Deja Vu #3: The Gelman (1972) and Trout (1997) Restricted Stock Studies

In the first post in this Deja Vu series, we discussed the Securities and Exchange Commission’s Rule 144 from a layman’s perspective as of pre-April 1997, when the mandatory period of restriction was lowered from two years to one year.  The second post reviewed the SEC Institutional Investor Study, which was published in 1969.  This third post reviews two more of the early restricted stock studies, the Gelman Study and the Trout Study.  These reviews were written and published in my book Quantifying Marketability Discounts (out of print) in 1997.  The reviews are repeated here with only light editing and a few current comments, which will be highlighted.

The years noted in the headers are the years of publication.

The Gelman Study (1972)

The Gelman Study, the first of three often-cited restricted stock studies from the early‑to-mid 1970s, was published in Journal of Taxation in 1972.[1] Gelman analyzed the prices paid for restricted securities by four closed-end investment funds over a period beginning in 1968 and ending in 1970.

The four funds were established in 1968; by the end of 1970, they had assets ranging from $16 million to $196 million. Gelman obtained information about the discounts paid by the funds for the purchase of restricted shares from the public disclosure documents of the issuing companies.

In total, he analyzed 89 transactions, which took place between 1968 and 1970. His results are summarized in Figure 2-3.

The median and mean discounts in the Gelman analysis were each 33%. We actually have little other information from this early study. The article was short and to the point. We can infer, however, that not all the discounts were 33%. Some 27 observations, or about 30% of the sample, had discounts of less than 25%. Alternatively, 32 observations, or 36% of the sample, had discounts of 40% or more. As Gelman observed in the article, about 60% of the transactions reflected discounts of 30% or more. Gelman concluded his article with the following observation:

Depending on size and other factors, these actual discounts obtained by knowledgeable investors may serve as a guide to the valuation analyst in determining the discount to apply to the gross value previously determined for the closely held stock, in order to arrive at final value for the shares involved.[2]

Current Comment.  There was not much to the Gelman Study.  Some 89 transactions were observed and stratified by percentage discount.  The study contributed to the “about 35%” for marketability discounts that became the mantra for business appraisers for years.

The Trout Study (1997)

The Trout study sought to develop an empirical model to determine appropriate discounts for restricted securities.[3]  Trout based his model on the purchases of restricted shares by six investment companies or mutual funds. The study was confined to purchases of restricted common stock by the selected funds from 1968 to 1972. Trout’s empirical model included the following variables:

  • Exchange listing. This variable was used to determine the liquidity effect, if any, of being traded on the New York Stock Exchange or the American Stock Exchange. [Recall the “exchange effect” noted in Deja Vu #2].
  • The number of shares outstanding. Trout postulated that there should be an inverse relationship between shares outstanding (as a proxy for liquidity) and the related restricted stock discount.  [The actual number of shares outstanding does not measure market capitalization, so would not provide a measure of market capitalization, which, it would seem, would be a more relevant variable for consideration.][4]
  • Percentage control involved in a transaction. Trout attempted to measure the impact of blockage on restricted stock discounts.
  • Small purchases constituting less than 1% control. Trout postulated that small purchases might warrant only small discounts.
  • Value of the purchase. Value was measured at the freely traded price times the number of shares purchased. [Trout measured the dollar value of the purchases of restricted stock.  The percentages of the issuers total shares represented by the purchase could have been a better measure.]

Trout’s statistics are provided in Figure 2-4.

The statistics above indicate the following:

  • All the t-statistics for Trout’s variables exceed 2.0, lending some credence to the value of the derived regression coefficients.
  • The signs on the regression coefficients were all in the directions that Trout had postulated, confirming the expected relationships between the various independent and dependent variables (i.e., the discounts).
  • The mean discount was 33.5%, and the standard deviation was 11.7%. The implication is that about two-thirds of the observed discounts were within a range of about 22% to 45%, with another one-third lying above or below this range.

The adjusted coefficient of correlation, or R in the table above, was 0.49, so the implied coefficient of determination, or R2, is 0.24. This R2 suggests that only about 24% of the observed variation in the dependent variable is explained by the model’s independent variables. The model should therefore not be considered robust in its explanatory power, since 76% of the observed variation is left unexplained. Nevertheless, the F-statistic is significant (measuring the statistical significance of the model as a whole), as are the individual t-statistics.

Trout comments that the results indicate a “moderate ability of this model to account for variations in the observed discounts.” Trout provides the following additional discussion of his analysis in the article:

Most purchases of restricted stocks are negotiated between buyer and seller and these agreements have specified characteristics that are not constant among all transactions. These characteristics, such as the exact agreement on registration responsibility, may differ widely among these transactions, and this fact would lead one not to expect any model to be extremely accurate in predicting discounts.

Another factor that may explain the “unexplained variation” in the discounts is the relative bargaining power of sellers of restricted securities. This strength may vary considerably among sellers and significantly influence the size of the discount that they must accept in order to sell unregistered securities. One must remember that the market for unregistered shares is not a continuous auction market as are the markets for most registered securities, so that buyers and sellers are both faced with a situation where one or the other, or both sides, may be lacking relevant information about the market.[5] [emphasis added]

The Trout study reflects the most rigorous statistical analysis of restricted stock transactions found in the early studies. Trout concludes his article with the following observation:

The models are useful in predicting the discount which should be accorded a transfer of restricted shares given information about the variables included in the models. Other relevant information, if any, should be used to adjust this predicted discount accordingly before it is applied to any transfer in a valuation case.[6]  [emphasis added]

Since Trout was aware that only 24% of the variation in observed discounts was explained by his model, a great deal of “other relevant information” should perhaps be considered by valuation analysts in developing marketability discounts applicable to nonmarketable minority interests in closely held businesses.

Current Comment.  The most important takeaway from the Trout Study is that he recognized the relative bargaining power of buyers and issuers of restricted stock and that such “relevant information” should be considered in any marketability discount determination. It is interesting that Trout’s regression equation does not include any variable(s) relating to financial performance or market capitalization (size).  This information is some of the “relevant information” obviously considered both by purchasers and issuers of restricted shares.

All of the studies that will be reviewed in this series were mentioned, if briefly, in Shannon Pratt’s Valuing a Business, 5th Edition.

The Trout, Gelman, Maher, or Moroney studies are mentioned only in a table in Pratt/ASA’s Valuing a Business, 6th Edition (“VAB6”). There is a review of the SEC Study and of a study prepared by Management Planning, Inc.  A study by Bruce Johnson, written in Pratt’s Business Valuation Update in 1997, is briefly reviewed. The Pluris DLOM Database is discussed. And the Stout Restricted Stock Database and the Stout DLOM Calculator are also mentioned. Perhaps this is an indication that the drafters of Chapter 19 of VAB6 have recognized the limited value of these earlier studies.

In the next post in this Deja Vu series, we will review the Moroney Study, which was published in 1973. Moroney, in addition to providing a study of discounts, suggested that several factors were important based on his review of public disclosures about the transactions, including the impact of liquidity, the uncertain holding period, and the general attractiveness of the investments from the viewpoint of the investment committees of the purchasing funds.  More coming on this.

In the meantime, be well,



[1] Gelman, Milton, “An Economist-Financial Analyst’s Approach to Valuing Stock of a Closely Held Company,” Journal of Taxation, June, 1972, at p. 353.

[2] Ibid, p. 354.

[3] Trout, Robert R., “Estimation of the Discount Associated with the Transfer of Restricted Securities,” Taxes, June, 1977, pp. 381-385.

[4] A measure of market capitalization or trading volume might have been preferable as a proxy for liquidity, but Trout used shares outstanding.

[5] Ibid, p. 384. Keep in mind that Trout is dealing only with the private placement of securities of publicly traded companies with mandatory disclosure requirements imposed by the SEC. The placements studied are with six specifically identified investment companies or mutual funds, i.e., with a small group of sophisticated investors. If this degree of uncertainty exists in the studied restricted stock transactions, how much greater uncertainty might there be in actual transactions involving shares of closely held companies with no disclosure requirements?

[6] Ibid, p. 385.

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2 thoughts on “Deja Vu #3: The Gelman (1972) and Trout (1997) Restricted Stock Studies

  1. As always, Chris effectively reminds the universe of business valuators that research, analysis, thinking, and measured judgment are both required and essential in completing all valuation tasks…especially in determining marketability discounts.