comment - 2011 - revisiting the illiquidity discount for private companies, a skeptical

VOLUME 24 | NUMBER 1 | WINTER 2012

APPLIED CORPORATE FINANCEJournal of

A M O R G A N S T A N L E Y P U B L I C A T I O N

In This Issue: Liquidity and Value

Financial Markets and Economic Growth 8 Merton H. Miller, University of Chicago

A Look Back at Merton Millers Financial Markets and Economic Growth 14 Charles W. Calomiris, Columbia Business School

Liquidity, the Value of the Firm, and Corporate Finance 17 Yakov Amihud, New York University, and Haim Mendelson, Stanford University

Getting the Right Mix of Capital and Cash Requirements in Prudential Bank Regulation

33 Charles W. Calomiris, Columbia Business School

CARE/CEASA Roundtable on Liquidity and Capital Management 42 Panelists: Charles Calomiris, Columbia Business School; Murillo Campello, Cornell University; Mark Lang, University

of North Carolina; and Florin Vasvari, London Business School.

Moderated by Scott Richardson, London Business School.

Statement of the Financial Economists Roundtable

How to Manage and Help to Avoid Systemic Liquidity Risk 60 Robert Eisenbeis, Cumberland Advisors

Clearing and Collateral Mandates: A New Liquidity Trap? 67 Craig Pirrong, University of Houston

Transparency in Bank Risk Modeling: A Solution to the Conundrum of Bank Regulation

74 David P. Goldman, Macrostrategy LLC

Revisiting the Illiquidity Discount for Private Companies: A New (and Skeptical) Restricted-Stock Study

80 Robert Comment

Are Investment Banks Special Too? Evidence on Relationship-Specific Capital in Investment Bank Services

92 Chitru S. Fernando and William L. Megginson,

University of Oklahoma, and Anthony D. May,

Wichita State University

80 Journal of Applied Corporate Finance Volume 24 Number 1 A Morgan Stanley Publication Winter 2012

Revisiting the Illiquidity Discount for Private Companies: A New (and Skeptical) Restricted-Stock Study

1. Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579 (1993). 2. For additional discussion of the discount rates used in fairness opinions, see Robert Comment, Business Valuation, DLOM and Daubert: The Issue of Redundancy, Busi-ness Valuation Review, 29 (2010).

BD

by Robert Comment

ata from studies of restricted stock are routinely used by business-valuation analysts and apprais-ers when valuing private companies to estimate liquidity discounts, often referred to as discounts

for lack of marketability, or DLOMs. The standard rationale for this use of DLOMs is that an asset that is hard to sell must be worth less, all other things equal, than an asset that is easier to sell. DLOMs as high as 20% to 40% are commonly used in practice for valuing small private businesses. (Low valuations are advantageous for some parties in gift-tax and divorce matters.)

The evidence supporting the use of such large DLOMs comes from so-called restricted-stock studies that analyze the average percentage price discount (market price less deal price) seen in private placements of restricted stock (stock not registered with the SEC for resale to the public). But these studies, as I discuss in this paper, are badly flawed. And insofar as hard to sell is treated as a type of risk, any supple-mental adjustment for illiquidity is potentially redundant; it amounts to a discounting for risk that is already reflected in the core valuation to which a supplemental adjustment, such as a DLOM, is applied. The evidence from my own study, which is summarized in the pages that follow, is consistent with use of a DLOM no larger than 5-6%.

Large DLOMs have also been used by accountants when determining the compensation expense associated with grants of equity. In this case, the justification is largely theoretical. The large DLOM is calculated as the value of a put option that protects its owner against all downside risk (with the value of the put expressed as a percentage of total value). The intuition, if one can call it that, is that an elimination of downside risk mitigates the inconvenience of illiquidity. The put estimate is based on the volatility of free-trading shares, perhaps based on comparable public companies, along with an estimate of the expected time before a liquidity event. But this option-based approach is overkill at best, and adds nothing to the purported empirical support for large DLOMs. Accordingly, in public disclosures, corporate executives would be well advised to characterize any double-digit DLOMs used in fair-value estimates as assumptions based on managements

highly speculative judgment, and not on hard evidence.Many business valuations are produced for the eyes of

a judge in a prospective future legal proceeding. Since the Supreme Courts ruling in Daubert,1 all federal judges (and by now most state judges) are obliged to exclude expert opinion that is not reliable. While judges have been slow to impose Daubert standards on business-valuation methods, perhaps in the belief that valuation is necessarily as much art as science, such judicial forbearance is unlikely to last. One takeaway from this paper is that a valuation that includes a large DLOM based on evidence from studies of restricted stock may not provide the anticipated degree of legal comfort.

Specifically, judges have not yet addressed the likely redundancy of large DLOMsa redundancy that results in a double discounting for the risk reflected in a core valua-tion methodology like discounted cash flow (DCF) analysis. In practice, discount rates depend strongly on the size of the company being valued, with higher rates being used for smaller companies. But it also happens to be true that company size is highly correlated (across companies) with liquidity or marketabilityan empirical regularity that has been shown to hold using almost every measure of size and liquidity. Because the effective size premium in discount rates is large, there is a large discount for lack of size (DLOS) embedded in core valuation methodologies. Because size and marketability are highly correlated, a large DLOM is likely to amount to just a second DLOS by another name, where the first DLOS is ample.

Just how ample effective size premiums tend to be can be seen in the discount rates used in the fairness-opinion valua-tions that investment bankers produce in support of their M&A transactions.2 Table 1 shows the average discount rates used in a random sample of 700 DCF valuations produced during 2007-2010 and publicly disclosed in an SEC filing, most often in a proxy statement for a shareholder vote to approve a merger. These 700 DCF valuations were produced by a total of 162 investment banks and valuation firms, with the four most active firms (Goldman Sachs, JP Morgan, Merrill Lynch, and Morgan Stanley) producing one-quarter of the total. Each valuation uses a range of discount rates, so

81Journal of Applied Corporate Finance Volume 24 Number 1 A Morgan Stanley Publication Winter 2012

3. See Viral V. Acharia and Lasse Heje Pedersen, Asset Pricing with Liquidity Risk, Journal of Financial Economics, 77 (2005).

4. See Table 4 in Mukesh Bajaj, David Denis, Stephen Ferris and Atulya Sarin, Firm Value and Marketability Discounts, Journal of Corporation Law, Vol. 27 (2001).

5. An extreme example where buyer skepticism may have played a role is the private placement by the development-stage pharmaceutical company HST Global, Inc., which sold restricted stock without registration rights in August 2008. The new shares, which

amounted to 4% of shares outstanding, were sold to 22 buyers at a price of $1.25/sharea discount of 86% off the (OTCBB) trading price on the day the deal closed. That market benchmark had risen over the prior 30 calendar days from $3.59 per share to $8.98 per share, or by 150%.

6. The known or potential rate of error is one indicia of reliability cited by the Su-preme Court in its Daubert ruling governing the admissibility of expert testimony. See Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579 (1993).

My study avoids four mistakes that are routinely made by studies of the liquidity discounts seen in private placements of restricted stock.

First and foremost, it is a mistake to assume that discounts in private placements of restricted stock are attributable solely to restricted marketability since discounts also occur in private placements of free-trading shares. My data include free-trading shares (28% of all deals) as well as restricted stock. Only the differential discount can be attributed to the restricted nature of restricted stock, and then only after controlling for deter-minants of discounts that are common to restricted stock and free-trading shares. But, as discussed below, my own and other studies have shown that actual discounts depend little on the restricted nature of restricted stock.

Second, one long dominant feature of the private-place-ment landscape has been the high participation by OTC companies (those with Pink-Sheet or OTCBB-traded shares). OTC companies account for 41% of the 1,103 private place-ments of common stock during 2004-2010 (that are included in my data). This is down from 82% of 88 deals during the period 1990-1995.4 This matters because almost all of the largest discounts (those above 50%) in my data occur in deals by OTC companies. The prevalence of OTC deals means that discounts are often calculated relative to market prices that are set in trading venues that are not often thought of as efficient markets. It is a mistake to overlook the effect of OTC status, especially insofar as such data provide the juice of the analysis.

The third mistake is related to the second. It is a mistake to overlook the change in the market price of the stock over the several weeks before the deal. The rationale is straight-forward. Buyers may be skeptical about a market price, and discount more heavily off that market price to compensate for any recent increases.5 Consistent with this possibility, the percentage change in stock price over the 30 days before the deal closes explains private-placement discounts as well as any other explanatory variable that I consider.

Fourth, the dispersion in discounts from one deal to the next is wide and it may be tempting to overlook this attribute of private-placement discounts when reaching conclusions. It is because the dispersion is wide, however, that it is impor-tant to address this feature of the data.6 Because t-statistics increase with sample size, statistical significance presents a low bar in a sample as large as mine.

One final mistake: it is wrong to assume that an average discount reflects blockage (a practical rather than regulatory

Table 1 reports the average high and average low. The effective size premium is simply the difference in the discount rates deemed appropriate for the smallest versus largest companies (row D minus row A in Table 1), which comes to 7.6% based on the low and 10.0% based on the high, or 8.8% overall. While size and liquidity are correlated, a size premium this large cannot be plausibly attributed to a difference in liquidity alone. In one model, illiquidity contributes 4.6% per year to the difference in annual risk premium between stocks with low versus high liquidity.3 Compared to this estimate, the effective size premium of 8.8% seen in Table 1 should be sufficient to address liquidity risk.

Finally, the size premium in an annual discount rate can be made comparable to a DLOM by converting it arithmeti-cally into a one-time, up-front discount for lack of size, or DLOS. Based on either the high or low rates in Table 1 and using a Gordon growth model with an assumed growth rate of 3%, the typical embedded DLOS approximates 53% of total value (such as the result of a DCF valuation). That the DLOS typically embedded in core valuation methods is this large suggests that there is little remaining justification for a DLOM of any significance.

Ideally, the size premium in the discount rate used in a DCF valuation should mimic a market-based size premium. Similarly, because it uses market data, a restricted-stock study holds the possibility of identifying an incremental, non-redundant DLOM. This is because the market price against which the price discount is measured already reflects a DLOS. Unfortunately, while a DLOM estimated in a restricted-stock study is inherently incremental, this benefit easily can be offset by an otherwise flawed methodology.

Size of Company Being Valued:(based on deal terms)

Discount Rate

Number Average Low Average High

A $1 Billion or more 224 9.7 11.8

B $200 to $999.9 Million 214 12.2 15.1

C $50 to $199.9 Million 141 15.8 19.4

D $0 to $49.9 Million 121 17.3 21.8

All Valuations 700 13.0 16.0

Table 1 Average Discount Rates Used in Fairness- Opinion Valuations, Classified by Size of Company, 2007-2010


7. Karen Wruck, Equity Ownership Concentration and Firm Value, Journal of Finan-cial Economics, Vol. 23 (1989); William Silber, Discounts on Restricted Stock: The Impact of Illiquidity on Stock Prices, Financial Analysts Journal, Vol. 47 (1991); Mi-chael Hertzel and Richard Smith, Market Discounts and Shareholder Gains For Placing Equity Privately, Journal of Finance, Vol. 48 (1993); Mukesh Bajaj, David Denis, Ste-phen Ferris and Atulya Sarin, Firm Value and Marketability Discounts, Journal of Cor-poration Law, Vol. 27 (2001); and Michael Barclay, Clifford Holderness and Dennis Sheehan, Private Placements and Managerial Entrenchment, Journal of Corporate Fi-nance, Vol. 13 (2007).

8. See Table 5 of Mark Huson, Paul Malatesta and Robert Parrino, The Decline in the Cost of Private Placements, working paper available at SSRN.com (June 2009).

9. Report of the Advisory Committee on the Capital Formation and Regulatory Pro-cess, U.S. Securities and Exchange Commission, July 24, 1996. (I served as the staff economist for the Wallman Committee.)

10. I understand that the change to six months applied retroactively to existing re-stricted stock. Accordingly, absent an effective registration, restricted stock issued before August 15, 2007 converted into free-trading shares no later than February 15, 2008, while restricted stock issued between August 15, 2007 and February 15, 2008 con-verted after six months.

11. See Mark Mitchell and Mary Norwalk, Assessing and Monitoring the Reliability of Marketability Discount Studies and the 7.23% Solution, Business Valuation Review, Vol. 27 (2008).

of common stock by seasoned public companies that are current in their periodic filings.9 The Committees recom-mendations coincided with the start of electronic filing, a change that made periodic filings far more accessible. These developments led the SEC to begin a gradual deregulation to facilitate post-IPO issuances of common stock. One facet was a modest lowering of the threshold to qualify for the use of shelf registration, with the result that the current thresh-olds mainly exclude OTC companies with a public float below $75 million. Earlier, during the period 1992-2007, all companies with float below $75 million had been excluded. More importantly, the SEC shortened the minimum holding period before restricted stock could be resold to the general public without registration. The regulatory holding period was reduced from one year to six months as of February 15, 2008,10 after being reduced from two years to one year in early 1997.

The Mists of Time One might imagine that the private placements most reveal-ing about and representative of the DLOM were those before 1997, when the regulatory holding period was longest. The catch is that these deals mostly pre-date electronic filing, which was phased in around 1995. Information about these deals is limited to what issuers disclosed in press releases. If better information was available at the time, it would have been in disclosure documents stored on microfiche at SEC headquarters. The press releases are vague about the initial and subsequent registration status of shares being sold.11 Because of these data limitations, it appears to be difficult to determine in these deals if a marketability restriction applied for the full two-year term, or if one ever applied at all.

In any event, these older data are of dubious relevance in the modern era. For one thing, the frequency of deals has increased ten-fold, from 15 per year during 1990-1995 to 158 per year during 2004-2010. Buy-side competition, along with the shift in composition away from OTC companies, may have reduced discounts over time.

Even if a longer period confers a theoretical advantage on pre-1997 data, these data are fuzzy, whereas a study using modern data can use exact information, including the date when restricted stock converts into free-trading shares. One of my regression analyses finds that discounts in placements of restricted stock vary little with the realized delay before free-

or contractual drag on marketability). The most immediate reason for this is that the shares sold in private placements are not usually sold as a single block. The buyers often number in double digits. As a consequence, the size of the whole deal (the macro block) is very different from the average size of the blocks actually purchased (mini-blocks).

While my study is novel in several respects, it largely follows a line of economic research on private-placement discounts.7 The latest work in this line, a study by Mark Huson, Paul Malatesta and Robert Parrino,8 uses multiple regression analysis and a large sample to estimate a differential discount for restricted stock after controlling for 15 other explanatory variables. While the DLOM is not their focus, they find that the part of the discount directly attributable to the regulatory restriction (which can be viewed as an estimate of the DLOM) is 2.6% over their whole sample period, falling from 4.8% during 1995-2001 to -0.5% during 2002-2007. These estimates are somewhat lower than what I find during 2004-2010.

SEC Deregulation The Securities Act of 1933 requires that companies sell stock to the general public only after filing a registration state-ment that discloses material information deemed necessary to level the playing field. Having said that, companies are allowed to sell their securities without registration and the investor protections associated with a prospectus, just not to the general public. Common stock sold without registration is known as restricted stock.

The SEC has discouraged the sale of restricted stock throughout its history, mainly by imposing a minimum holding period before restricted stock can be resold to the general public. The social utility of this sand in the gears deterrence was always dubious, however, given that most purchases of shares of seasoned public companies occur in the open market, supported by the companys periodic filings (mainly on Forms 10-K, 10-Q and 8-K). If these disclosures are sufficient to level the playing field, then why would (post-IPO) buyers need registration, staff review, and a prospectus when the seller happens to be the company rather than another investor?

Applying this logic, a blue-ribbon advisory panel convened by the SEC and known as the Wallman Committee recommended in 1996 that the SEC deregulate the issuance


12. See Bernardo Bortolotti, William Megginson and Scott B. Smart, The Rise of Accelerated Seasoned Equity Underwritings, Journal of Applied Corporate Finance, Vol. 20 (2008).

the buyers in private placements of free-trading shares. For instance, the prospectus supplement filed by Orthovita, Inc. in July 2007 lists the buyers in its private placement of free-trading shares, a group that includes one natural person, one investment bank, and five mutual funds or hedge funds. A common clientele is not surprising since the same placement agents handle either type of deal.

Table 2 reports the distribution of deals by the delay before conversion, and does so separately for deals with and without registration rights. It takes longer to accomplish free-trading status without registration rights, as expected, but registration rights do not eliminate delay. The data in Table 2 show that quick registrations (in 90 days or less) rarely happen without registration rights. If you do not have a shelf in place but think a quick registration is feasible because your public disclosures are complete and you face a level playing field, you might as well grant registration rights and reap the benefit of a (slightly) lower discount.

Blockage DiscountsThe fact that three-quarters of all the common stock of U.S. public companies is held by institutional investors makes the possibility of blockage discounts implausible as a general matter. (A blockage discount at time of purchase anticipates that exiting the investment through retail sales will drive down the market price before the sale can be completed.) But since institutional investors (even small-cap mutual funds) avoid OTC stocks, blockage discounts are possible for these smallest of small-cap stocks. In theory, then, since OTC companies have been responsible for the lions share of all private placements of common stock, part of the average discount reported by past studies of restricted stock could represent a blockage discount akin to a DLOM. But the evidence for this discount, insofar as it assumes that there is just one buyer per deal, is highly questionable.

trading status obtains. The insensitivity of average discounts to the length of the regulatory holding period suggests that data originating in the distant past when the regula-tory restriction was most severe offer no real advantage over modern data, whereas modern data offer the considerable advantage of timeliness.

Free-Trading Shares Technically, it is the issuance and resale of shares that is regis-tered. Because the shares themselves are not, I use the term free-trading shares rather than registered shares. Private placements of free-trading shares take place after a shelf registra-tion, a type available since 1982. Although some underwritten equity offerings resemble private placements,12 my sample of private placements of free-trading shares does not include any underwritten offerings. A shelf-registration differs in that it authorizes generic, future issuances rather than one specific, immediate issuance. For example, IMAX Corp. stated in its shelf filing in 2009 that: We may offer and sell, from time to time in one or more offerings, any combination of debt and equity securities that we describe in this prospectus having an aggregate initial offering price of up to $250 million.

So, once the SEC has declared effective a shelf registra-tion that includes boilerplate language describing the legal attributes of the registrants common stock and sets a dollar maximum, the registrant may sell free-trading shares in subsequent private placements without further regulatory permission or review. Being generic, a shelf-registration filing does not include deal-specific information. That gets disclosed in a prospectus supplement filed later, at time of sale, which can be several years later.

While the buyers of private placements of free-trading shares need not be accredited investors, they mostly are. The same sort of institutions and wealthy individuals that are the buyers in private placements of restricted stock appear to be

All Deals With Registration Rights Without Registration Rights

N % N % N %

Free Trading Immediately 307 28 0 0 0 0

Free Trading in 9 to 90 Days 198 18 194 42 4 1



All Deals 1,103 100 461 100 335 100

Table 2 Distribution of Delay Before Free-Trading Status Occurs, Classified by Whether the Buyers Receive Registration Rights


13. I was able to identify the exact number of buyers in 57% of all deals, either from a count reported in the initial disclosure on Form 8-K or in a follow-on registration state-ment where the buyers in the earlier placement are all named and thus countable. Also, where no specific count of buyers is provided, disclosure documents nevertheless refer to the buyers using the singular or plural tense.

as a percentage of prior shares outstanding) as an explanatory variable in my multiple regression, but not as a measure of potential blockage. I see it instead as a measure of potential dilution. Dilution will depend partly on how many shares are sold and partly on the size of the discount. But since one cannot use the discount itself to construct an explana-tory variable, I settled for a measure of potential rather than actual dilution.

While dilution is a better explanation for why discounts might depend on deal size, it is not a simple explanation. One would not expect discounts to depend on potential dilution if (1) the size of the deal is disclosed before the time when the discount is measured and (2) the market price quickly and fully reflects the mix of public information. Under these conditions, the potential for dilution should be reflected equally in the market price and the deal price and net out the calculated discount. I was unwilling to assume that these two conditions hold routinely in my data. Also, there may be other explanations besides blockage or dilution.

Why Regression Analysis?When financial economists study private-placement discounts, it is standard practice to use multiple regression analysis to estimate the effect of the regulatory restriction as a differen-tial discount. In contrast, when business-valuation analysts produce restricted-stock studies, it has been standard practice to limit the sample to restricted stock in order to sustain the assumption that the regulatory restriction is the sole cause of the average discount and the associated assumption that the unconditional average discount constitutes a valid estimate of the DLOM. Moreover, with this setup, one can further maintain that every variable that correlates with discounts necessarily tells a story about the DLOM. This is all problem-

Most private placements of common stock are sold to groups of accredited investors who are assembled by private-placement agents for finders fees. The individual members of the groups seem to be unrelated except in the sense that some participating mutual or hedge funds have a common money manager. It is unlikely that group members would eventually sell in unison. They are unlikely to seek to exit their invest-ments at the same time, and unlikely to conspire to flood the market with coordinated sales if doing so will reduce their sale proceeds.

Table 3 compares the average number of shares sold per deal to the average number of shares sold per buyer.13 Each is expressed as a percentage of the number of pre-sale shares outstanding and, alternatively, as a percentage of the trading volume in the market during the last full calendar month before the close of the sale.

Private placements were sold to a single buyer just 18% of the time (201 of 1,103). The size of the macro-block has actually been an inverse proxy for the size of the typical mini-block in that the smallest mini-blocks are associated with the largest macro-blocks. In other words, as the number of shares sold increases from one deal to the next, the number of buyers tends to increase even more. In the extreme, in cases with 10 or more buyers, the total shares sold averaged 22.1% of prior shares outstanding while the typical block sold averaged 0.9% of prior shares outstanding. Similarly, when there were 10 or more buyers, the total shares sold typically amounted to over 200% of one months volume while the typical mini-block amounted to 9% of one months volume. A discrepancy this great means that any correlation between discounts and the overall size of the deal, the macro-block, cannot be indicative of a blockage discount.

I nevertheless included the shares sold per deal (expressed

Buyers Per Deal:

Number of Deals

As a % of Shares Outstanding As a % of 1 Months Volume

Mean Per Deal

MeanPer Buyer

Median Per Deal

Median Per Buyer

1 201 7.9 7.9 104 104

2 9 183 13.2 3.6 214 55

10 or more 242 22.1 0.9 201 9

N/A, but >1 477 15.1 182

All Deals 1,103 14.9 176

Table 3 Shares Sold Per Deal versus Shares Sold Per Buyer

Classified by number of buyers, alternatively expressed as a percentage of shares outstanding and as a percentage of trading volume during the calendar month before the deal closed.


14. For a primer on multiple regression analysis, see Daniel Rubinfeld, Reference Guide on Multiple Regression in Reference Manual on Scientific Evidence, 2nd Edition, 2000, Federal Judicial Center. (A 3rd edition is forthcoming.)

15. Registration rights often oblige the issuer to use its best efforts or commer-cially reasonable efforts to cause a registration statement to be declared effective by the SEC. A registration-rights agreement can be difficult to enforce insofar as issuers statu-tory obligations regarding investor protection trump any obligation arising under a private contract. The version of the registration-rights agreement with teeth specifies liquidating damages that the issuer must pay at recurring intervals, regardless of effort or feasibility, for as long as a timely registration is not accomplished.

filings. Sales of restricted stock in material amount are disclosed on Form 8-K. While some smaller deals are disclosed only on Forms 10-K or 10-Q (which I included when I happened upon them), my sample came mostly from 8-K filings. Private placements of free-trading shares are disclosed differently in prospectus supplements. Finally, conversions of restricted stock into free-trading shares are disclosed in registration state-ments filed after the sale. These SEC filings generally disclose whether any buyer is an affiliate of the company and whether buyers receive registration rights.15

I excluded private placements of common stock for any of the following reasons:

grossproceedsarebelow$100,000; thedealpriceorthemarketpriceisbelow$0.10per

share; sharesaresoldforconsiderationotherthanimmediate

cash; sharesaresoldinapackagewithwarrantsorother

securities; additionalsharesmightultimatelybedeliverabledue

to a make-good provision; thesharesareissueduponexerciseofanoptionto

buy; thesharesareissuedpursuanttoastandbyequityline

atic to the extent that discounts are caused by factors other than the regulatory restriction.

One reason that multiple regression analysis is so perva-sive in economic research is that the estimated coefficient for any one explanatory variable is supposed to measure the separate effect of that factor, after controlling for effects that are statistically attributable to the other explanatory variables included in the analysis.14 This multivariate capabil-ity addresses a problem with bivariate analyses, where variable X proxies for variable Y and the separate effect of X on Z, if any, is revealed only after controlling for the effect of Y on Z. Multiple regression analysis is the recommended method in this situation in part because it allows one to control for many different Ys at once. Accordingly, the purpose of regression analysis in the present study is to isolate the separate/direct effect of the regulatory restriction on the average discount in private placements after controlling for other determinants.

The Data for My Study I analyzed 1,103 private placements of common stock that closed over the seven-year period from January 1, 2004 through December 30, 2010. These deals were completed by 724 different companies. I found these private placements using various keyword searches of Bloombergs archive of SEC

Restricted Stock Free-Trading Shares All DealsAttribute: Mean Median Mean Median Mean Median

Market Capitalization 177.0 66.3 275.8 160.2 204.5 93.8

Total Assets 201.0 16.9 202.8 50.5 201.5 27.7

Cash & Short-Term Investments 13.2 2.2 28.4 16.8 17.5 4.1

Revenue (last 12 months) 141.4 5.2 281.5 9.4 180.4 6.4

Net Income (last 12 months) -7.0 -3.0 -21.0 -14.9 -10.9 -4.6

Shares Sold as a % of Prior Shares 16.0% 9.4% 12.4% 11.6% 15.0% 10.1%

Gross Proceeds of Sale 19.4 4.1 23.9 16.5 20.7 7.0

Deal Price Per Share 5.39 1.78 7.10 4.50 5.87 2.50

Change in Stock Price Over Prior 30 Days 13.8% 2.5% 2.8% -1.6% 10.7% 1.5%

Days Delay Before Free Trading 185 183 0 0

Fraction with Net Income < 0 79.8% 81.1% 80.1%

Fraction with Revenue = 0 21.2% 15.3% 19.6%

Fraction OTC 54.8% 3.9% 40.6%

Fraction with Deal Price


16. In a few instances, insiders participated as buyers but were made to pay a higher price than the other buyers (generally paying the market price without discount). In these several instances, I include the deal but only insofar as it relates to the unaffiliated buy-ers.

17. Discounts Involved in Purchases of Common Stock (1996-1969), Institutional Investor Study Report of the Securities and Exchange Commission, H.R. Doc. N.64, part 5, 92nd Cong., 1st Session, 1971, 2444-2456.

The scarcity of large, well-known companies in this sample is not surprising since such companies have operating cash flow, ready access to debt financing, and correspondingly less need for external equity financing. Consistent with this, the largest companies in the sample tend to be master limited partnerships and real estate investment trusts. Of the 20 companies with the largest market capitalizations, half are MLPs or REITs. For tax reasons, these entities pay out most of their earnings as dividends or partnership distributions, and consequently resemble smaller, growth companies in their reliance on exter-nal financing to fund new projects and expansions.

The smallest companies are usually excluded from studies of private-placement discounts, albeit indirectly by excluding those with stock prices below $1 or $2 per share. Discounts are correlated with OTC status, and only OTC companies (and fallen angels) trade at stock prices this low. To have an influential explanatory variable like OTC status effectively serve double duty as a sample-selection criterion introduces an unneeded complication. My sample includes companies with stock prices as low as $0.10 per share (but they must trade on the day of the close, which excludes quite a few OTC companies), and I then controlled for OTC status in my regression analysis.

In sum, although my sample is large, it is unrepresentative of the population of all companies. Most of the companies that have done private placements of common stock are smaller, cash-burning growth companies. Private-placement companies are especially notable for the prevalence and size of their losses in the year before the deal. Finally, the largest companies in my sample (measured by market capitalization) are dispropor-tionately MLPs or REITs. While MLPs and REITs comprise just 46 (or 4%) of all the deals in this sample and thus have little effect on the regression estimates reported below, these companies comprise half of the largest 20 companies in the sample. Accordingly, the very largest companies that do these deals are not especially representative either.

Regression Model The dependent variable in the regression analysis is the private-placement discount, which compares the per-share deal price to the prevailing market price. In calculating the discount, I measured the prevailing market price as the volume-weighted average price (VWAP) on the day the deal closes. The discount is the difference between the deal and market prices expressed as a percentage of the market price, which has a positive value when the deal price is below the market price.

In its Institutional Investor Study Report published in 1971,17 the SEC found that restricted-stock discounts were

that gives the company the right to put shares to the purchaser periodically at a formulaic price;

thesaleconstitutesachange-in-controltransaction; thebuyergroupincludesanofficer,directororaffiliate

of the selling company;16 thebuyerisacompanythatisastrategicpartnerofthe

selling company; thesellingcompanyisabank;or thesellingcompanysstockdoesnottradeontheday

the sale closes.The common stock sold in private placements is often

packaged with warrants (a right to buy more shares at a set price over, typically, five years). Warrant-sweetened deals are more frequent than are stock-only deals. I followed standard practice and excluded sweetened deals because there is not a contemporaneous trading price for the warrants, and thus no market price for the package (or unit) of shares and warrants that a discount can be calculated against. In the alterna-tive, one could venture to use an option-pricing formula to value the warrant component of the package, but this would produce a benchmark price that is based in part on a level-3 input and not solely on observed market values, meaning the resulting estimate of the DLOM would seem to fall short of the fair-market-value standard of value. In any event, stock-only deals are plentiful.

Table 4 shows some of the attributes of the deals and the companies in my sample. The real eye-opener here is that 80% of the companies report negative net income over the last four quarters before the deal closes, with the average loss being $10.9 million. Losses are equally frequent for the companies that sell free-trading shares and restricted stock, but the average loss is three times greater among the compa-nies that sell free-trading shares ($21.0 million) compared to those that sell restricted stock ($7.0 million).

The busiest of the seven years was 2007, with 21% of all deals, while the slowest years were 2008 and 2009, each with 11% of the total. Pharmaceutical companies accounted for 19% of all deals, oil & gas companies 14%, manufactur-ers 10%, medical technology 8%, non-medical technology 7%, and mining companies 5%. Smaller public companies predominate. Of all deals, 5% were done by NYSE companies, 13% by Amex companies, 30% by NASDAQ Global Market companies (regular Nasdaq companies), 11% by NASDAQ Capital Market companies (the junior tier) and 41% by OTC companies (all those not NYSE, Amex or NASDAQ). Compa-nies that pay cash dividends comprise 6% of the sample. As previously noted in the literature, the typical company that sells common stock in a private placement has been a compar-atively small, cash-burning growth company.


18. I calculate market capitalization as pre-deal shares outstanding times an average of two market prices: the VWAP for the day 30 calendar days before the close and the VWAP on the day of the close.

before the sale, expressed as a percentage of market capitaliza-tion;18

anindicatorvariablefornegativenetincome; salesrevenueoverthelastfourquartersbeforethesale,

expressed as a percentage of market capitalization; anindicatorvariableforzerorevenue; holdingsofcash,marketablesecuritiesandshort-

term investments last reported before the sale, expressed as a percentage of market capitalization.

Buyer SkepticismThe sophisticated buyers in private placements may demand a discount from the trading price because of skepticism about that benchmark price. These variables include:

anindicatorvariableforOTCcompanies; anindicatorvariableforNASDAQ Capital Market

companies (the junior tier of NASDAQ and the next closest category to OTC status);

thepercentagechangeinthemarketpriceoverthe

most dependent on (1) net income, (2) sales, (3) OTC status, and (4) registration rights. My explanatory variables were inspired by these four. Because my data are numerous, however, I could employ a comparatively large number of explanatory variables. I used 15 explanatory variables: five as indicators of solvency (more or less); three for buyer skepti-cism about current prices; one for potential dilution; one for deals done possibly not at arms length; and five to cover aspects of the regulatory restriction on marketability.

Ten of the 15 explanatory variables are simple indicator variables (sometimes called dummy variables). An indicator variable is a construct that equals one when a given condi-tion prevails and zero otherwise. The included explanatory variables, and brief rationales, are as follows:

SolvencyLow solvency may weaken a companys bargaining position when negotiating a sale price. These variables include:

netincome(mostlylosses)overthelastfourquarters

Regression 1 Regression 2 Regression 3

Explanatory Variable:

Coefficient P-value Coefficient P-value Coefficient P-value

Intercept 6.281 0.000 4.075 0.017 3.938 0.021

Net Income as a % of Mkt. Cap. 0.045 0.000 0.045 0.000 0.044 0.000

Indicator for Net Income < 0 5.357 0.001 5.600 0.000 5.698 0.000

Revenue as a % of Mkt. Cap. -0.002 0.339 -0.002 0.271 -0.002 0.273

Indicator for Revenue = 0 4.915 0.001 4.991 0.001 5.186 0.001

Cash & STIs as a % of Mkt. Cap. -0.138 0.000 -0.130 0.000 -0.129 0.000

Indicator for OTC 13.961 0.000 11.575 0.000 11.842 0.000

Indicator for Junior Tier of Nasdaq 2.523 0.188 2.145 0.263 2.284 0.235

% Change in Market Price over 30 Days 0.107 0.000 0.105 0.000 0.105 0.000

Total Shares Sold as a % of Prior Shares 0.094 0.000 0.093 0.000 0.090 0.000

Indicator for One Buyer -8.834 0.000 -9.239 0.000 -9.147 0.000

Indicator for Restricted Stock Sold without Registration Rights

5.238 0.006

Indicator for Restricted Stock Sold with Registration Rights

3.464 0.021

Indicator for Free Trading in 990 Days 3.232 0.066



R-Square 0.270 0.276 0.276

Adjusted R-Square 0.264 0.268 0.268

Standard Error 18.96 18.90 18.91

Number of Observations 1,103 1,103 1,103

Table 5 Multiple Regression Analysis Dependent Variable is Percentage Private-Placement Discount


this size. It is conventional to accept a coefficient as being significantly different from zero if the P-value is at or below 0.05 or 0.10. These correspond to confidence levels of 95% and 90% (one minus the P-value, expressed as a percent).

Four of the five explanatory variables that are more or less related to company solvency (rows 2 through 6 of Table 5) are influential and statistically significant. Percentage discounts include a component of 5% to 6% if the company reports negative net income over the four quarters before the deal, and another 5% if the company is at a stage of development where it has yet to generate any revenue. That the coefficient estimate for net income (as a continuous variable) is positive may seem surprising at first, but it may seem less of a surprise when one considers (as reported in Table 4) that the losses of companies that sell free-trading shares (at generally lower discounts) are three times greater than the losses reported by those that sell restricted stock. A private placement may signal a faster-than-expected burn rate at the same time that it reveals that funding is now in hand to keep the company operating a while longer. But having said that, I dont claim to understand the role that pervasive losses (the cash-burn rate) play in determining private-placement discounts.

The coefficient for holdings of cash and short-term invest-ments is negative, which is consistent with intuition: The more cash on hand, the lower the discount. More cash on hand implies greater bargaining power, since the company is less desperate for funding to continue its operations. Thus one reward for better planning and more-deliberate fundraising is a lower discount.

Two of the three explanatory variables related to buyer skepticism about the validity or sustainability of the market price (against which the discount is calculated) are economi-cally and statistically significant. Statistically, the most significant explanatory variable (the one with the highest t-statistic) is the percentage change in the market price during the 30 calendar days before the closing date of the deal. The discount is approximately 1.1 percentage points greater for every ten percentage points of recent run up in the market price (and vice versa for a decline). Discounts are 11% to 14% greater for OTC companies, depending on the regression. Companies with stock listed in the junior tier of NASDAQ are the closest thing to OTC companies, but are not so close with respect to discounts and this variable explains little. Discounts are 2% higher for companies in this category.

The explanatory variable that covers the effect of potential dilution on discounts is the size of the deal (the macro-block) expressed as a percentage of pre-sale shares outstanding. Discounts are 0.9 percentage points greater for every ten percentage points of increase in the number of shares outstanding by virtue of the new shares that are sold. For example, if a firm with 100 shares issues 10 new shares, shares outstanding increase by ten percent and the discount increases by 0.9 percentage points.

30-calendar-day period ended the day of the close, measuring the market price by the VWAP for the day.

Potential for DilutionAs discussed in the earlier section on Blockage Discounts, this variable is calculated as the total number of shares sold expressed as a percentage of pre-sale shares outstanding.

Possibly Not at Arms LengthI excluded deals where the buyer is an affiliate of the company, insofar as that is disclosed, but disclosure of ulterior motives is inherently incomplete. Beyond that, companies may reveal positive inside information to select buyers, perhaps inappro-priately, and want to limit the number of recipients of this information. This variable is:

anindicatorvariablefordealssoldtoasinglebuyer.

Restricted MarketabilityI measured every aspect of the marketability restriction I could. These variables include:

anindicatorvariableforwhetherthesharesinitiallytake the form of restricted stock without registration rights;

an indicator variable forwhether the shares arerestricted stock with registration rights;

anindicatorvariableforrestrictedstockthatendsupconverting into free-trading shares within three months (1 to 90 days);

anindicatorvariableforrestrictedstockthatendsupconverting into free-trading shares in four to six months (91 to 183 days);

anindicatorvariableforrestrictedstockthatendsupconverting into free-trading shares in seven to twelve months (184 to 365 days).

For technical reasons (some of the indicator variables just cited are a linear combination of the others), all five of these cannot be included as explanatory variables in the same regression. I express certain accounting values as percentages of market capitalization because, so scaled, their explanatory power in the regression is much enhanced. The rationales for these explanatory variables are not all strong, as I err on the side of inclusion. What matters is that none of the included variables (and no omitted variable) be directly related to, or a significant proxy for, the regulatory restriction other than the five intended for that purpose.

Regression ResultsTable 5 summarizes the results of three formulations of multi-ple regression analysis. The estimated coefficients for most of the control variables are statistically significant, as would be expected in a sample as large as this. Statistical signifi-cance is reported in Table 5 as a P-value (there is one for each coefficient estimate), which tells you whether the estimated coefficient is significantly different from zero in a sample of


19. R-square is the fraction (ranging from zero to one) of the total variance in the dependent variable that is explained in a given regression. The adjusted R-square statis-tic differs from the raw R-square statistic in that the adjusted R-square increases only if the added explanatory variables improve the model more than would be expected by

chance. The validity of this final test does not depend on the accuracy of the estimated coefficients of the individual explanatory variables.

The coefficient estimate reported in Table 5 that is most relevant for the DLOM is the one (5.238) that appears in the column labeled coefficient under the heading Regression 2. After controlling for determinants of discounts unrelated to the regulatory restriction, the portion of the typical discount that can be tied directly to the regulatory restriction in its most severe form is thus 5.2%, which is significantly different from zero but much smaller than conventional DLOMs of 20% to 40%. As for the companion indicator variable, when the regulatory restriction is mitigated through a grant of registration rights that could serve to accelerate the conversion of the restricted stock into free-trading shares, discounts are 3.5% higher instead of 5.2% higher.

In Regression 3, the regulatory restriction is represented by the realized delay before free-trading status obtains. This information is not available to participants at the time of the deal, but these data may proxy for the expectations of the participants at the time of the deal. Discounts are 3.2% higher when conversion occurs within 90 days, 3.6% higher when conversion occurs within 91 to 183 days, and 5.6% higher in the remaining cases where restricted stock ends up converting into free-trading shares 184 to 365 days follow-ing the close. The last two of these estimates of the DLOM is significantly different from zero. Accordingly, discounts depend some, though not much, on the realized delay before the regulatory restriction is lifted.

As I explain below, data on the CD-Treasury yield spread imply a DLOM of 2.5%. Because the DLOM on the riskless asset can be calculated most directly, without need for multi-ple regression analysis, the interesting statistical test is not whether an estimate of the DLOM from a multiple regression differs from zero, but whether it differs from 2.5%. In other words, one concedes a DLOM of 2.5% and then asks of any additional data whether the concession is merited.

Of the two coefficient estimates in Regression 2 that relate to the regulatory restriction, even the higher of the two estimates, 5.2%, is not statistically significantly different from 2.5% (t-statistic of 1.44, P-value of 0.150). Likewise, the highest of the three estimates in Regression 3 is 5.6%, an estimate that is not statistically significantly different from 2.5% (t-statistic of 1.61, P-value of 0.110).

Finally, and most importantly for my conclusions, one can ask if the inclusion of the several explanatory variables related to the regulatory restriction on marketability adds to the overall explanatory power of the multiple regression analysis. The relevance of additional explanatory variables is established by comparing the adjusted R-square statistics (reported near the bottom of Table 5) of two alternative models.19

Discounts are around 9% lower when there is a single buyer. Some of this may be due to sweetheart deals (oddly, ones that favor existing shareholders, in contrast to friends and family allocations of underpriced IPOs). While I exclude deals known to be made with affiliated buyers, informal relationships are commonplace among the small companies that do private placements of common stock and informal relationships and ulterior motives are not necessarily disclosed. Also, as I noted earlier, lower discounts in single-buyer deals are consistent with a desire by companies that improperly leak positive inside information as part of a sales pitch to limit the number of recipients of such information to a single investor.

Regression 1 in Table 5 is the base regression, meaning that it excludes all of the explanatory variables related to the regulatory restriction. This formulation yields information about how much of the overall variance in discounts can be explained without any help from the explanatory variables related to the regulatory restriction.

Regression 2 includes the indicator variable for restricted stock sold without registration rights, along with the compan-ion indicator variable for restricted stock sold with registration rights. Because registration rights serve to mitigate the effects of the regulatory restriction, the estimated coefficient on the first of these two indicator variables (without registration rights) should reflect the effect of the regulatory restriction on discounts more fully than will the second indicator variable (with registration rights).

Chart 1 CD-Treasury Yield Spreads, Monthly from June 1998 through June 2011

1%

2%

3%

4%

5%

6%

7%

1% 2% 3% 4% 5% 6% 7%

Yiel

d on

5-Y

ear

CD

s

Yield on 5-Year Treasuries


20. Historical data on CD yields are available from mid-1998 for several different maturities, including the five-year CD. My source for Treasury yields is also Bloomberg, which offers a screen for a yield curve based on U.S. Treasury Actives from which the yield on a hypothetical security of exactly five years maturity can be obtained, as of any given date, via interpolation from the actual yields on that date on Treasury notes and bonds with remaining lives closest to five years. Because the time of day of the CD measure is ambiguous, I compare the CD yield on a given day to the average of the (close

of day) Treasury yields for that day and the preceding day. 21. See Susan Chaplinsky and Latha Ramchand, The Impact of SEC Rule 144A on

Corporate Debt Issuance by International Firms, The Journal of Business, Vol. 77 (2004).

22. See Yakov Amihud and Hiam Mendelson, Liquidity, the Value of the Firm, and Corporate Finance, Journal of Applied Corporate Finance, Vol. 20 (2008).

buildup method of finding a discount rate for use in a DCF valuation.

Equivalently, one can convert the CD-Treasury yield spread into a DLOM to be applied supplementally to the results of a core valuation methodology. An initial invest-ment of $97,500 in the average five-year CD would result in approximately the same ending balance (including reinvested interest) after five years as would an initial investment of $100,000 in a five-year Treasury security. So, a CD-Treasury yield spread of 0.5% implies a supplemental, non-redundant illiquidity discount, or DLOM, of 2.5% (since $97,500 is 2.5% lower than $100,000).

That the DLOM on the riskless asset approximates 2.5% leads to the conclusion that any discounting for lack of marketability beyond 2.5% constitutes a second round of discounting for risk (where the first round occurs in a DCF or similar valuation). While illiquidity and the risk of future cash flows are separate factors in valuation,22 redun-dant discounting represents a potential problem with any business valuation that includes a large DLOM. As discussed earlier, liquidity is highly correlated with company size, where size is already an important determinant of discount rates. So, while liquidity matters to valuation, the close association between liquidity and company size, along with the ample size premiums used in business valuations, mean that any supplemental DLOM in excess of 2.5% is likely to constitute redundant discounting.

That any DLOM in excess of 2.5% represents a second round of discounting for the risk of owning a private business frames the reliability issue. How confident can one be that a second round of discounting for risk is not redundant to the first? The evidence furnished by past restricted-stock studies provide a questionable basis for this practice.

ConclusionThe purpose of this study has been to determine if data on discounts in private placements of restricted stock imply a DLOM that is different from the DLOM on the riskless asset. This analysis is skeptical in the sense that it is not config-ured, as many past studies have been, to document what is being hypothesized and, perhaps to some degree, desired by some interested parties. Specifically, this study allocates to the DLOM only that portion of the restricted-stock discount that can be tied directly to restricted marketability. No portion is allocated to the DLOM by default or presumption.

This approach yields estimates of the DLOM that are no larger than 5.2% or 5.6%, which is consistent with some

The adjusted R-square statistics for Regression 2 and Regression 3 are both 0.268, which is remarkably close to the adjusted R-square of 0.264 for Regression 1, the base model with no explanatory variables related to the regula-tory restriction on marketability. That only one-quarter of the dispersion in discounts is explained by the regression analysis reflects the wide dispersion in private-placement discounts. That these adjusted R-square statistics are so close (0.268 versus 0.264) means that the several explanatory variables related to the regulatory restriction on marketability, consid-ered as a group, add almost nothing to the explanatory power of the base model.

DLOM on the Riskless AssetThe DLOM on the riskless asset can be calculated from the difference in yields between a five-year bank certificate of deposit (illiquid due to penalties for early withdrawal) versus a five-year U.S. treasury security (highly liquid). Here, the requisite calculations go beyond mere arithmetic only in that one must use an average of the yields on CDs offered by some sample of banks. Data on yields offered on CDs by various banks are compiled by bankrate.com, which reports averages that are available on the Bloomberg service.20

Chart 1 is a scatterplot that compares the yields on five-year bank CDs versus five-year U.S. Treasuries. It shows a CD-Treasury yield spread as of the last day of each month from June 1998 through June 2011. The CD-Treasury yield spread equals the CD yield minus the Treasury yield. It appears in the scatterplot as the distance from a given months dot to the diagonal line. A normal, positive yield spreadone that compensates for restricted marketabilitywill plot above the diagonal. The plot shows that yields on bank CDs tend to track Treasury yields less closely when five-year Treasury yields are high, and shows that the CD-Treasury spread is nearly always positive when the Treasury yield is below 5%.

Mainly, the CD-Treasury spread is just small. It averages an implausible -0.053% per year in the 26 months when the yield on 5-year Treasuries exceeded 5.0%, but still averages only 0.49% in the other 131 months. My conclusion from these data is that a typical CD-Treasury spread is no greater than 0.5%. A CD-Treasury yield spread of 0.5% is almost identical to the estimated yield spread of 0.49% between Rule 144A bonds (the fixed-income counterpart to restricted stock) and otherwise-comparable free-trading corporate bonds.21 Restricted bonds are typically issued with registra-tion rights. A yield spread of 0.5% could be included as an illiquidity premium in an implementation of the Ibbotson


tory restriction is the sole cause of discounting. Considerable research, some of it my own, suggests that regulatory restric-tion is not even the primary cause of discounting. And without this false assumption and its consequences, little of the average discount can be tied to the restricted nature of restricted stock.

Private-company status may merit a discount below what core valuation methods (such as DCF analysis) would indicate; indeed, it may even merit a double-digit discount. But any merited large discount is not primarily a discount for lack of marketability. Based on evidence from modern private placements of common stock, the DLOM is not reliably different from the DLOM on the riskless asset, or 2.5%.

robert comment is an Accredited Valuation Analyst who has taught finance at Johns Hopkins University, New York University, and the Univer-sity of Rochester. He served as the SECs Deputy Chief Economist under Chairman Arthur Levitt and has appeared as an expert witness in over 50

litigations. Dr. Comment can be reached at [email protected].

previous findings. Moreover, my estimates based on private-placement data are not statistically significantly different from the DLOM on the riskless asset of approximately 2.5%.

Valuations are a kind of expert opinion and, in the Supreme Courts Daubert decision governing the admissi-bility of expert opinion in court,23 there is no grandfather clause that permits continued reliance on methods that are seasoned but unreliable. In Daubert, the Supreme Court demoted general acceptance from being the sole requirement for the admissibility of expert opinion, as it had been for 70 years (under the Frye rule),24 to one of several items in a non-exclusive list of indicia of the ultimate goal of reliability. Moreover, the acceptability contemplated by the Supreme Court is that within the relevant scientific community.

Daubert requires reliability and fealty to the scien-tific method. In a follow-on decision in Kuhmo Tire,25 the Supreme Court told the many clinician critics of its Daubert ruling, in effect, to get with the program. Yet, proponents of double-digit DLOMs have overlooked scientific studies of private-placement discounts and continued to rely on evidence that depends on a false assumption: that the regula-

23. Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579 (1993). 24. Frye v. United States, 293 F. 1013 (D.C. Cir. 1923).25. Kumho Tire Co. v. Carmichael, 526 U.S. 137 (1999).

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comment - 2011 - revisiting the illiquidity discount for private companies, a skeptical

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