< PreviousUnder the baseline approach and for all alternatives excluding Alt 3 and Alt 4, the size premium for decile 10 is significantly larger than the size premium for decile 1 at around the 10 percent significance level. A p-value of 0.10 means that even if there truly is no difference between the size premiums for deciles 1 and 10, in the underlying population of firms as a whole (we are only dealing with a sample here), 10 percent of studies would still obtain the reported (or even larger) size premium differential just because of random sampling error. Even under the baseline approach, this is considered tenuous evidence that the size premium for decile 10 exceeds the size premium for decile 1. Under Alt 3 and Alt 4, there is no significant difference between the size premiums for deciles 1 and 10 at any reasonable confidence level. 6. Conclusion There are many possible interpretations of the results presented in Section 5. One may consider the results of the sensitivity analysis to undermine the very existence of a coherent size premium. If the calculation of size premiums is not robust to small, reasonable changes in assumptions, perhaps the size premium itself is unreasonable. This view has wide ramifications, as it suggests an abandonment of the size premium and the implicit retirement of the modified CAPM. As the original CAPM has serious empirical shortcomings, a sizeable gap would exist in the valuation analyst’s toolbelt for calculating the cost of equity. Accordingly, even if this view is shared by many in the profession, movement away from the size premium would likely require a significant phase-out period. Alternatively, one may interpret the size premium as being fluid, changing under different facts and circumstances. The discussion in Section 5 attempts to accommodate this view by providing guidance on use cases for each size premium. Such a view might invite additional research, as only six assumption changes were tested in our study. Some readers may entirely reject deviations from the baseline, concluding that the changes in assumptions tested here are not reasonable. This may be defensible for certain assumptions, though not all. In particular, Alt 3 and Alt 4 deserve serious consideration as plausible specifications for calculating the size premium. As mentioned above, there are many more specifications not covered in this article that might also deserve attention. Whichever camp one is in, the size premium is interesting and unsettled and will be of increasing importance as we move further away from 1980. For now, practitioners may consider multiple size premiums and their impact on valuation. Derek Zweig, CFA, FRM, cofounded Value Analytics LLC in 2020 and currently serves as its chief executive officer. Mr. Zweig is an expert in asset valuation and has performed or contributed to over 1,000 valuation engagements involving businesses, business interests, and intangible assets of privately held and publicly traded companies. He is an active member of the CFA Institute and the Global Association of Risk Professionals. Mr. Zweig earned an MS in applied economics from Johns Hopkins University and a BS in finance from The Ohio State University. Email: derek@valueanalytics.org. Timothy Sumner has been a data professional since holding his first data analyst job in 2019. He earned his bachelor’s and master’s degrees in statistics from the University of South Florida and the University of Central Florida, respectively. He has assisted in numerous data-driven research projects, ranging from pricing crypto assets for FTSE Russell to forecasting COVID-19 cases for the CDC. Mr. Sumner specializes in probability theory and stochastic methods and processes. Before studying statistics, he spent five years in the U.S. Navy as a corpsman attached to both the 1st and 2nd Marine Divisions. Email: sumner.tim@outlook.com. Adam Luke, PhD, cofounded Value Analytics LLC as chief technology officer. Before founding Value Analytics, Mr. Luke worked as a data scientist at both established and early phase technology companies. His experience across business scales and application domains provides a robust background for producing innovative software services. Mr. Luke holds a PhD in engineering from the University of California, Irvine. Email: adam@valueanalytics.org. 30 The Value Examiner ValuationUltimateSoftware Subscription #1 Best-Selling Business Valuation Software Software Subscription Includes PLUS FOUR Valuation Applications, One Low Annual or Monthly Price T he Ultimate Software Subscription (built around Excel and Word) gives you access to ALL of our valuation software products for ALL versions of Microsoft Office back to 2013, includes ALL software updates, PLUS technical support. Both single and multi-user licenses are available. BUSINESS VALUATION MANAGER™ PRO BVM Pro (used by NACVA to train professional valuators), with over 90% market share, has been used by thousands of CPAs, valuators, and financial professionals for over three decades. VALUSOURCE PRO INTERNATIONAL ValuSource Pro International is built around International Financial Reporting Standards (IFRS) instead of GAAP so you can provide comprehensive valuation analysis and reports based on IFRS. 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Business Valuation Manager Pro ValuSource Pro International Express Business Valuation Report Writer (works with all valuation products) TECHNICAL SUPPORT With the Unlimited Software Subscription, you get full technical support, including: support for technical issues like installation, program operation, database integration, as well as access to our team of certified valuators to help you use the software to complete specific valuation engagements. COMPLETE DATABASE INTEGRATION KeyValueData® integrates directly into all the valuation software in the Ultimate Software Subscription. 1 2 3 4By Dorothy Haraminac, MBA, CFE, MAFF, CCI, PI Cryptocurrency in Litigation Practice: Tips and Pitfalls for the Financial Forensics Practitioner This column discusses blockchain forensics, cryptocurrency valuation, and other cryptocurrency issues in litigation. It provides financial forensics practitioners with tips and practice tools, and alerts them to the many potential pitfalls in these cases. Measuring Volatility in Cryptocurrency Cryptocurrency is an interesting asset class. It functions as a store of value and a means of exchange, which means it can be transferred like the U.S. dollar. It also can be bought and sold with dollars, like stock, which means there are markets for some of it and a price that can go up or down. Unlike the dollar, however, cryptocurrency does not have a physical representation; it exists only as a result of blockchain software and is stored only on that blockchain. Arguably, this is similar to the dollar as it exists today as simply a product of banking software interacting with card payment software and bill payment software, etc. Most dollars exist only digitally and are stored only in the inner workings of a bank’s ledger software. Unlike stock, most cryptocurrency does not convey ownership in a company; however, this too is debatable because most retail stock owners do not own (and likely will never own) enough stock to have any meaningful voting impact. It is also debatable because, sometimes, the SEC disagrees and attempts to classify some cryptocurrency offerings as securities. 1 1 Nearly 70 cryptocurrencies have been labeled as securities by the SEC. These attempts are ongoing and a summary can be found here: Jesse Coghlan, “SEC Lawsuits: 68 Cryptocurrencies are Now Seen as Securities by the SEC,” CoinTelegraph, June 6, 2023, https://cointelegraph.com/news/sec-labels-61-cryptocurrencies-securities-after-binance-suit. 2 Figure 1 shows the fluctuations of average daily prices for bitcoin, measured in U.S. dollars for each bitcoin and for natural gas, measured in U.S. dollars per million Btus (MMBtus) at the Henry Hub spot price for the period beginning April 28, 2013, through April 5, 2022. The Henry Hub is a natural gas distribution hub in Louisiana, which serves as the official delivery location for futures contracts on the New York Mercantile Exchange. These prices are available publicly through various price aggregators, such as CoinMarketCap.com (https://coinmarketcap.com) for cryptocurrency and the U.S. Energy Information Administration (https://www.eia.gov/dnav/ng/hist/rngwhhdD.htm) for natural gas. 3 Figure 1 is misleading because the number of times natural gas has a 0 percent daily change, rounded to the nearest hundredth, is much higher than 120. See the discussion of truncation, below. 4 Perhaps the adage should have been “verify” all along. Cryptocurrency’s price fluctuations are measurable with respect to anything else that is also exchanged for something measurable. For instance, you could measure those fluctuations in terms of dollars and make observations about price volatility. You could also compare that measure to the price fluctuations of some other asset, like natural gas, and make more observations about comparative price volatility. Try it yourself; your results may be surprising. Spoiler alert: As indicated in Figure 1, 2 bitcoin appears to be less volatile than natural gas. 3 One major caveat here is that a futures market exists for natural gas to hedge against such daily price fluctuations and this simplistic measure may not be appropriate for various fact patterns. The major point of this illustration is to show that broad statements about cryptocurrency’s volatility are not appropriate without the support of calculations and may not be appropriate once the context, such as industry and risk profiles, are considered. Another major caveat regarding Figure 1 is that the maximum axis has been truncated to show the detail of each leg. An indicator of truncation is that the orange line at the center, representing natural gas at 0 percent, meets the maximum axis value of 120. Table 1 shows that natural gas has a 0 percent daily change more often than bitcoin; in fact, five times as often. The manipulation of measurements and visualization is not exactly breaking news, but it is a stark reminder of the importance of an analyst’s professional skepticism. The old adage, “Believe none of what you hear and half of what you see,” should be updated to simply, “verify.” 4 32 The Value Examiner Financial Forensics Table 1: Percentage Daily Change—Bitcoin and Natural Gas Percentage Daily Change BitcoinNatural Gas -0.0058487 -0.0046990 -0.0039489 -0.00210947 -0.00110316 098584 0.0017511 0.0026857 0.0036283 0.0046298 0.0055699 5 Named for the pseudonym used by the creator(s) of bitcoin and its whitepaper, Satoshi Nakamoto. The smallest unit of bitcoin is 10 -8 , as compared to the smallest unit of the dollar, cents, which is 10 -2 . 6 Named for Wei Dai, the developer of Crypto++, a cryptographic library for use in C++, and B-money, a cryptocurrency concept based on the notion that politics should not be connected with currency and economies. The smallest unit of ether is 10 -18 . 7 Named for Ada Lovelace, arguably the first person to publish an algorithm for a computing machine in the mid-1800s. The smallest unit of Ada is 10 -6 . “For a computing machine” is an important distinction because the 9th century mathematician, al-Khwarizmi (shortened from Muhammad ibn Musa al-Khwarizmi), who ran Baghdad’s House of Wisdom and with whom the term “algorithm” originated, is responsible for the technique itself. See Violet Moller, The Map of Knowledge: A Thousand-Year History of How Classical Ideas Were Lost and Found (New York: Doubleday, 2019). “Verify” is the colloquial term for exerting professional skepticism, which is a critical component of assessment sometimes lost in the cloud of a cryptocurrency engagement. The analyst must ask not only whether this measure is accurate, but also whether this measure is appropriate, is fair, is too oversimplified for the matter, and is significant within the context of the matter. Bitcoin is not the only cryptocurrency. There are more than 25,000 different cryptocurrencies transferred on approximately 40 different blockchains, and some are transferred across blockchains. This means that many cryptocurrencies are non-native tokens (also known as "altcoins"). A native token is the original unit of transfer for a blockchain. For example, bitcoin is the unit of transfer for the Bitcoin blockchain (the smallest unit is called a Satoshi 5 ), ether is the unit of transfer for the Ethereum blockchain (the smallest unit is called a Wei 6 ), and Ada is the unit of transfer for the Cardano blockchain (the smallest unit of it is Lovelace). 7 Thousands of other tokens are Figure 1: Daily Price Fluctuations—Bitcoin and Natural Gas 33 May | June 2024 A Professional Development Journal for the Consulting Disciplinesbuilt on top of the Ethereum blockchain and can be transferred on it; at the time of this writing, these are ERC-20 type tokens, ERC-721 type tokens, and ERC-1155 type tokens. 8 Appropriate Measures The fact that markets exist where ether can be converted for other tokens without U.S. dollars means that a new measure of volatility may be more appropriate: the measure of price in terms of ether for a non-native token running on the Ethereum blockchain. Unsophisticated analysts often convert a non-native token to U.S. dollars and discuss volatility in that way. A slightly more sophisticated analyst may convert a non-native token to U.S. dollars and compare that to ether’s U.S. dollar price to discuss volatility. However, neither of these measures is appropriate when an actual conversion to U.S. dollars did not occur within the factual context of an engagement. The appropriate measure in that scenario, where non-native tokens are held and converted to or from ether tokens, may well be a measure of the non-native token in terms of ether conversion rates. The intermediary conversion to U.S. dollars may yield inaccurate results when the non-native token’s 8 ERC-### refers to a code standard within the Ethereum blockchain software. relationship to U.S. dollars differs from the relationship of ether tokens to U.S. dollars. The U.S. dollar is not a stable measure for that purpose, and using it as an intermediary currency, when such intermediate transactions did not actually occur, may overstate or understate volatility. In scenarios where an analyst is determining sales volumes, the use of an intermediary conversion currency may result in inaccurate quantities, thereby allocating an inappropriate, unnecessary, and entirely avoidable windfall to either the buyer or seller. Relying on conversion rates limited only to U.S. dollars, when conversions to U.S. dollars did not occur, may illustrate an analyst’s lack of expertise. Average Illusions Calculations to demonstrate volatility as a basis for risk produce even more interesting data points when averages come into play. For instance, Table 2 shows the average of the highest and lowest daily price fluctuations for bitcoin, ether, and natural gas. The table could be used to show that bitcoin is less than half as volatile on average than natural gas and that ether is about half as volatile as natural gas, but that may not be a fair comparison. 34 The Value Examiner Financial ForensicsAn analyst may use such calculations to conclude that both bitcoin and ether are less volatile than natural gas, but the discerning analyst must ask whether this measure is appropriate for the particular engagement, or at all. There is yet another caveat to such an analysis, and that is the times of open trading in each market. Both bitcoin and ether are traded in a 24/7/365 market, which means there is a higher denominator when annualizing. The salient point here is that many more factors may deserve consideration—such as the comparative asset (a crypto token is volatile compared to what?) and the base asset (a crypto token is volatile in terms of what?)—but so does the time period for market activity and, importantly, whether or not a futures market exists. Emotional Appeals Many factors contribute to purchasing cryptocurrency as opposed to natural gas, including the utility of each product, the ease of delivery and storage, and the need for the product (e.g., for fueling a bus or for fueling a smart contract). Even when viewed strictly from an investment perspective, many factors contribute to an investor’s decision, including not only the price and expected return, but also the impact, the political statement, the ease of market entry, and the cool factor. Who gets all the attention at a party? The commodities trader or the crypto trader? Cryptocurrency markets are incredibly easy to enter; just a few button clicks and some transfers, and you are in the action regardless of background (and regardless of wealth, because some cryptocurrency can be purchased with a credit card). The industry itself has an underlying ideology that stems from its creation by privacy idealists with a varying anti-government theme. Investment, therefore, may bring the allure of a secret, may be the outlet for mild (or quite spicy) political dissidence, and may stand in as a proxy for various ideals. In fact, part of the reason so many different cryptocurrencies exist today is because they are a product of the monetization of one ideology or another. In 2017, one of the resounding themes around new cryptocurrency projects stood alongside the microfinance industry in banking the unbanked. BitcoinMinMaxDifference 2016-9.23%12.80% 22.03% 2017-13.20%24.57%37.77% 2018-15.64%13.54%29.18% 2019-10.81%17.79%28.60% 2020-26.37%18.72%45.09% 2021-11.41%16.61% 28.02% Average-14.44%17.34%31.78% EthereumMinMaxDifference 2016-28.53%29.42% 57.96% 2017-14.95%37.61% 52.56% 2018-19.58%18.48% 38.05% 2019-14.45%15.76% 30.21% 2020-29.58%21.13%50.70% 2021-15.46%27.93%43.39% Average-20.42%25.06%45.48% Natural GasMinMaxDifference 2016-11.40%19.77% 31.17% 2017-8.09%24.24% 32.33% 2018-37.85%69.11% 106.96% 2019-25.18%33.23% 58.41% 2020-25.87%51.01% 76.88% 2021-64.12%110.78% 174.90% Average-28.75%51.36%80.11% Table 2: Average of Highest and Lowest Daily Price Fluctuations Today, there are cryptocurrencies or altcoins (that is, non-native tokens) representing thousands of ideologies, from expanding access to global exchange to carbon reduction. 35 May | June 2024 A Professional Development Journal for the Consulting DisciplinesToday, there are cryptocurrencies or altcoins (non- native tokens) representing thousands of ideologies, from expanding access to global exchange to carbon reduction. There is even an altcoin that represents a logical fallacy—the reductio ad absurdum . Dogecoin (an altcoin), was created in 2013 to illustrate the absurdity of 9 David Lavie, “Dogecoin Started as a Joke. Nobody’s Laughing Now,” Robb Report, May 24, 2021, https://robbreport.com/lifestyle/finance/dogecoin-investing-what-to-know-1234614620/. Fair warning: the article states that dogecoin is “extremely volatile.” a new system of exchange and experienced a resurgence in demand in 2021, when a public figure expressed his interest. 9 The term “real-world application” can be found in many altcoin prospectuses, but the real-world application for dogecoin was nonexistent; its sole purpose was to express a view. Conclusion In engagements where cryptocurrency risk is a factor, the analyst must ensure that measures of risk are appropriate in light of the parties’ risk profiles, the factual context of transactions, and the overall marketplace. For impact investments, an aligning ideology may lower a party’s risk aversion. Simply stating that an asset is volatile and including an article citation is not sufficient; volatility is a comparative measure, which is significantly impacted by an analyst’s choice of which things to compare over which periods. The analyst must ensure that the ease with which data can be selected and manipulated does not interfere with the objective discernment of associative values and comparable volatility. Dorothy Haraminac, MBA, CFE, MAFF, CCI, PI, is one of the first court-qualified experts in bitcoin asset and cryptocurrency tracing. She has provided consulting, tracing, valuation, and expert witness testimony in complex commercial disputes in the oil and gas industry and in high net worth, crypto-centric matrimonial cases. She conducts traditional fraud investigations, blockchain forensic engagements, and financial forensic engagements, deploying sophisticated methods to determine whether indications of fraud exist, to prevent fraud, to assess the risk of fraud in an organization, and to monetize risk assessments in valuations. Email: dh@ybr.solutions. 36 The Value Examiner Financial Forensics 36 The Value ExaminerCustomize Your CPE with Unlimited Options Annual subscription benefits—for first user: • Membership Dues + Tri-Annual Recertification Fee • Recertification Bonus Point Program Registrations + CPE • In-Person Course Registrations + CPE • Hybrid Course Registrations + CPE • Virtual Course Registrations + CPE • BVTC Recorded Training Videos On-Demand • All CPE On-Demand Courses (nearly 500) + CPE • Business Valuation and Financial Litigation Super Conference Registration + CPE • Self-Study Courses + CPE (electronic format) • The Value Examiner ® and QuickRead ® CPE Quizzes Credentialed Designees - CVA and MAFF certification exams included at no additional cost for credentialed designees. New or Non-Credentialed Candidates - One, Two, Three, and Four-Year Options for new or non-credentialed candidates. - Certification exams included with two or more years options. 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Ultimate KeyValueData® Titanium Subscription For first user (access to 21 separate databases, reports, libraries, and presentations) Ultimate Software Subscription For first user (licenses to four valuation and report writing software packages, plus technical support) For the first user (receive everything included in all three other subscriptions, plus Damages Advocate calculation software) Ultimate Triple Play Subscription Best Value!Courtside View: Valuation and Financial Forensics Perspectives from the Bench By Michael J. Molder, JD, CPA, CFE, CVA, MAFF Courtside View highlights recent decisions by federal and state courts addressing significant valuation, financial forensics, and expert witnessing issues. These cases offer valuable insights to BVFLS professionals that can help them develop sound, defensible valuation and damages analyses, and present them more effectively in court. Cases Reviewed • Demenno v. Demenno, 2024 Alas. LEXIS 22 (February 28, 2024) • Smith v. Smith, 2024 Miss. App. LEXIS 71 (February 13, 2024) Ted Lasso was right, “Divorce is hard. It doesn't matter if you're the one leaving or if you're the one who got left. It makes folks do crazy things.” Conveniently, valuation and financial forensics professionals need only deal with the numbers, but those can also be challenging. These two recent cases dealt with one of those challenges: determining whether business interests are separate property or part of the marital estate. Demenno v. Demenno The Facts David (“Husband”) and Tamerra (“Wife”) Demenno met in the 1980s but did not marry until January 2003. In 1998, Husband founded Alaska Land Clearing Contractors, LLC (“ALC”), an excavation company based in Anchorage, Alaska. In 2002, Wife began working for ALC, providing bookkeeping, payroll, and other back-office assistance, and receiving an annual salary of approximately $104,000. According to Husband’s testimony, she also “had a history of using his credit to its limit, taking money out of the companies, paying herself a double salary, and shutting down business contracts when the parties were fighting.” Also in 2002, Husband purchased real estate (the “East 56th Avenue” property), which he leased to ALC to house its operations. In 2011 and 2012, East 56th Avenue received substantial improvements. In 2008, the parties formed Alaska Clearing and Grinding with Wife as the sole owner, enabling the couple to pursue contracts available to minority- and women-owned businesses. After a few successful years, Alaska Clearing and Grinding ceased 1 The parties also had an investment fund using marital assets, but the trial court’s allocation of this asset was not addressed on appeal. operations in 2013. ALC assumed its equipment lease and loan payments, and took possession of its equipment. 1 At the trial court level, Wife argued that ALC, despite having been organized before the marriage, had transmuted to marital property. She testified that, on several occasions, Husband had said he would make her a co-owner of ALC. The marriage was a tumultuous one, with Wife seeking divorce five times before the current proceeding. According to Wife, in an effort to persuade Wife to reconcile, Husband had promised her that she would be added to property titles and bank accounts, and made a co-owner of ALC. Wife also testified that the success of ALC had been due to her efforts; that she had been the one to bring order to the business operations and had been responsible for successfully completing the improvements to the East 56th Avenue property. Both parties offered expert valuations of the property used in the business. Wife’s appraiser concluded that the value of the 56th Avenue property was $1,150,000, due to a combination of improvements made during the marriage—including the 2011 and 2012 renovations—and general appreciation in real estate values from increased development in the area. Husband did not dispute that valuation. Husband offered an equipment appraiser who valued ALC’s equipment at approximately $5.3 million 38 The Value Examiner Legal Insightsin June 2017, based on its “fair market value” on the date of separation (the “DOS Value”), and at approximately $3.5 million in January 2019, based on an orderly liquidation and an additional 18 months of depreciation (the “Current Value”). The trial court ruled in favor of Husband, saying that while Husband may have made vague promises as part of his negotiations with Wife during their disagreements, he never manifested an intent to follow through with those promises. The promise without an intent to donate the property to the marital estate would not transmute the separate property to marital property. Following that order, the lower court conducted a trial on the valuation of the various disputed assets and the active appreciation attributable to them. 2 Both parties proffered expert witnesses on the value of ALC. Husband’s expert had experience with at least 20 active appreciation valuation engagements. She valued ALC at the date of separation in September 2017, using both adjusted book value and capitalization of earnings methods. To capitalize earnings, the expert looked to annual earnings from 2012 through 2016, with a reasonable compensation adjustment to reflect the fact that Husband did not receive a salary but took all compensation in the form of owner’s draws. For the adjusted book value method, the expert looked to an appraisal prepared by a different appraiser, which valued the equipment in January 2019, based on an “orderly liquidation,” at approximately $3.5 million. Husband’s expert concluded that ALC’s date-of-separation value was 2 In Alaska, the marital estate includes both marital assets and active appreciation of separate property, which “occurs when marital funds or marital efforts cause a spouse's separate property to increase in value during the marriage.” 2024 Alas. LEXIS 22 at *8, quoting Layton v. O'Dea, 515 P.3d 92, 106 (Alaska 2022). $1,460,000 using the capitalization of earnings method and $1,400,900 using the adjusted book value method. To calculate active appreciation, Husband’s expert determined the 2003 date-of-marriage value using only the capitalization of earnings method, as there was no equipment appraisal at the time. She concluded that most of ALC’s customer relationships already existed at the date of marriage and new equipment and expanded staff accounted for most of the increase in value from 2003 through 2017. Accordingly, Husband’s expert assigned only 40 percent of the increased value during the marriage to active appreciation, concluding that the marital value of ALC was $337,040. With regard to the East 56th Avenue property, the court determined that it was also separate property, but that most of the increase in value was due to actions taken during the marriage, including the construction and renovation of buildings on the premises. The court found that Husband failed to negate the existence of a causal link between the increase in value and the improvements made to the property, concluding that, except for inflation, all of the increase was attributable to active appreciation. Wife’s expert, while experienced in business valuation, had never done an active appreciation analysis. She also used both capitalization of earnings and adjusted book value methods. In applying the capitalization of earnings method, the expert used a valuation date of December 31, 2017 (after the September 2017 date of separation) to capture all of the 2017 earnings. She did not make any adjustments to earnings, 39 May | June 2024 A Professional Development Journal for the Consulting DisciplinesNext >