A Companion Guide to the FMV Restricted Stock Study 2017: Bridging Theory and Market Data

This article concludes our series on illiquidity discount (DLOM) as it applies to valuing restricted or hard-to-sell assets. Our aim is to evaluate the 11 theoretical models previously presented against market data.

Let’s recap some key takeaways from our previous discussion on market data:

• Most empirical studies rely on U.S. data, the most active market for trading restricted shares. Many countries lack sufficient trading activity in this type of share to provide useful data. (See the bibliographic references at the end of this article.)

• Market studies fall into two main categories:

  1. Restricted Stock Studies: DLOM is estimated by comparing the trading prices of two shares of the same company. Both shares possess identical economic and political rights, except one is restricted from trading for a specific period. This category provides the most extensive data, with over 50 surveys. Recent years show average discounts in the 10%-20% range, median discounts between 15%-20%, and standard deviations from 15% to 20%.
  2. Pre-IPO Studies: DLOM is calculated as the difference in the price of identical shares immediately before and after an initial public offering (IPO). This approach is potentially skewed because IPO prices may already include discounts to attract investors, influencing the illiquidity discount measurement. This may explain the smaller number of pre-IPO surveys and their wider range of results (average and median discounts from 6% to 82%, standard deviations from 16% to 73%), making them less reliable.

• The studies encompass various historical periods, sample sizes, and discount measurement methodologies (timing of prices, price adjustment formulas), making direct comparisons challenging.

• A common critique is that survey metrics represent more than just illiquidity discount. They incorporate company-specific factors (industry, revenue, profitability), asset/transaction features (restriction time, block size), and macroeconomic conditions (volatility), some of which are integrated into the theoretical models we have reviewed. While some authors use statistical regression to analyze DLOM variations based on these factors, they often lack theoretical models to support the analysis. The diverse data samples also lead to inconsistent regression parameters, limiting their practical application.

Considering these limitations, comparing market data with theoretical results is expected to be complex. This is further complicated by the fact that the authors of the empirical studies do not publish the full data sets, but only summaries of them.

Before we proceed, some disclaimers are in order:

• The models can be sensitive to up to five input variables.

• Of the studies examined, only a few published the sensitivity of DLOM to input variables, and none published sensitivity to all variables.

• The authors typically publish only data summaries, resulting in small sample sizes.

Despite these limitations, we aim to statistically test the fit of the theoretical models to the empirical data using the following approach:

• We calculate theoretical DLOMs using available data from each study, filling data gaps with long-term historical averages of the variables for all models.
• We assess the fit of the resulting DLOMs to the empirical values using a linear regression analysis (theoretical DLOM = empirical DLOM). The regression slope should be close to 1, and the intercept close to 0, with 95% probability. We also aim for a low chance of a spurious fit (less than 5%), as determined by the F probability distribution.

The tables below summarize the fit of the models to the data:

• When share price volatility is the input variable, no model fits the data from FMV, Bajaj et al., part of Finnerty 2002, Finnerty 2012, or Trugman 2011. The models of Abbott, Ghaidarov, and Asian Put each fit two sets of data: Abbott fits part of Finnerty 2002 and Finnerty 2012, while Ghaidarov and Asian Put fit part of Finnerty 2012 and Stout 2023. The Finnerty models do not fit any set of data. Data from Finnerty 2012 prior to February 1997 best fits five different models.

• For restriction time as the input variable, only the data from Trugman 2011 and Stout 2023 are represented by the models. The models of Finnerty 2002 and Longstaff do not fit any data set.

• Regarding block size, the Abbott model is the only applicable model, but it does not fit any data set.

Overall, Abbott and Ghaidarov models demonstrate the best empirical validation, fitting two data sets for volatility and two for restriction time. Finnerty 2002 shows the weakest performance.

The most recent studies – Trugman 2011, Finnerty 2012, and Stout 2023 – tend to align better with the theory than older studies.

Recommendations for Estimating DLOM

If I were to recommend the best estimator of DLOM, I would suggest averaging all methods, except for Finnerty 2002. Concerning empirical data, all studies except Stout are likely outdated and should be disregarded. Even for Stout, it would be beneficial to separate DLOM estimates from different time periods to discern the impact of the most recent transactions in comparison with older ones.

This concludes our article series on DLOM. Thank you to Wulaia Consultoria’s team for their valuable input and review.

Bibliographic references – Restricted stock studies

Angrist et al.

Angrist, E.; Curtis III, H.; Kerrigan, D. Regression analysis and discounts for lack of marketability. Business Valuation Review, Vol. 30, Issue 1. 2011, pp. 36-48.

Bajaj et al.

Bajaj, M.; Denis, D.J.; Ferris, S.P.; Sarin, A. Firm Value and Marketability Discounts. Journal of Corporation Law. 2001.

Barclay et al.

Barclay, M.J.; Holderness, C.G.; Sheehan, D.P. The Block Pricing Puzzle – Working Paper No. FR 01-05. University of Rochester. March 2001.

Brophy et al.

Brophy, D.J.; Ouimet, P.P.; Sialm, C. Hedge funds as investors of last resort? The Review of Financial Studies, Vol. 22, Issue 2. 2009, pp. 541-574.

Chaplinsky & Haushalter

Chaplinsky, S. Haushalter, D. Financing under extreme risk: Contract terms and returns to private investments in public equity. The Review of Financial Studies, Vol. 23, Issue 7. 2010, pp. 2,789-2,820.

Columbia

Aschwald, K.F. Restricted Stock Discounts Decline as Result of 1-Year Holding Period. Shannon Pratt’s Business Valuation Update. May 2000, pp. 1-5.

Comment

Comment, R. Revisiting the Illiquidity Discount for Private Companies: A New (and “Skeptical”) Restricted-Stock Study. Journal of Applied Corporate Finance. 2012. Cited by Crisostomo, A. The Discount for Lack of Marketability – An Investigation of Privately Held Companies in North Italy. Master’s degree in Global Development and Entrepreneurship – Final Thesis. Università Ca’ Foscari Venezia. 2020, pp. 37-39.

Finnerty 2002

Finnerty, J.D. The impact of transfer restrictions on stock prices. The American Finance Association – AFA 2003, Washington, DC Meetings. Washington, DC. 2002.

Finnerty 2012

Finnerty, J.D. An Average-Strike Put Option Model of the Marketability Discount. The Journal of Derivatives, Vol. 19, Issue 4. Summer 2012. New York. 2012, pp. 53-69.

FMV 1994

Hall, L.S.; Polacek, T.C. Strategies for Obtaining the Largest Valuation Discounts. Estate Planning. January-February 1994, pp. 38–44. Cited by Pratt, S.P.; Reilly, R.F.; Schweihs, R.P. Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 4th Ed. New York: McGraw-Hill. 2000, p. 404.

FMV 2001

Robak, E. FMV Introduces Detailed Restricted Stock Study – 2001. Business Valuation Resources. 2009. Cited by Crisostomo, A. The Discount for Lack of Marketability – An Investigation of Privately Held Companies in North Italy. Master’s degree in Global Development and Entrepreneurship – Final Thesis. Università Ca’ Foscari Venezia. 2020, pp. 34-39.

FMV 2005

FMV Opinions, Inc. Cited by Dorrell, D.D.; Gadawski, G.A.; Brown, T.S. 2008 Update: Marketability Discounts – A Comprehensive Analysis. The Value Examiner. September-October 2008, pp. 12-33.

FMV 2007

FMV Opinions, Inc. Cited by Hitchner, J.R. Financial Valuation: Applications and Models, Third Edition. John Wiley & Sons, Inc. 2017, Chapter 9, Addendum 1.

Gelman

Gelman, M. An Economist Financial Analyst’s Approach to Valuing Stock of a Closely Held Company. Journal of Taxation. June 1972, pp. 353-354.

Glegg et al.

Glegg, C.; Harris, O.; Madura, J.; Ngo, T. The Impact of Mispricing and Asymmetric Information on the Price Discount of Private Placements of Common Stock. The Financial Review, Vol. 47, Issue 4. 2012, pp. 665-696.

Hertzel & Smith

Hertzel, M.; Smith, R.L. Market Discounts and Shareholders Gains for Placing Equity Privately. The Journal of Finance. 1993.

Hertzel et al.

Hertzel, M.; Lemmon, M.; Linck, J.S.; Rees, L. Long-run Performance Following Private Placements of Equity – Working paper. Arizona State University – ASU. December 2001.

Johnson

Johnson, B. Quantitative Support for Discounts for Lack of Marketability. Business Valuation Review. December 1999, pp. 152-155.

Johnson & Racette

Johnson, R.D.; Racette, G.A. Discounts on letter stock do not appear to be a good base on which to estimate discounts for lack of marketability on closely held stocks. Taxes – The Tax Magazine, Vol. 59. August 1981, pp. 574-581. Cited by Elmore, J.E. Determining the Discount for Lack of Marketability with Put Option Pricing Models in View of the Section 2704 Proposed Regulations. Willamette Management Associates, Inc.: Insights. Winter 2017, p. 35.

Krishnamurthy et al.

Krishnamurthy, S.; Spindt, P.; Subramanium, V.; Woidtke, T. Does Investor Identity Matter in Equity Issues? Evidence from Private Placements? Journal of Financial Intermediation, Vol. 14, Issue 2. April 2005.

Maher

Maher, M.J. Discounts for Lack-of-marketability for Closely Held Business. Interests, Taxes. September 1976, pp. 562-571.

Management Planning

Oliver, R.P.; Meyers, R.H. Discounts Seen in Private Placements of Restricted Stock: The Management Planning, Inc., Long-term Study (1980-1996). Cited by Reilly, R.F.; Schweihs, R.P. Handbook of Advanced Business Valuation. McGraw-Hill. 2000, Chapter 5.

Moroney

Moroney, R.E. Most Courts Overvalue Closely Held Stocks. Taxes. March 1973, pp. 144-154.

Pluris Valuation

Robak, E. Restricted Securities and Illiquidity Discounts. Trusts & Estates. February 2007. Cited by Pratt, S.P.; Reilly, R.F.; Schweihs, R.P. Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 4th Ed. New York: McGraw-Hill. 2000, Chapter 19.

SEC

Securities and Exchange Commission. Discounts Involved in Purchases of Common Stock (1966-1969). Institutional Investor Study Report of the H.R. Doc. No. 64, Part 5, 92nd Congress, 1st Session. 1971, pp. 2,444-2,456.

Silber

Silber, W.L. Discounts on Restricted Stock: The Impact of Illiquidity on Stock Prices. Financial Analysts Journal. July-August 1991, pp. 60-64.

Standard Research Consultants

Pittock, W.F.; Stryker, C.H. Revenue Ruling 77-276 Revisited. SRC Quarterly Reports. Spring 1983, pp. 1-3.

Stout 2020

Stout Risius Ross, LLC. Stout Restricted Stock Study – Companion Guide. 2020 edition.

Stout 2021

Stout Risius Ross, LLC. Stout Restricted Stock Study – Companion Guide. 2021 edition.

Stout 2023

Stout Risius Ross, LLC. Stout Restricted Stock Study – Companion Guide. 2023 edition.

Stumpf et al.

Stumpf, A.M.; Martinez, R.L.; Stallman, C.T. The Stout Risius Ross Restricted Stock Study: A Recent Examination of Private Placement Transactions from September 2005 through May 2010. Business Valuation Review, Vol. 30, Issue 1. 2011, pp. 7-19.

Trout

Trout, R.R. Estimation of the Discount Associated with the Transfer of Restricted Securities. Taxes. June 1977, pp. 381-384.

Trugman 2009

Harris, W. Trugman Valuation Associates, Inc. – TVA – Restricted Stock Study. Business Valuation Review, Vol. 28, No. 3. American Society of Appraisers. 2009, pp. 128-139.

Trugman 2011

Harris, W. Trugman Valuation Associates, Inc. – TVA – Restricted Stock Study – An Update. Business Valuation Review, Vol. 30, Issue 4. 2011, pp. 132-139.

Verdasca

Verdasca, A. Common Stock PIPE Discounts and Long-term Performance. New York University. The Leonard N. Stern School of Business. April 2007.

Willamette

Willamette Management Associates, Inc. Cited by Pratt, S.P.; Reilly, R.F.; Schweihs, R.P. Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 4th Ed. New York: McGraw-Hill. 2000, p. 404.

Wruck

Wruck, K.H. Equity ownership concentration and firm value: Evidence from private equity financings. Journal of Financial Economics, Vol. 23, Issue 1. June 1989, pp. 3-28.

Wruck & Wu

Wruck, K.H.; Wu, Y. Relationships, Corporate Governance and Performance: Evidence from Private Placements of Common Stock. The Ohio State University, Fisher College of Business. Working paper 2008-03-019. May 2008.

Wu

Wu, Y. The Choice between Public and Private Equity Offerings. Unpublished paper. National Tsing Hua University – Department of Quantitative Finance. November 2000. Cited by Elmore, J.E. Determining the Discount for Lack of Marketability with Put Option Pricing Models in View of the Section 2704 Proposed Regulations. Willamette Management Associates, Inc.: Insights. Winter 2017, p. 35.

Bibliographic references – Pre-IPO studies

Emory

Emory Sr., J.D. Eight articles cited by WMA, pp. 72-81.

Emory 1997-2002

Emory Sr., J.D.; Dengel III, F.R.; The value of marketability as illustrated in initial public offerings of dot-com companies – May 1997 through March 2000. Available at https://emoryco.com/wp-content/uploads/2022/09/dotcomIPOstudy.pdf.

Pastusiak et al.

Pastusiak, R.; Keller, J.; Radke, M. Marketability Discount in Various Economic Environments. Comparison of Developed and Emerging Markets on the Example of the USA and Poland. Journal of Risk and Financial Management, Vol. 13, Issue 6. 2020, pp. 132-150.

VA

Valuation Advisors, LLC. Cited by WMA, pp. 72-81.

WMA

Nicholls, S.S.; Reilly, R.F. Discount for Lack of Marketability in the Professional Practice Valuation. Willamette Management Associates Insights, Issue 133. Summer 2022, pp. 67-82.