Editorial Type: research-article
 | 
Online Publication Date: 03 Jan 2025

On Improving Size and Leverage Adjustment Methods for Equity Volatilities

CFA, ABV/CPA, ASA
Article Category: Research Article
Page Range: 44 – 53
DOI: 10.5791/2163-8330-43.2.44
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Although in practice equity volatility remains one of the most significant value drivers for many earnout and derivative valuations, equity allocation analyses, and liquidity discount assessments, awareness regarding appropriate methods and techniques for adjusting volatility is still lacking in the industry. The paucity of available academic literature on the topic is confusing and comes with inappropriate guidance from industry publications. Size and leverage methodologies for adjusting equity volatility—presented in a Business Valuation Review article published in 2024 by Covrig, Travers, and Harms—are examined here. A size-adjustment method developed by this author fifteen years ago is compared with the size-adjustment method of Covrig and colleagues. Leverage adjustments and problems associated with various methodologies suggested in industry publications when adjusting volatility for size are discussed.

In a recently published 2024 article in Business Valuation Review, Covrig, Travers, and Harms (2024) presented methods for estimating size and leverage adjustments for volatility.1,2 The article included a good description of the methods the authors currently use to adjust volatility for differences in size and leverage, but appears to have overlooked several additional methods for adjusting equity volatilities (Covrig, Travers, and Harms 2024).

In three previously published articles in Business Valuation Review (two of which were referenced in Covrig, Travers, and Harms [2024]), I presented a simple volatility size-adjustment methodology based on empirical data (hereafter referred to as the H Method) that substantially differs from the Covrig, Travers, and Harms (2024) methodology for size adjustment (Herr 2008, 2018a, 2018b). Further, industry publications such as the American Institute of Certified Public Accounts (AICPA 2019; PV Guide)3 and the 2019 Appraisal Foundations’ Valuation of Contingent Consideration (Earnout Guide) suggest additional methods for adjusting volatility for size.4

This article discusses several shortcomings in the CMT Method (Covrig, McConaughy, and Travers 2018), which occur primarily due to reliance on data inconsistent with volatility assessments. Then, a summary of key differences between the CMT Method and the H Method is presented. I make a few observations associated with the authors' suggested method for making leverage adjustments. Finally, comments are provided associated with proposed volatility adjustment methods in industry publications. Tips gathered over the years are shared with the hope that readers will find them useful in their own practices.

Adjusting Volatility for Size (CMT Method)

The CMT Method (Covrig, McConaughy, and Travers 2018) relies on Kroll’s (2023d) Risk Premium Report Study (RPRS) as its sole source of data. The RPRS is well known and well regarded among valuation specialists for its primary design of being used to develop cost of equity capital estimates (Kroll 2023d). The data were not prepared nor meant for the purpose of assessing volatility adjustments. As a result of the data’s use, several potential issues arise, including a lookback period mismatch, low observed volatilities in the RPRS, failure to recognize that relative size within an industry matters, incorrect size measurement, and the use of a ratio versus a differential mechanism.

Lookback period mismatch

The data in Kroll’s (2023d) RPRS cover a period from 1963 to the most current year. As a result, the RPRS’s standard deviations for each of the twenty-five portfolio-size rankings represent an approximate sixty-year lookback period using the latest RPRS.5 As many complex financial instrument, contingent consideration, and liquidity discount specialists would agree, concluding on a volatility adjustment based on a lookback period substantially longer than the subject instrument’s forward period creates a timing mismatch. Covrig, Travers, and Harms (2024) acknowledge this mismatch but do not clearly address why it would not be expected to bias size adjustments.6 Specialists do not typically rely on sixty-year lookback periods when performing valuations of complex financial instruments, earnouts, and liquidity periods because these generally are shorter term in nature. Even under an option pricing method for the purpose of equity allocation, it is rare to rely on a forward period exceeding five years. Instead, generally accepted practice is to match the historical lookback period with the forward period of the instrument being valued when using a lookback approach.7 This is impossible using the RPRS.

Although the effect of the timing mismatch is hard to measure, theoretically the direction of the bias is toward overstatement. The literature and theory suggest that longer holding periods are of greater risk than shorter holding periods and therefore would be expected to have greater volatility compared with shorter holding periods.8 Intuitively, longer lookback periods would have a greater likelihood to include larger swings in the market, industry, or proxy company.

Low observed RPRS volatilities

A comparison of the standard deviations in RPRS to real-world volatilities shows the unusually low standard deviations in RPRS (Kroll 2023d). As shown in Covrig, Travers, and Harms (2024), average standard deviations by portfolio ranking in Kroll’s (2023d) RPRS range from around 16% for the largest company ranking to 33% for the smallest portfolio group ranking (twenty-fifth portfolio ranking, with a market value of invested capital [MVIC] of $620 million or less).9 As a point of reference for readers, in my article the five-year median lookback volatility among all industries (a) without the exclusions made in Kroll’s (20234d) RPRS, (b) based on a market capitalization over that same lookback period of between $1 million and $687 million, and (c) over the period from 1998 through 2017 ranged from approximately 48% to 64% (Herr 2018b). In an unpublished study presented at the 2019 ASA International BV Conference, Marina Kagan found that asset volatilities in her smallest size deciles (one to three) ranged from 28% to 53%.10

There are two primary reasons and several minor reasons for the RPRS low observed volatilities (Kroll 2023d). After classifying companies into each of the twenty-five differently sized buckets, Kroll (2023a, p. 2) calculates “annual portfolio returns … by compounding the monthly portfolio returns” for each bucket.11 The use of price returns calculated from a portfolio of companies leads to lower variance for each of the twenty-five portfolio groupings compared with the median returns from individual companies in each of the groupings because of the existence of nonperfectly correlated returns among the companies in the portfolio (commonly known as the diversification effect).

In practice, equity volatilities for individual companies should not include any diversification effect; those price returns should be based on a company’s own price returns. It is not clear how the diversification effect can be unwound in RPRS for use with the CMT Method.

As a second primary cause for low observed volatilities, RPRS excludes high financial risk companies (Kroll 2023d).12 This contrasts with the CRSP decile study, which includes those companies. Kroll (2023d) publishes a separate high financial risk study like the RSRP for those specific companies. Under the logic that smaller portfolio rankings would normally contain higher-risk companies, use of RPRS data would lead to understatement of the size adjustment, particularly for smaller, higher-risk subject companies. This shortcoming could potentially be resolved if the authors incorporated the second study into their analysis.

Further contributing to low volatilities is the fact that RPRS standard deviations are calculated from annual price returns rather than monthly, weekly, or daily price returns (Kroll 2023d),13 leading to an inconsistency between standard deviations based on daily or weekly price observations calculated by the valuation specialist and RPRS's annual price observations (Kroll 2023d).14

Recognition that relative size within an industry matters

An additional concern with the use of RPRS is that there is no breakdown of volatility by industry. A company’s industry can materially impact the magnitude of the size adjustment, as shown empirically.15 As a simple illustration of the bias introduced from ignoring industry-specific impacts, I use the same example used in Covrig, Travers, and Harms (2024) to show how size adjustments are affected by industry. The example starts by assuming an MVIC of $32 billion for a guideline company and $500 million for the subject company. These values would lead to selection of the seventh and twenty-fifth portfolio rankings, respectively. With these portfolio rankings, the example concludes on an effective size adjustment of 14.2%.16

Table 1 shows volatility size adjustments based on different industries using empirical data from 1998 through 2017 (Herr 2018a)17; it details that size adjustments vary widely depending on the industry of the subject company. For comparison purposes, assume that the CMT Method’s size adjustment of 14.2% is consistent with the average size adjustment that would be made without regard to any industry (Covrig, McConaughy, and Travers 2018). Using the data in Table 1, if the subject company were in the Financials sector, the size adjustment would be overstated by 13.1% (based on a 1.1% size adjustment for Financials from Table 1). If the subject company were in the Health Care sector, the size adjustment would be understated by 14.3% (based on a 28.5% for Health care from Table 1). It is unclear how one could account for the impact of industry when relying upon RPRS data.18

Table 1Volatility Size Adjustment by Industry from the 1st to 7th Size Decile
Table 1

Incorrect size measurement

If one concludes, consistent with empirical data, that size matters for equity volatility, a key subsequent question should be at what time or over what period should size be measured? Should one classify the size of a guideline company based on its equity (and debt) value at the start of the lookback period, at the end of the lookback period, or by some other metric?

Lookback volatility is a time-based measure because it views changes in returns over time. Over that period, a company may decline or grow in value or have limited or no change in value. However, if a company grows in value over the relevant lookback period, using the start of the lookback period for assessing a guideline company’s size will tend to overstate volatility. This is because the company will tend to have experienced higher volatility over the period when it was smaller, but the higher-volatility portion will be treated as though it had occurred when the company was larger.

In the CMT Method’s case, it is the opposite. The RPRS relies on end-of-period sizes for creating the portfolio size rankings. As a result, reliance upon RPRS Method leads to understated volatilities for each of the size rankings (Covrig, McConaughy, and Travers 2018; Kroll 2023d).19 The understatement magnitude will depend on the relative degree to which companies have grown or declined in each portfolio ranking. A size classification methodology using average equity values over the lookback period should be viewed as a superior method for assessing volatility size adjustments.20 The H Method relies on a size classification methodology consistent with this premise.21

A second natural question regarding size measurement is what the appropriate base for size classification should be. Covrig, Travers, and Harms (2024, p. 4) indicate that MVIC is the size measure “proxy we consider most appropriate” for classifying companies by size and in selecting appropriate equity volatility measures. While I am curious as to the arguments for the use of the MVIC, I note the market value of equity (MVE) is predominantly used for both classifying size risk for discounting as well as for volatility. MVE has the benefit of maintaining consistency as an equity-level measure.

Another reason for perhaps preferring MVE over MVIC could lie in the impact of leverage. If one believes that volatility should be adjusted for leverage, use of an MVIC creates an unresolved circularity. While MVE is agnostic to the impact of leverage, MVIC includes it. If leverage does indeed matter, one must now account for two impacts of leverage - the first from potentially reducing volatility through the selection of a larger size ranking and a second through the unlever/relever process handled by the Merton model. If size is a function of leverage, then the Merton leverage formula either already accounts for it (by relying on MVE with asset value as an output) or the Merton model does not fully account for the relationship between leverage and size, which would cast doubt on its use.

My take is that if one believes that the Merton model correctly accounts for leverage, one should rely on the MVE when classifying a company by size. Any other method necessarily creates interdependencies that may not in fact exist.22

Ratio versus absolute differential mechanism

Most of my comments to this point have been based on use of a study unfit for the purpose of calculating volatility size adjustments. One difference between the CMT Method and the H Method not based on the data itself is how the size adjustment should be applied. The CMT Method relies upon a ratio of average volatilities between two size categories (the numerator being the average volatility from the subject company’s size ranking and the denominator being the average volatility from the guideline company’s size ranking). That ratio is then multiplied to the guideline company’s actual volatility to estimate the size-adjusted volatility for the subject company. The H Method instead relies upon an absolute difference between the median volatility from the subject company’s size ranking and that from the guideline company’s size ranking to calculate the size adjustment, which is then added to or subtracted from the guideline company’s actual volatility to estimate the size-adjusted volatility for the subject company.

What is the right way to adjust volatility – using a ratio or an absolute differential? While I don’t claim to know with certainty the answer here, Figure 1, originally presented in Herr 2018b, is informative. The figure shows median, 5-year equity volatilities by size decile and quarter from 1998 through 2017. Median volatility spreads by size decile are observed to generally be consistent across time. While volatilities over time did fluctuate, for the most part median volatilities between decile groups moved similarly. Volatility spreads were generally consistent over time, apart from 10th decile volatility spreads, where, in the 2002-2004 period, the spread compared to the 9th decile rose in connection with higher market volatility. Interestingly, in the 2015-2017 period, the opposite occurred - the spread compared to the 9th decile rose in connection with lower market volatility. For other years, the 10th decile spread appeared to be consistent relative to the 9th decile. From these observations, an absolute size differential may be preferred, since it relies on a consistent spread between deciles.

Figure 1
Figure 1Median 5-year equity volatilities by size decile and quarter from 1998 through 2017

Citation: Business Valuation Review 43, 2; 10.5791/2163-8330-43.2.44

Table 2 below summarizes the main points discussed above. Most of the identified discussion points lead to expected understatement of volatilities for each size ranking, but the true impact will depend on the relative degree of understatement or overstatement of volatilities relied upon to calculate the volatility adjustment ratio.

Table 2Expected Volatility Ranking Impacts by Identified Issue
Table 2

Side-by-Side Comparison of Size Adjustments Using the CMT and H Methods

I first provided evidence of the impact of size on equity volatility in 2008, in which a simple method to adjust proxy equity volatilities for size based on empirical pricing data from publicly traded companies was presented (Herr 2008). The size-adjustment methodology was based entirely on empirical equity volatilities as a proxy for investor expectations.

Ten years later, I published two articles that updated that first set of size-adjustment tables, relying on an expanded market pricing data set, where I demonstrated the muted impact of leverage on equity volatility and the strong impact of industry on equity volatility size adjustments (Herr 2018a, 2018b).

I showed, among other things, that leverage empirically matters only to equity volatility at either very low or high levels of leverage (Herr 2018b). Working with a different set of data, others have found similar leverage relationships with equity volatility (Choi and Richardson 2016).

I have also shown that industry matters when it comes to size adjustments for equity volatility (Herr 2018a).23 Because of this impact, the size-adjustment table was expanded to include an industry classification.

To better understand the CMT and H Methods, Table 3 above lists key differences between the two.

Table 3Comparison of the CMT and H Methods
Table 3

Adjusting Volatility for Leverage

The leverage-equity volatility relationship

There appears to be a widespread belief of a strong positive relationship between leverage and equity volatility. This is in fact disputed in the academic literature. Choi & Richardson (2016, p. 257) indicate that equity volatility literature finds a “weak relationship between equity volatility and leverage,” and then using a comprehensive data set built from monthly debt and equity returns from 1980 through 2012 from publicly traded companies, went on to show that leverage only impacts equity volatility in very low and high leverage decile bands (see Figure 2, an excerpt from Choi & Richardson 2016). They found that the flat portion of the equity volatility/leverage relationship is primarily due to significant negative correlation between asset volatility and leverage. Until leverage becomes high enough, any increase in equity volatility due to an increase in leverage gets effectively offset by a decline in asset volatility (related to the change in leverage), leading to a relatively stable equity volatility for standard levels of leverage.

Figure 2
Figure 2Relationship of Leverage to Equity and Asset Volatilities

Citation: Business Valuation Review 43, 2; 10.5791/2163-8330-43.2.44

Independent from Choi & Richardson (2016), I demonstrated that under the limiting assumptions of the Merton Model, for a given unconditional asset volatility the expected relationship between leverage and equity volatility is strongly positively correlated, which is consistent with that expected under finance theory (nondashed lines, Figure 3; Herr 2018b). I then show, using weekly equity returns from 1998 through 2017, a similar result to Choi and Richardson (2016): little to no leverage impact on equity volatility for standard leverage ratios occurs (dashed line, Figure 3).24 It is only in the lower and higher leverage ratios that we start seeing a relationship between equity volatility and leverage, where initially the asset effect outweighs the leverage effect and where for leverage ratios generally beyond 50% the opposite is true. In an upcoming journal issue, I will demonstrate using a different analytical approach added evidence of this leverage to equity volatility relationship.

Figure 3
Figure 3The expected relationship between leverage and equity volatility

Citation: Business Valuation Review 43, 2; 10.5791/2163-8330-43.2.44

In summary, adjusting leverage for a guideline publicly traded company to a subject company when both have standard leverage ratios will likely lead to a misstatement in equity volatility by failing to account for the offsetting effects of leverage and asset volatilities.

Compounding rather than isolating effects

In their examples, the authors apply leverage adjustments inside of size adjustments or vice versa, implying that these adjustments are dependent on each other, as opposed to applying the adjustments separately and independent of each other (Covrig, Travers, and Harms 2024). In doing so, ordering matters using the authors’ approach, since different ordering of adjustments leads to different outcomes.25 It is not clear why Covrig, Travers, and Harms (2024) chose a method that compounds size and leverage effects, but this compounding is the reason they find ordering has an impact.

I believe the preferred approach is to apply the effects independently. This avoids subjectiveness because of ordering impacts. It also avoids the unproven assumption that size should be dependent upon leverage when adjusting for volatility.

Volatility Adjustments in Industry Publications

It is key to recognize that sparse literature is available to help valuation specialists develop supportable equity volatility adjustments for company size, despite equity volatility in many cases being more relevant than the discount rate in assessing value. This is unfortunate, since an equity volatility can be the most important input when assessing the value of a financial instrument. To demonstrate the degree to which the importance of volatility estimation is overlooked, I noted 34 references in the Earnout Guide to how one would adjust a cost equity for size. Contrast this with about half a page in the Earnout Guide on adjusting volatility for size. Even then, the “suggested methods” found there provide really poor guidance on adjusting equity volatility for size.

The first listed method in the Earnout Guide suggests using the “upper half of the [volatility] range” indicated from guideline company volatilities.26 This is effectively a rule of thumb. When do we use such a practice in other valuation work? Do we use the upper half of all size premia from the CRSP Study to select an applicable size premium? Even for multiple selections under a market approach, significantly more underlying work goes into the selection of a multiple within a multiple range (or at least should). So why would we use a rule of thumb for volatility? It is difficult to see how this method would ever be capable of capturing most real-world cases where guideline companies are frequently larger in size compared with the subject company.

The PV Guide states it well:

[I]t may be appropriate to adjust the volatility to account for differences between the portfolio company and the selected guideline companies … [which] may result in an estimated volatility that is outside the observed range, reflecting the risk of these types of businesses [i.e., early-stage]. (AICPA 2019)27

I would add that nothing special about the risk of early-stage companies occurs that would cause a specialist to make an “outside of the guideline company volatility range” exception. It should in fact be just the opposite. Any company smaller than the guideline company group should be expected to have an estimated equity volatility higher than the maximum guideline volatility. To expect any differently would be to ignore the proven strong impact that size has on volatility. A variant of this rule of thumb shows up in the PV Guide:

For early-stage companies, it is likely that the public guideline companies will be larger, more profitable, and more diversified; thus, the appropriate volatility may be best represented by the higher end of the range of comparables, especially for shorter time frames, migrating toward the median of small public companies over the longer term. (AICPA 2019)28

If volatilities can differ by more than 50% between small and large companies, why would anyone reasonably expect that the “higher end of the range” of large, diversified companies could possibly be representative of a small company’s volatility? Such an approach would lead to a proxy volatility clearly out of line with real world volatilities, with no reasonable justification for the method’s use. Only when there are one or more companies of similar size would one expect that the higher end of the range would begin to make sense, since the higher end would presumably capture the same-sized companies’ volatilities. If true, what benefit is there in the first place from including the larger sized companies as representative of volatility for the subject company?

The second listed method in the Earnout Guide is to adjust the volatility for each comparable company using a ratio based on a numerator equal to a required metric risk premium (RMRP) that includes an appropriate size premium for the subject company and a denominator that uses that same RMRP but with a size premium consistent with the comparable company.29 This suggested adjustment ratio, akin to the literature on how one might adjust a multiple for a size impact, is heavily based on the assumption that cost of equity changes are proportional to equity volatility changes. I am not aware of any studies that would confirm this assumption (if such studies did in fact exist, one would expect them to be referenced in the publication as support for this method indicative of best practice).

Although the direction of the adjustment will generally be correct, where is the empirical data confirming that the magnitude of any implied adjustment under this method is consistent with empirical data? This methodology also begs the question on whether a ratio adjustment is more appropriate than an absolute differential adjustment.

The last listed method appears to be consistent with the CMT Method (Covrig, McConaughy, and Travers 2018) and specifically references Kroll’s RPRS in a footnote (Earnout Guide, 2019). However, as I have discussed earlier, the RPRS data is not fit for use in volatility size adjustment estimation for a number of previously-discussed reasons.

With regard to leverage adjustments, the PV Guide states:

For later-stage privately held companies, consideration should be given to the effect of the company’s leverage … the effect of [significant debt financing] can be to significantly increase the volatility of the firm’s equity. (AICPA 2019)

While, leverage adjustments make sense under high leverage, the PV Guide appears to suggest that for later-stage privately held companies, there is no need to adjust for size—leverage adjustments are sufficient (AICPA 2019). This of course is not likely to be true if the guideline companies are at all different in size from the subject company’s size. Size adjustments, in fact, should be of primary consideration in this case, especially given that leverage impacts on volatility have been shown to be secondary to size impacts (Herr 2018b), and in fact for standard leverage ratios, may be inappropriate to apply in the first place.

In fairness, the timing of these publications would have been around the same time as the publication of my 2018 articles and the first publication of the CMT Method, so the working groups would likely not have had sufficient time to digest or incorporate the methods fully into industry publications (Covrig, McConaughy, and Travers 2018; Herr 2018a, 2018b). This is particularly true of leverage adjustments, where no mention of when leverage adjustments are appropriate is provided. The empirical data clearly show that leverage adjustments may not be applicable for standard leverage ratios; however, because these industry publications are not regularly updated, they provide a frequent source for errors by appraisers that rely on, or are required to rely on, these publications from auditors and other reviewers of the specialist’s work that may argue that these volatility adjustment methods are best practices because they are included in those publications.

Summary

Although size adjustments can be avoided altogether by selecting guideline publicly traded companies of similar size, in practice this is very hard to do, especially for small, privately held companies. Most of the time, we end up with at least one guideline company (and many times most of them!) not fitting nicely with our subject company’s size. In such cases, we can try relying on some rule of thumb statistic or other unproven method, but such an approach would collapse under a reasonable level of scrutiny.

In this article I discuss several methodologies for making size adjustments to volatility. I find that most of these methodologies are inadequate for use. Size adjustments for volatility should be supported with as much care and consideration as we make for other standard adjustments in a valuation engagement, and some methods are less supported than others. I find that there are key concerns with the CMT Method, not based on the methodology of the adjustment, but instead based on the use of a study that was not designed or intended for use in performing volatility size adjustments.

I also discuss two points related to leverage adjustments, with the primary point being the unique relationship between leverage and equity volatility and the second, which is the benefit or applying isolated adjustments versus compounding adjustments. The first leads to oversized leverage adjustments using the Merton model for standard leverage ratios and the second leads to potentially multiple value results.

Although the H Method avoids many of the the underlying data issues associated with the CMT Method and those faced when using rules of thumb for making volatility size adjustments, its primary criticism has been the reliability of fitting guideline publicly traded companies and a subject company today into a decile-ranking band created at the end of 2017, more than six years ago (Covrig, McConaughy, and Travers 2018). Arguably, as time passes and companies grow, companies would soon begin to be misclassified into equity deciles. To improve volatility estimation, I plan to annually publish industry-specific volatility size-adjustment tables based on six-month, two-year, and five-year lookback periods, starting with data through the end of 2024, which are consistent with the H Method. Although these size adjustments will not cover all volatility adjustments required in an engagement, I hope that the availability will provide valuation specialists with a reliable source for adjusting equity volatilities for size.

Acknowledgment

I thank Jonathan Grubbs at Alvarez & Marsal Valuation Services for his thoughtful comments on this article.

References

  1. 1

    I noted that most, if not all, of the methodology related to size adjustments discussed therein comes from an article published six years earlier (Covrig, McConaughy, and Travers 2018), hereafter referred to as the CMT Method.

  2. 2

    It is important when talking about volatility to distinguish the type of volatility. Equity and asset volatilities are not the same, just as cost of equity and WACC are not the same. These two are also different from other types of volatility, such as revenue, EBITDA, or cash flow volatility (although, depending on the facts and circumstances, they may be viewed as proxies). I also want to avoid confusion by pointing out that when I note a volatility difference, I am specifically talking about a level difference and not a ratable difference (e.g., a difference of 30% for volatility would be from, say, an initial volatility of 40% and a subsequent volatility of 70%.

  3. 3

    I note that the 2019 Practice Aid related to estimating volatility is a refinement to the 2013 Practice Aid for the Valuation of Privately Held Equity Securities Issued as Compensation; therefore, the earlier guide is not addressed separately from the 2019 Practice Aid.

  4. 4

    I note a tendency in current industry guidance and practice to place a high level of rigor around size and leverage adjustments when addressing discount rates and beta determinations yet virtually no rigor in assessing adjustments for equity volatility, despite some cases where the estimate of volatility is more relevant than that of the discount rate in determining value.

  5. 5

    In the study, Kroll (2023d) indicates that the presented standard deviations are calculated using annual data points, which effectively annualizes these volatilities without adjustment. This, however, should not be confused with the meaning of a one-year lookback period. For data points on a more frequent basis, a valuation specialist would normally annualize that data from a daily, weekly, or monthly volatility measure to an annual measure because models such as the Black Scholes model rely on an annual volatility input. In contrast, a lookback period represents the period length up to the assessment date over which data are collected and used to assess the volatility measure. I am not arguing that discount rates or components therein should not consider a long period of time because a discount rate for a business is a different risk measure than equity volatility and is used differently. The latter is usually required in valuing short-term instruments that do not require a long forward period for determining value, in contrast to assets such as an equity interest in a privately held company that would generally have cash flows extending into perpetuity.

  6. 6

    “We acknowledge that there is a mismatch between (a) the Kroll/Duff and Phelps data, which capture information from 1963 through the most current period, and (b) the GPC’s equity volatility, which is calculated over a recent period” (Covrig, Travers, and Harms 2024, p. 4). By extension, this mismatch is also imposed on the subject company or asset.

  7. 7

    Or forward contract period for options when looking at implied volatilities.

  8. 8

    As discussed in the Earnout Guide, “Volatility in the value investors place on investments generally increases with the time horizon” (Appraisal Foundation 2019). This statement is supported by referencing higher volatility observed in long-term US Treasury bond prices with a high remaining term relative to those same bonds with a low remaining term. This relationship can also be observed in my 2018 article by a simple comparison of historical volatilities with six-month, two-year, and five-year lookback periods (the five-year periods have, on average, higher volatilities than the six-month periods) observed over a twenty-year period (Herr 2018b).

  9. 9

    See Covrig, Travers, and Harms (2024) and Kroll’s (2023e) Cost of Capital Navigator indicating this threshold as the MVIC twenty-fifth portfolio ranking maximum value.

  10. 10

    See Kagan (2019); asset volatilities would be expected to be less than equity volatilities given that debt volatility is generally expected to be less than equity volatility.

  11. 11

    According to Kroll, “the methodologies and data used to form the CRSP Decile portfolios are similar to the methodologies and data used to form the Risk Premium Report portfolios,” with exceptions relating to financial service companies (Center for Research in Security Prices [CRSP] includes, Risk Premium Report portfolios [RPRS] excludes), coverage of high financial-risk companies (CRSP includes, RPRS excludes), rebalancing (CRSP is quarterly, RPRS is annual), and company weightings (CRSP is market-cap weighted, RPRS is equal-weighted; Kroll 2023a, p. 1).

  12. 12

    RPRS defines high financial risk companies as those that (a) have less than a five-year historical trading period, (b) are losing money, (c) have high leverage, or (d) are distressed based on a company’s Altman z-Score (Kroll 2023b, 2023c, 2023d).

  13. 13

    See Exhibit 10.2 of the last available Cost of Capital Guide from Kroll (Duff and Phelps, 2018), which states that for the twenty-five size-ranked portfolios, the standard deviation was based on annual historical equity returns.

  14. 14

    Although use of annual observations reduces the likelihood of observing periods with no change in pricing, it is still likely that zero-volatility observations were included based on limited trading, lowering the overall volatility measures.

  15. 15

    In addition to evidence in my article (Herr 2018a), the impact of industry and size on volatility is also consistent with research presented by Marina Kagan of PwC. See, for example, her 2019 ASA presentation on volatility (Kagan 2019), also cited by Covrig, Travers, and Harms (2024).

  16. 16

    The CMT Method uses a multiplier rather than an additive or subtraction factor (Covrig, McConaughy, and Travers 2018). The example begins with a guideline company volatility of 20.0% and is adjust by a multiplier of 1.71 to arrive at a 34.4% “adjusted” volatility, which is effectively a 14.4% upward adjustment.

  17. 17

    Note that I am using a five-year lookback period, which is closest to the reliance of an approximate sixty-year lookback period by Covrig, Travers, and Harms (2024). The size adjustments using data from my article rely on the simple assumption that MVIC is equivalent to equity because Covrig, Travers, and Harms (2024) did not provide equity values in their first example (Herr 2018a).

  18. 18

    In contrast to an adjusted Capital Asset Pricing Model, the effect of industry on size adjustments is not implicitly included by simply choosing guideline companies in the correct industry and averaging volatilities to get a selected starting base when applying a volatility size adjustment. Empirical data clearly show that size adjustments are affected by both decile ranking and the industry in which a company operates. This is different from a cost of equity, which relies on beta to capture industry risk, with an independent size premium added on.

  19. 19

    Take the extreme case where a company spends nearly all of an assumed five-year lookback period hovering around $500 million and then suddenly spurts to $2.5 billion at the end of the fifth year. In this case, an end-of-period measurement would place the guideline company not in the lowest twenty-fifth ranking but instead in the twenty-first ranking, despite most of the volatility being generated when the company would have been classified in the twenty-fifth portfolio ranking.

  20. 20

    For clarification, I am specifically referring to guideline publicly traded company sizes when either creating a size-adjustment table (e.g., the H Method) or when a practitioner is assessing where a guideline company fits into a particular decile ranking to estimate a proxy volatility or volatility size-adjustment amount. I normally expect the current (or future expected average) value to be the best estimate for estimating future equity volatility based on size when relevering asset volatilities to the subject company, selecting an appropriate decile for the subject company, or using implied volatilities as of a certain date.

  21. 21

    Incidentally, this is the primary reason why capitalization deciles in my previous articles would not be expected to line up with Kroll’s CRSP deciles (Herr 2008, 2018a, 2018b). Kroll’s methodology also sets the deciles based on only New York Stock Exchange (NYSE)-traded companies to set the decile rankings before adding in companies traded on the NYSE MKT (former AMEX) and NASDAQ exchanges (which tend to be smaller companies), leading to a further difference in decile breakpoints (Kroll 2023d).

  22. 22

    Toward the end of this article, I discuss the way in which reliance by Covrig, Travers, and Harms (2024) on the interdependency assumption also leads to two different outcomes, depending on the adjustment ordering.

  23. 23

    A wide empirical difference between equity volatility size adjustments based on industry for a similar change in decile rankings was demonstrated (Herr 2018a). For example, going from a first size decile (for a guideline company) to a tenth size decile (for the subject company), the Health care industry exhibits more than a 50% volatility size differential for five-year lookback periods, whereas the financial and utility sectors over the same lookback period show a substantially smaller volatility size difference of approximately 5%.

  24. 24

    As an aside, these results could be seen as appealing intuitively because a high-risk company may find it difficult to raise any third-party debt financing (for low-leverage companies) or alternatively, may have higher expectations of insolvency (for high-leverage companies). In other cases, leverage may be reasonably expected not to cause material solvency issues for the business; therefore, one would expect a nonmaterial impact on volatility.

  25. 25

    Covrig, Travers, and Harms (2024) note that their standard practice is to first make the size adjustment and then apply the leverage adjustment, based on empirical data that the leverage impact is weaker than the size impact.

  26. 26

    See Section 5.2.4.4 of the Earnout Guide.

  27. 27

    Q&A 14.61 of the PV Guide.

  28. 28

    Section 8.48(a) of the PV Guide.

  29. 29

    The RMRP, as defined in Section 10.2 of the Earnout Guide (on page 117), is a measure of the excess return, or risk premium, that investors demand to bear the nondiversifiable risk associated with a specific metric.

Copyright: © 2024, American Society of Appraisers 2024
Figure 1
Figure 1

Median 5-year equity volatilities by size decile and quarter from 1998 through 2017

Figure 2
Figure 2

Relationship of Leverage to Equity and Asset Volatilities

Figure 3
Figure 3

The expected relationship between leverage and equity volatility

Contributor Notes

James Herr is a Senior Director with Alvarez & Marsal Valuation Services in Houston, Texas. Mr. Herr has provided valuation and financial modeling consulting services for more than 25 years. During that time, he has performed close to 1,000 valuation engagements. Before joining Alvarez & Marsal Valuation Services, Mr. Herr was formerly with PwC, KPMG, and BDO. Mr. Herr earned his Bachelor of Arts degree (graduating Magna Cum Laude) in economics and Russian from Brigham Young University, his Master of Arts degree in economics from the University of California at Berkeley, and a Master of Business Administration degree from California State University at East Bay. He is a CFA charterholder, an ASA with the American Society of Appraisers, and a CPA in the state of Texas; Mr. Herr also holds the ABV credential

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