Discounts for illiquidity: where are we standing now? Part 9

This is the ninth and last article of our series on illiquidity discount – DLOM as applied to the valuation of restricted or hard-to-sell assets. We will try to test the 11 theoretical models presented in the second to the seventh articles against the market data from the eighth article.

I refresh some or the key takeaways from our article on market data:

• Almost all empirical studies were published with USA data, the most active in trading restricted shares, as, in most countries, there is virtually no trade of that kind of shares. See bibliografical references at the end of the article.
• There are two big groups of market studies:

1.????? Restricted stock studies: the DLOM is estimated by comparing the actual trading prices of two shares of the same company, both with all economic and political rights, except that one of the shares that cannot be traded during a certain period. This is the largest group with most data, including more than 50 surveys. For more recent years, average discounts are in the range of 10%-20%, median discounts are in the 15%-20% range, and standard deviations are 15% to 20%, high in comparison with the average and median.

2.????? Pre-IPO studies: the DLOM is calculated as the difference of the prices of the identical shares of a company immediately before and after an initial public offering – IPO. The main problem with this group is that, probably, most of the IPO prices may be offered with some other discount to attract investors, that will bias the pure illiquidity discount measurement. Maybe because of that, or because the scarcity of IPO data in comparison with the restricted stock studies, there is a much smaller number of pre-IPO surveys – I found only four. Their results are more widely spread – average and medians discounts from 6% to 82% and standard deviations from 16% to 73% – and, therefore, less reliable.

• The studies cover several different historical periods, have very different sizes of transaction samples and measure discounts differently both in terms of timing of prices and price adjustment formulas. Therefore, it is a very sensitive task to compare the results of the individual studies.
• One common critique is that the metric provided by the surveys is not a pure illiquidity discount, but it includes company specific factors (industry, revenues, profitability, etc.), features of the individual asset/transaction (restriction time, block size, etc.) and industry and macroeconomic specific conditions (volatility), some of which are built in the theoretical models we examined before. Some authors analyze variations of DLOM according to those factors using statistical regression, but do not provide a theoretical model to support the analysis. In addition, since their data samples are so diverse, their regression parameters seldomly agree with each other, which make them virtually unusable for practioners.

With that in mind, our exercise of comparing market data with theoretical results is expected to be a strenuous undertaking, even more when the authors of the empirical studies do not publish the full data sets, but only summaries of them. Nevertheless, we will try.

To start with it, some disclaimers are due:

• The models are sensitive to up to five input variables.

• Of the nearly forty studies we could retrieve, only nine published the sensitiveness of DLOM to those input variables, and none published sensitiveness to all variables. Therefore, we need to circumvent the data gap in order to test the accuracy of each theoretical model against the empirical data.

• The authors publish only summaries of their data; the samples we can use contain no more than a dozen data points at best.

Despite all those limitations, we need to find a way to test the fit of the theoretical models to the empirical data with statistical reliability. Here are our ideas:

• We calculate the theoretical DLOMs with the data available in each study, and fill the data gap with long-term historical averages of the variables for all models.
• The fit of resulting DLOMs to the empirical ones is checked using a linear regression analysis for the equality theoretical DLOM = empirical DLOM, where the incline of the regression should be close to 1 (one), and the intercept should be close to 0 (zero) in statistical terms, with 95% probability. Furthermore, the chance of a spurious fit should be small say less than 5%, as measured from the F probability distribution.

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

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

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

• When it comes to block size, the only model applicable is Abbott, but it fits to no data set.

Overall, the best models in terms of empirical validation are Abbott and Ghaidarov, as they fit to two data set for volatility and two for restriction time. The worst performance comes from Finnerty 2002.

As for empirical data, the most recent studies – Trugman 2011, Finnerty 2012 and Stout 2023 – tend to be best represented by the theory than the older studies.

If I were to recommend my readers about the best estimator of DLOM, I would say that is the average of all methods, except Finnerty 2002. As to use empirical data, all studies, except Stout, are probably now outdated and should be discarded. Even for Stout, it would be best to break its DLOM estimates from different time periods, so that we could sense what the most recent transactions say in comparison with older ones.

So that is the end of our article series of DLOM. I hope you found the discussion objective, thorough and useful. Please, leave your impressions in the comment section and/or suggestions for new topics.

As always, thanks to Wulaia Consultoria 's team for the comments 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.

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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.

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