the expected term of the award. However, question 2(s) in Section D.1 of SAB Topic 14 indicates that such exclusions are expected to be rare.
One-time events may also lead to increased expected volatility as compared to unadjusted historical volatility. For example, if a company recently announced a merger that would increase its business risk in the future, then it would consider the impact of the merger in estimating its expected future volatility if it is reasonable that a marketplace participant would also consider this event.
In the rare situations when nonrecurring events such as those described above imply that historical data may not be representative of the future, a company may simply exclude stock-price data from the affected period(s) and use the remaining history so long as there remains sufficient historical data to make an estimate. Companies should carefully analyze volatility estimates from periods that include breaks to ensure that those gaps are not treated as market-price movements. In some cases, such as when the excluded period is an extended period of time, a company may consider using a blended estimate that incorporates peer-group data for the excluded period.
Some companies may be tempted to exclude historical volatility data caused by extraordinary market conditions, such as the effects of the credit crunch in 2008 and the COVID-19 pandemic. We generally believe that data should only be excluded when the volatility relates to one-time events specific to the reporting company that are reasonably within the control of the company’s management or shareholders. Data related to events affecting the broader market should not be excluded from a company’s analysis, even when those events are considered extremely unlikely to recur. In addition, data from periods of significant stock price changes over a short period of time, such as may occur due to lawsuits, failed product trials, or recalls, generally should not be excluded.
Mergers, acquisitions, divestitures and changes in financial leverage
The volatility of a merged company may differ from either predecessor, while a spin-off may affect volatility of the new entity and its former parent. With merged companies, each of which represents a major component of the merged entity, typically a weighted average of the two entities' historical volatility is appropriate, with the volatility of each company weighted by relative market capitalization prior to the transaction. Spin-off companies will probably have to use peer-group data to estimate volatility, and their former parent may have to do the same if the spin-off fundamentally changes the parent.
Lastly, financial leverage needs to be considered as a factor in examining historical volatility. If a company's debt-to-equity ratio has shifted dramatically over recent history whether due to a merger, spinoff, or just re-leveraging, consideration of other data points such as peer group information may be appropriate.
Mean reversion and term structure
A statistical phenomenon referred to as mean reversion occurs when a series of values is more likely to move towards its longer-term mean than away from it. Volatility is often observed to be cyclical, moving between temporary or short-term highs and lows but then reverting back to the long-term average. Therefore, if a stock’s price has been extraordinarily volatile for the past year when compared to a longer period, it may be reasonable to assume that, within another year, the stock price volatility will begin to migrate toward its longer term average volatility level. Under these circumstances, the long-term volatility assumption for options granted in the next year might fall between that of the more volatile recent period and the less volatile long-term average. The mean-reversion theory would also apply when recent volatility has been extremely low compared to long-term average volatility. Companies should consider mean reversion when significant cyclical swings in volatility are observed in the historical data.
Term structure refers to how historical volatilities may vary over specific intervals. This may be relevant in determining the volatility assumptions over the option's expected term (or contractual term when a lattice model is used). The justification for incorporating term structure into an estimate of expected volatility would ordinarily be based on mean-reversion. Thus, if last year's volatility was 20%, but average annual volatility over the previous five years was 40%, the annual volatility assumption for each of the next five years might be closer to 20% at the beginning of the expected term and eventually move toward 40%. An explicit term structure approach to the expected volatility assumption might be used in a more refined lattice model instead of a single fixed volatility assumption, where exercises and vested cancelations are assumed to occur not just after a single weighted average expected term, but throughout the option's entire contractual life. However, the mean-reversion concept may also be applied to a single-value volatility forecast input into the Black-Scholes model.
Mean reversion will generally be most applicable in developing the volatility assumption when expected term is relatively long and recent short-term volatility is very different from long-term average historical volatility. In practical terms, applying the concepts of mean reversion and term structure to expected volatility assumptions involves looking for evidence of possible mean reversion by examining volatility over at least two historical periods of varying lengths, assuming a company has the data. According to ASC 718-10-55-37(a)(2)
, a company using the Black-Scholes model should start with a period equal in length to the option's expected term, then use progressively shorter periods to determine whether there is a pattern of changing volatility (though longer periods may be examined as well).
If consistent volatility experience is exhibited by using periods of varying lengths, or if actual experience exhibits no clear pattern over various sub-periods of the historical period that corresponds with the option's expected term, then it may be more appropriate to use an unadjusted volatility estimate based on data from a consistent historical period equal to or greater than the length of the expected term. While mean reversion may not be apparent in the historical data based on periods shorter than the expected term, companies should also consider whether it applies on a longer time scale. A company that has typically used five-year volatility for an award with a five-year expected term might also consider data over seven- and ten-year windows, as well as over periods shorter than five years. If the five-year volatility appears unusual, using a blend with longer-term data may be more appropriate. However, using data that is too old (much longer than the typical contractual terms of ten years) is likely to be less relevant and not the best predictor of expected volatility.
It may be difficult to assess whether changes in volatility relate to mean reversion or are due to specific circumstances, such as a company's growth, diversification, reorganization, merger, or spin-off. Careful examination of year-by-year volatility in this context compared to volatility measured over the entire expected term may be helpful in assessing whether a mean-reversion adjustment is appropriate.