Deja Vu #6: The Silber Restricted Stock Study (1981-1988)

Recap of Deva Vu Series to Date

This is the sixth post in a series on the original restricted stock studies developed into the 1990s based on transactions occurring during the late 1960s, 1970s, and 1980s.  For those new to the series, this is the sixth post and it summarizes the Silber Study.

There was one other “study,” but there is so little information from it that is not feasible to summarize it.  This was the Styker/Pittock Study (1991), which had an average restricted stock discount of 45% based on 29 transactions.  The range of observations was from 7% to 91%.

Looking ahead to today’s post, The Silber Study had an average restricted stock discount of 34%.  By the early 1990s, there were a handful of studies with average restricted stock discounts in the broad range of 25% to 45%.  The die was cast for most appraisers at that time, and for many appraisers, even today, this is the extent of analysis in developing marketability discounts.

The Silber Restricted Stock Study – Performance Matters

The initial restricted stock studies did not generally provide sufficient performance data to enable business appraisers to see the impact of performance on restricted stock discounts.  In Quantifying Marketability Discounts, we wrote about one study that did provide some performance information.  It was the Silber Study, written by Professor William L. Silber and published in the Financial Analysts Journal. [1]

The figures in this post are from Chapter 8 of Business Valuation: An Integrated Theory Third Edition, “Restricted Stock Discounts and Pre-IPO Studies.”

  • The average discount in this study was 34%, as seen above, which is in line with averages from other studies of transactions during the 1970s and 1980s.
  • The Silber and other studies considered transactions occurring prior to April 1997, when the SEC Rule 144 base period of restriction was two years.
  • Note that the standard deviation is 24%, so the variation was wide in the sample.  In fact, the range was from a negative 13% (that’s a premium to the public share price for the company) to a discount of 84%.  All of the transactions were subject to the same period of restriction, so what caused the wide variation in restricted stock discounts?
  • We see immediately that there was a wide range in the size of the issuers. The lowest revenue was apparently a startup with no revenues.  The highest revenue company in the sample was $595 million.  That’s a wide range.  Excluding that one company, average revenue falls from $40.0 million to $31.8 million.  There are a lot of smallish companies in the sample.
  • The average dollar size of issuances was $4.3 million, which represented an average of 13.6% of the capitalization of the companies involved in the transactions
  • The average of prior year earnings in the sample was $0.9 million. Excluding the highest earnings figure in the sample reduces average earnings to breakeven.
  • The bottom line is that, given the information in the summary table above, what we do know is that the average restricted stock discount was 34% and there was a wide range around that average.

Fortunately, the Silber study provided additional information that provides insights into what causes restricted discounts to vary so widely.

In Exhibit 8.5, the overall Silber sample of 69 observations was divided into two sub-samples based on the observed restricted stock discounts.  Those with discounts greater than 35% are shown on the left side of the exhibit and those with discounts less than 35% are on the right.

Since the issued restricted shares were alike in all respects to their publicly traded counterparts, we would assume that companies with better performance would tend to have lower discounts than those with poorer performance.  The table confirms this observation.  Look first at the left side of the exhibit.

  • For companies with restricted stock discounts greater than 35%, the average discount is 54%.
  • These companies are losing money, with an average loss of $1.4 million in the previous year.
  • Average revenues were $13.9 million, and average market capitalization was $33.8 million.
  • The companies with larger discounts are small, speculative companies with, in all likelihood, relatively high perceived risk when viewed by investors.

Now look at the right side of Exhibit 8.5.

  • For companies with restricted stock discounts less than 35%, the average discount is 14%.
  • Those companies are, on balance, at least somewhat profitable, with average prior year earnings of $3.2 million.
  • Average revenues were $65.4 million, and average market capitalization was $74.6 million.
  • The companies with smaller discounts are larger, less speculative companies as a group than the companies with larger discounts.

What we see in the Silber study, because some performance information was provided, is an entirely different picture than a simple average of a group of discounts.  Any particular discount in the Silber study was determined based on facts and circumstances and negotiations between sellers and buyers.  Different situations at the companies involved resulted in widely different discounts.  This fact alone should cause appraisers to be concerned about thinking that an average discount from any (or all studies) means anything.

The Silber transactions can be summarized graphically as follows.  There are really three groupings and three averages.

The picture in Exhibit 8.6 does not suggest there is much meaning in an average restricted stock discount of 34% for the Silber study.  There is an entirely different picture when Silber breaks his sample into two relevant groups by discount size.  We point out the obvious here:

  • A 14% average restricted stock discount for better performing companies is hugely different than an average discount of 54% for poorer performing companies.
  • The 34% overall sample average tells readers nothing about the diversity of performance in the sample. In fact, the overall average tells nothing about the sample (other than it’s the average of the group for one statistic).
  • The thought processes of investors clearly led to widely differing assessments of the riskiness of holding restricted shares over an expected holding period that exceeded two years.
  • The required returns leading to average discounts of 14% for better performers were different from those leading to average discounts of 54% for the poorer performers.

Professor Silber tried to tell the business appraisal profession that there is more to a group of restricted stock transactions than their simple averages.

That is why, when we employ the QMDM as a shareholder-level discounted cash flow model, we focus on expected cash flows to subject interests, the growth of those cash flows, and the risks (i.e., required returns) of achieving expected cash flows.

Let me point out that this analysis was originally written in 1997, as Quantifying Marketability Discounts was coming to market.  It does not present any new thinking, but rather, it is repeated because it is not a new thought, but an old one.  The appraisal profession has had its proverbial head in the sand for too long.

Brief Recap and Look Ahead

What do we have after examining most of the evidence on restricted stock discounts that have been used by appraisers for decades?  Frankly, not much.  The following figure is excerpted from Figure 8.15 of Business Valuation: An Integrated Theory Third Edition.

The shaded area above indicates the famous “benchmark” range of 35% to 45%, or from 25% to 35%.  Literally, this is the extent of information cited by many appraisers in 2022 in assessing marketability discounts.

Many appraisers now add an additional method based on Judge David Laro’s Memorandum Opinion in Mandelbaum.  In the next post of this series, we will review the Mandelbaum decision one more time.  Published in 1995, the decision took as a starting point a “benchmark range” of marketability discounts of 35% (based on one appraiser’s citing of the above studies) to 45% (based on the average of pre-IPO discount studies).

We will not review the Mandelbaum case in its entirety.  Rather, we will focus on the now-famous “Mandelbaum Analysis,” which is generally based on Judge Laro’s consideration of a series of factors in relation to the benchmark range.

Until next time, be well!  And, of course, feel free to comment on this blog or to me privately.




  • [1] Silber, William L., “Discounts on Restricted Stock: The Impact of Illiquidity on Stock Prices,” Financial Analysts Journal, July August, 1991, pp. 60-64.  An analysis of this study was provided in Chapter 2 of Quantifying Marketability Discounts (Mercer, 1997)

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One thought on “Deja Vu #6: The Silber Restricted Stock Study (1981-1988)

  1. Hopefully, the specific information sets and subsequent analysis in the grouping of data points in the Silber Study should not be news to thoughtful appraisers. Once again Chris has made it clear that no one should have been using “averages” for data with a wide dispersion as a reference point without significant future investigation.