The Impact of Transfer Restrictions on Stock Prices

John D. Finnerty* Professor of Finance, Fordham University Managing Principal, Finnerty Economic Consulting, LLC

* The author would like to thank Larry Darby, Esq., Carl Felsenfeld, Esq., Peter Jurkat, Susan Long, Francis Longstaff, Haim Mozes, Gordon Phillips, Richard Smith, and Larry Thibodeau for helpful comments on earlier drafts and Jack Chen, Ernie de Rosa, Pablo Alfaro, Dina DiCenso, Elpida Tzilianos, Peter Eschmann, Alberto Chang, and Xiaoling Wang for research assistance. Financial support was provided by a summer research grant from the Fordham University Graduate School of Business. Earlier versions of the paper were presented at the annual meetings of the American Finance Association, the Financial Management Association, and the Southern Finance Association. JEL Classification: G1 Keywords: Transferability, Liquidity, Discount, Stock, Valuation Fordham University 113 West 60th Street New York, NY 10023 Tel: (212) 599-1640 Fax: (212) 599-1242 e-mail: [email protected] November 2007

The Impact of Transfer Restrictions on Stock Prices Abstract

Two sets of factors are significant in driving the private placement discount: those that explain the loss of option value implicit in the Rule 144 transfer restrictions as well as variables that proxy for a stock private placement’s information and equity ownership concentration effects. The announcement reaction is positive for traditional private placements but is negative for a private investment in public equity (PIPE), like a public offering announcement, when the firm commits to register the shares promptly. I develop an average-strike put option model for calculating the marketability discount and show that the model predicted discounts are consistent with the empirical predicted discounts when the observed discounts are adjusted for information and equity ownership effects. The average-strike put option model fits observed discounts better than the lookback put option model even when the shares are placed with related or strategic investors.

The Impact of Transfer Restrictions on Stock Prices

The impact of transfer and other marketability restrictions on stock prices continues to be of both theoretical and practical interest.

Numerous studies have documented significant

discounts in private placements of letter stock, which is not freely transferable because of resale restrictions imposed by Rule 144 under the Securities Act of 1933, averaging between 13 percent and 34 percent (SEC, 1971; Wruck, 1989; Silber, 1991; Hertzel and Smith, 1993; and Hertzel et al., 2002).1 The conventional wisdom in the business appraisal field is that the appropriate marketability discount is between 25 and 35 percent for a 2-year restriction period and between 15 and 25 percent for a 1-year restriction period (Longstaff, 1995).2 Longstaff (1995) obtains an upper bound on the marketability discount consistent with this range by modeling the value of marketability as the price of a lookback put option.3 The marketability hypothesis predicts that the entire discount on restricted shares at the time of issue is due to the Rule 144 transfer restrictions, and accordingly, the private placement discount is commonly referred to as a “marketability discount.” The information and equity ownership concentration hypotheses suggest that the private placement discount is driven by a separate set of factors (Wruck, 1989; Hertzel and Smith,1993). A private placement discount compensates private investors for their due diligence and monitoring costs, reflects the ownership-structure-change effects that result from the direct sale of common stock to a small group of sophisticated investors, and embodies the implied certification effect of the private placement announcement. Discounts of the magnitude observed in private placements of letter

stock (averaging 20 percent in their study and as much as 42 percent in others) would provide powerful incentives at the time of the private placement for firms to commit to register the shares promptly following the private sale if they were due solely to the Rule 144 restrictions. There are many large financial institutions with long-dated liabilities, such as life insurance companies and pension funds, that may be less concerned about liquidity than other investors, which brings into question whether investors should require such large discounts just for agreeing not to resell their shares in the public securities market for two years (Hertzel and Smith, 1993).4 A private resale market exists, and the options market provides hedging opportunities. When they allow for the information and equity ownership concentration effects that accompany a private placement, Hertzel and Smith (1993) find that the discount attributable to lack of registration is only 13.5 percent. Hence, transfer restrictions may be far less important than traditionally believed.

However, Longstaff (2001) solves the investor’s intertemporal portfolio choice

problem for an investor who is restricted to trading strategies of bounded variation and obtains values for the shadow cost of illiquidity that are consistent with the apparently large 35 percent discounts for lack of free transferability that have been measured empirically.

His model

demonstrates that such large discounts are sustainable in a rational model of investor behavior. Thus, a ‘private placement discount’ may reflect both a ‘marketability discount’ as well as information and equity ownership concentration effects, although the relative importance of the two sets of factors is unrersolved. This paper tests their relative importance in explaining private placement discounts. The paper is organized as follows. Section I shows that a firm should choose a private placement over a public offering when the private placement elicits the more favorable information effect or the old shareholders retain a greater percentage of the firm. Section II

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explains the legal restrictions on hedging that make the Rule 144 transfer restrictions costly. Section III describes the sample of private placements. Section IV shows that the initial private placement announcement and the completion announcement both convey useful information and that, in contrast to the findings in earlier studies, these announcements are negative signals when the stock’s recent trading momentum is positive and also when the firm precommits to register the shares promptly. Section V shows that the loss of timing flexibility inherent in the Rule 144 transfer restrictions and information/ownership concentration effects are both significant drivers of the private placement discount. Section VI models the marketability discount as the value of an average-strike put option. Section VII shows that the average-strike put option model is more consistent than the lookback put option model with observed private placement discounts. Section VIII furnishes evidence that the discounts predicted by the average-strike put option model are consistent with the empirical predicted discounts after adjusting for information and ownership structure effects. Section IX concludes. I. Why Firms Place Shares Privately Firms subject to asymmetric information issue common stock privately, rather than through a registered general cash offer, to finance an investment when (a) the net present value of the new information (about the firm and the investment) released to the market through the private placement exceeds what it costs the old shareholders to inform new shareholders about the firm’s true value and (b) the fraction of ownership the existing shareholders retain after a private placement (with full information disclosure) is greater than the fraction they would retain after a public offering. Privately placing stock can improve economic efficiency by eliminating the underinvestment problem (Myers and Majluf, 1984) when information asymmetries prevent investors from recognizing that a firm is undervalued (Hertzel and Smith, 1993). If a private

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placement signals undervaluation (Wruck, 1989) and a public offering signals overvaluation (Smith, 1986), old shareholders can be better off with a private placement even if the discounted price at which firms usually sell shares privately results in the old shareholders retaining a smaller percentage of the firm if the private placement’s information signal increases firm value sufficiently. The relative advantage of a private share placement under asymmetric information depends on the offering’s announcement effect and the fraction of the firm the old shareholders surrender. The change in the value of the old shareholders’ claim ( ∆VOld ) when new information with value ∆NPVPr ivate is released through the announcement of a private equity placement is5

∆VOld = ( PAfter − PBefore ) S Before = ∆NPVPr ivate − ( PAfter − POffer ) S Offer − T

(1)

where the price of the firm’s shares is PBefore before and PAfter after the private financing, the firm has S Before shares before the financing, new shareholders pay POffer per share to buy S Offer shares, and the firm pays T in placement expense (Wruck, 1989). A private equity placement increases the old shareholders’ claim when the net present value of the new information exceeds what it costs to inform new shareholders about the firm’s true value. An equation similar to (1) holds for the change in the old shareholders’ claim due to a public offering. I use a carat over V , P , S , and T to distinguish a public offering. To make the public and private alternatives comparable, both must raise the same net proceeds:

POffer S Offer − T = PˆOffer Sˆ Offer − Tˆ The old shareholders’ fractions of the firm’s equity following a private placement ( α ) or a public offering ( αˆ ) are:

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(2)

αˆ = Sˆ Before /( SˆOffer + S Before )

α = S Before /( S Offer + S Before )

(3)

Take the difference between the changes in the value of the old shareholders’ claim with a private placement and with a public offering and use equation (2) to simplify. A private placement increases the value of the old shareholders’ claim more than a public offering when ∆VOld − ∆VˆOld = ∆NPVPr ivate − ∆NPVPublic + (1 − 1 / α )[ PAfter S Before ] − (1 − 1 / αˆ )[ PˆAfter S Before ] = ∆NPVPr ivate − ∆NPV Public + (α − αˆ )V * > 0

(4)

V * is the post-offering value of the firm apart from any information effects. A shareholder-

wealth-maximizing firm should choose a private placement over a public offering to finance a positive-NPV investment only if the private placement leads to the greater increase in the wealth of the old shareholders. This can occur when the private placement (a) elicits the more favorable information effect (∆NPVPr ivate > ∆NPVPublic ) (Wruck, 1989) or (b) the old shareholders retain a greater percentage of the firm (α > αˆ ) (Hertzel and Smith, 1993). The old shareholders can be better off with a private placement even if a large private placement discount causes a greater decrease in their ownership percentage if the positive information effect of the private placement announcement is large enough. The positive information effect occurs only if the private placement announcement is a credible signal concerning the firm’s undervaluation. An overvalued firm could benefit by privately placing its shares, and the purchasers would not suffer a loss if they could resell the shares before the firm’s true value is revealed. Placing unregistered shares that cannot be resold to public investors without an effective registration statement and forcing purchasers to wait a significant length of time before the shares can be registered makes the signal credible. However, they also make the signal costly because private investors might require a discount to

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compensate for the loss of resale flexibility and also for the cost of gathering private information about the firm’s true value and how it might change during the Rule 144 holding period before they agree to purchase the shares. In the 1990s, investment bankers developed the PIPE (Private Investment in Public Equity) offering method as an alternative to the traditional private placement (Dresner and Kim, 2006). In a PIPE offering, a firm with publicly traded shares sells newly issued but unregistered securities, typically stock or debt convertible into stock, directly to accredited investors, usually hedge funds, in a private transaction.6 It usually requires the firm to file a shelf registration statement on Form S-3 as quickly as possible but in any event no later than between 10 and 45 days after closing and to use its best efforts to have it declared effective within 30 days after filing. Registration allows the investors to resell the shares in the public market well before the Rule 144 period expires. An overvalued firm can capitalize on its overvaluation by issuing a PIPE, which can be completed within about two to three weeks, as compared to months when a firm registers the shares beforehand using Form S-1 (Dresner and Kim, 2006). The registration commitment potentially undercuts the credibility of the private placement signal because registering overvalued shares might enable the purchasers to resell them before the firm’s true value is revealed. Thus, a PIPE is likely to have a negative signaling effect, like a public offering announcement, if investors perceive that the firm is using the PIPE method to capitalize on overpricing. I expect that the announcement effect of a PIPE will be less positive, and possibly negative, because of the negative implication of the registration commitment. II. Legal Restrictions on Hedging Privately Placed Common Stock

A traditional common stock private placement involves the direct sale of a fixed number

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of shares of common stock at a fixed price to accredited investors in compliance with Section 4(2) of the Securities Act of 1933 and Regulation D thereunder. The price may be fixed when a purchaser “circles” the number of shares it wants to buy at an agreed price, or it may be based on an agreed-upon discount to the closing price, or an average of recent closing prices, just prior to the closing. In the former case, the price may be adjusted downward right up to the closing date to attract enough investors to sell the entire offering. The shares are not freely transferable because they have not been registered with the SEC for public resale. Purchasers may receive limited rights to demand SEC registration of their shares (demand registration rights), request that their shares be included in a public stock offering (piggyback registration rights), or in the case of a PIPE, the firm’s commitment to register the shares as quickly as possible (mandatory registration right). The persistently large average private placement discounts found in empirical studies over more than 30 years raise an intriguing question: Why don’t arbitrageurs purchase restricted shares, hedge their price risk exposure, and capture the discount net of hedging costs as their profit? Such a strategy might not eliminate the marketability discount but it would reduce it to the cost of the hedge plus a return on the arbitrageur’s capital. A stockholder can hedge its price risk exposure in any one of at least three ways: (1) at the time it buys the restricted shares, it could purchase an average strike put option on an equal number of shares with an exercise price equal to the arithmetic average of the forward prices of the unrestricted shares and a time to expiration that matches the restriction period;7 (2) each day during the resale-restriction period, it could sell short against the box an equal fraction of the block of restricted shares it purchased; or (3) each day it could sell equity swaps covering an equal fraction of the block of restricted shares. The arbitrageur could exercise the put option or

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cover the short sales after the resale-restriction period expires using the previously restricted shares.8 There are legal impediments to all three hedging strategies for capturing the private placement discount. First, Rule 144 bars purchasing a put option or selling short against the box to hedge the price risk exposure in holding unregistered shares (Federal, 1980; Hicks, 1998; and SEC, 1997b). Specifically, Rule 144 prohibits an option holder who purchased the option before the Rule 144 resale-restriction period expires from exercising the put option after the resalerestriction period terminates and delivering the previously restricted shares to settle the option transaction.9 In addition, a short seller is prohibited from covering a short position entered into during the resale-restriction period – even when the short seller borrows registered shares to effect the short sale – by delivering the Rule 144 shares; this prohibition applies even if the short covering were to occur after the resale-restriction period expires (Federal, 1980; Hicks, 1998; and SEC, 1997b). In the SEC’s view, both hedging strategies are tantamount to the resale of unregistered shares during the resale-restriction period. The third strategy, equity swaps, also faces potential legal impediments. The equity swap market is generally limited to large-capitalization stocks.

Table 1 contains a summary

description of a sample of private placements of letter stock that took place between April 1, 1991 and February 1, 2005. The characteristics of this sample suggest that the public companies that issue unregistered shares through private placements tend to be smaller, relatively unprofitable NASDAQ or OTC companies. Equity swaps are unlikely to be available for such stocks. Even in those cases where an equity swap could be arranged, the prohibitions against hedging through option or short-sale transactions would imply that hedging through equity swaps might entail a significant risk that the SEC could successfully challenge the transaction.10

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Other hedging strategies are available that would appear to involve less legal risk. For example, the purchaser of restricted shares could purchase stock index put options or sell stock index futures short. Both hedging strategies expose the shareholder to basis risk. Nevertheless, to the extent such strategies reduce the price risk exposure inherent in purchasing unregistered shares, they could reduce the size of the discount that investors require when purchasing letter stock. Consequently, marketability discounts are likely smaller since the advent of the equity derivatives markets, which postdate the seminal SEC (1971) study, but at least some residual unhedged transfer restriction risk remains. III. Data and Methodology

I collected a sample of 244 private placements of letter stock that took place between April 1, 1991 and February 1, 2005. A.

Description of the Issuers I searched on 10kwizard.com using ‘private placement of common stock’ and similar key

words Wruck(1989) and Allen and Phillips(2000) employed. I identified an initial sample of 348 private placements by public U.S. firms that sold unregistered shares of common stock to U.S. investors for cash. I excluded private placements that were accompanied either by a non-U.S. offering (under Regulation S) or by the simultaneous sale of another class of securities (publicly or privately). I also excluded placements by regulated utilities and depository institutions. I searched the Dow Jones Interactive-Publications Library, the Bloomberg database of company announcements, and the Wall Street Journal Index to confirm the private placement information and identify the earliest announcement date for each offering. I checked each firm’s Form 10-K report for the year of the financing to obtain any reported details concerning the offering and the purchasers.

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Forty-eight of the firms in the sample conducted two or more private placements. In three cases, two private placements were less than three months apart. The second private placement was dropped from the sample. In all the other cases, the private placements were at least five months apart.

Investors will react to a contemporaneous significant corporate

announcement. I dropped from the sample the 14 issues with a significant corporate announcement that occurred within 5 trading days prior to and 10 trading days following the pricing announcement in order to isolate the information effect of the private placement announcement. I restricted the sample to public firms with at least three months of continuous historical stock prices in the Center for Research in Security Prices (CRSP) monthly stock files immediately prior to the announcement date. Eighty-seven issues had to be dropped from the sample because of insufficient historical trading prices or missing financial data.11 This left a reduced sample of 244 private placements. Table 1 describes the sample. Panel A reports that the public shares of the firms making 162 of the 244 placements, or roughly two-thirds of the sample, were listed on the NYSE, AMEX, or NASDAQ National Market. The remaining third were quoted in the NASDAQ Small Cap, OTC Bulletin Board, or Pink Sheet markets. As reported in Panel B, 52 of the private placements occurred before and the other 192 occurred after the SEC reduced the Rule 144 resale-restriction period to one year from two years on February 20, 1997 (SEC, 1997a). Also, 155 of the private placements, or roughly two-thirds of the sample, occurred during the five-year period 2000-2004. This period marks the development of the PIPE (Private Investment in Public Equity) market. Thirty-nine of the 244 private placements were priced at a premium to the closing price of the public shares the day immediately preceding the announced issue date. The listing breakdown and the chronolgical breakdown for the discounted placements are very

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similar to the respective breakdowns for the full sample. Panel C describes the issuers. The average market value of firm equity is $186.01 million (median market value $86.75 million). The average net income and cash flow from operations for the latest fiscal year immediately preceding the offering are both negative. Of the 244 issuers, 186 had negative net income and 120 had negative cash flow from operations for the latest fiscal year. Sixteen of the 58 with positive net income earned less than $1 million. These sample characteristics are consistent with Hertzel, Lemmon, Linck, and Rees’s (2002) findings that private equity issuers are generally small, young, and unprofitable, and tend to issue equity privately following periods of relatively poor operating performance. B.

Description of the Private Placements Table 2 describes the private placements. The average gross proceeds are $12.87 million

for the pre-February 1997 offerings and $17.12 million for the post-February 1997 offerings. I report gross proceeds because the private placement agent’s fee was disclosed publicly for only one quarter of the offerings. The average proceeds for my sample compare to average proceeds of $31.5 million for Wruck’s (1989) sample of private placements by (larger) exchange-listed firms, $4.3 million for Silber’s (1991) sample, and $11.4 million for Hertzel and Smith’s (1993) sample. In the private placements in my sample, the new shareholders purchase an average of 15 percent of the equity in the pre-February 1997 offerings and an average of 13 percent in the postFebruary 1997 offerings, which compares to 19.6 percent in Wruck (1989), 13.6 percent in Silber (1991), and 16.0 percent in Hertzel and Smith (1993). None of the differences between the pre-February 1997 and post-February 1997 means or medians is significant at conventional levels. C.

Discount for Lack of Marketability

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Panel B reports the mean and median percentage discount calculated with respect to the closing price on the last trading day immediately prior to the date the pricing terms of the private placement are announced and also with respect to the closing price 10 trading days after this announcement date. The discount off the prior day’s closing price is calculated: Discount (day prior) =

P-1 - P0 P-1

(5)

where P-1 is the closing price on the trading day immediately preceding the pricing announcement date and P0 is the private placement offering price.12 Because of evidence presented below that the market reacts to the information contained in the private placement announcement and that firms generally do not announce the private placement until it has been priced, I also calculate an alternate measure of the marketability discount with respect to the closing price 10 trading days after the pricing announcement date, Pt+10, which gives the market time to react fully to the offering. I adjust Pt+10 to reflect the change in the company’s stock price that would be expected to result from changes in market prices generally: ⎡ ⎞⎤ ⎛ SAP+10 P+10 ⎢1 - beta ⎜⎜ - 1⎟⎟⎥ - P0 ⎠⎦ ⎝ SAP-1 ⎣ Discount (10 days after) = ⎡ ⎞⎤ ⎛ SAP+10 P+10 ⎢1 - beta ⎜⎜ - 1⎟⎟⎥ ⎠⎦ ⎝ SAP-1 ⎣

(6)

where beta is the common stock beta calculated using the Scholes-Williams (1977) procedure. Comparing the results based on the discount calculation (6) to those based on (5) will shed light on the importance of the information and ownership structure effects that accompany a private placement. The private placement price is usually determined on the closing date (Dresner and Kim,

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2006; and Morrison & Foerster, 2006). Of the 244 private placements, 205 took place at a discount relative to the closing price the preceding trading day, and 202 of these were also at a discount when measured relative to the closing price of the stock 10 trading days later.13 The average Discount (day prior) is 21.00 percent for the pre-February 1997 offerings and 15.94 percent for the post-February 1997 offerings, and the average Discount (10 days after) is 21.61 percent for the pre-February 1997 offerings and 18.70 percent for the post-February 1997 offerings. For the discounted offerings, the average Discount (day prior) is 24.98 percent for the pre-February 1997 offerings and 22.47 percent for the post-February 1997 offerings, and the average Discount (10 days after) is 27.92 percent for the pre-February 1997 offerings and 27.17 percent for the post-February 1997 offerings. The discount should be lower after February 1997 because the SEC halved the resale-restriction period in February 1997. However, none of the differences is significant at conventional levels. This lack of significance may be due to the importance of information and ownership sructure effects, which were not directly affected by the change in regulation. The average discount is greater when measured relative to the market price 10 days after the pricing announcement, which suggests that the market price increases in response to the private placement announcement (Hertzel and Smith, 1993). However, none of the differences between the corresponding discounts for days -1 and +10 is statistically significant. The discounts in Table 2 compare to average discounts of 13.5 percent for unregistered sales reported by Wruck (1989), 33.75 percent for unregistered sales reported by Silber (1991), and 20.14 percent for all private placements reported by Hertzel and Smith (1993).14 As Wruck (1989), Silber (1991), and Hertzel and Smith (1993) have all observed, private placement discounts vary widely. In my sample, 68 of the private placements were made at relative-to-

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prior-day discounts that exceeded 25 percent (99 when the discount is measured relative to the closing price 10 days after), and 145 were at a relative-to-prior-day discount that exceeded 10 percent (163 when the discount is measured relative to the closing price 10 days after). IV. Market Reaction to the Announcements

The firm usually does not announce a private placement until it has received definitive purchase commitments from investors (Morrison & Foerster, 2006). Two announcements may occur in connection with a private placement: (1) an initial announcement of the firm’s intention to place shares of common stock privately and (2) the firm’s announcement that it has completed the offering, which furnishes the terms on which it sold the shares and may also identify the investors.

I refer to the former as the “offering announcement” and to the latter as the

“completion announcement.” I refer to the first announcement of either kind as the “initial announcement.” The private placement is supposed to remain confidential until the firm announces it. However, information is released privately as soon as the placement agent approaches prospective investors to offering shares. I find evidence that information does leak into the marketplace and affect the price of the firm’s stock. A.

Reaction to the Initial and Completion Announcements Sixty-eight issues were initially announced prior to the completion announcement. In the

other three-quarters of the private issues, the firm waited until the offering had been completed before making any public announcement.15 The offering announcement and the pricing announcement coincide in the other 176 private placements. A private placement is a bestefforts undertaking – in contrast to a general cash offer, which is usually underwritten – and there is no assurance beforehand that this effort will be successful. Investors will not know that

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the offering has succeeded until the firm announces its completion and provides the terms on which the shares were sold to investors. In none of the 68 cases did the offering announcement indicate the offering price; it was first disclosed in the completion announcement.

The

completion announcement also disclosed the number of shares sold. It identified institutional investors in 93 cases, strategic investors in 12 cases, and related investors (directors and 5% shareholders) in 23 cases. It also provided the private placement agent’s fee in 23 cases. Thus, both the offering announcement (when one occurs) and the completion announcement may contain useful information.

However, if a private placement announcement signals

management’s belief that the firm’s stock is undervalued, investors should react more strongly to the offering announcement even though there is no assurance the private placement will be successful. The event study results support this hypothesis. Table 3 reports average and median cumulative abnormal returns (CARs) and the percentage of positive CARs around the private placement announcements for the 244 private placements. The abnormal daily returns are calculated using the market model and the ScholesWilliams (1977) procedure to estimate beta.16 I used the CRSP value-weighted index of all NYSE, AMEX, and NASDAQ stocks as the proxy for the market portfolio. Percent positive is the percentage of positive CARs. The comparison period extends from 120 trading days prior through 21 trading days prior to the date the firm first publicly announces the private placement. Panel A reports the market impact of the initial announcement. Six of the eight mean CARs are positive but only two of the median CARs are positive and only two of the % Positive exceed 50 percent. Three of the mean CARs and two of the median CARs are significant at the 10 percent level or better based on a one-tailed test. The mean CAR for (-10, 10) is 5.87%, which is significant at the 1 percent level. The median CAR for (-10,10) is significant at the 5

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percent level, and more than 50 percent of the (-10,10) CARs are positive. These results are generally consistent with those of Wruck (1989), Hertzel and Smith (1993), and Hertzel, Lemmon, Linck, and Rees (2002).17 Panel B reports the market impact of the completion announcement. The results are very similar to those for the initial announcement reported in Panel A, although the mean and median CARs and % Positive are greater for all windows except (-10, 0), (-5, 0), and (-3, 0) in Panel A than in Panel B. The initial announcement appears to have a slightly stronger market impact. The positive mean CAR for (-10, 0), which is greater than the mean CARs for (-5, 0) and (-3, 0), coupled with similar patterns for the median CARs and % Positive in Panels A and B also suggest an information effect. The pre-announcement positive CARs may reflect the effect of the pre-announcement marketing of the private placement by firms (or their investment bankers) that refrain from making an announcement (as with 176 of the 244 issues in the sample) until the shares have been successfully placed. To test whether the initial announcement has a stronger market impact, I performed separate tests of the market reaction to the 68 separate offering and completion announcements. I report these results in Panels C and D. Any conclusions are tentative due to the small sample size. Nevertheless, a comparison of the results in Panels C and D is striking. All of the mean CARs and seven of the median CARs are negative and none of the % Positive exceeds 50 percent in Panel C. The seven negative median CARs are all statistically significant, four of them at the 5 percent level. All of the mean and median CARs are negative and none of the % Positive exceeds 47.06 percent in Panel D. Six of the median CARs are significant at the 5 percent level and one at the 10 percent level. Three of the % Positive are significantly less than 50 percent at the 1 percent level, and two are significant at the 5 percent level in Panel D

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whereas three of the % Positive are statistically significant, all at the 5 percent level, in Panel C. The negative market reaction is surprising in light of previous studies that have found a positive reaction to the private placement announcement. The initial announcement and the pricing announcement both provide useful information to investors. Finally, in Panel E, the impact of the coincidental announcement of the offering and its completion is very similar to the impact of the initial announcement reported in Panel A. The mean CAR is greater for every window in Panel E, the median CAR is greater for every window except (-1, 1), and % Positive is greater for every window except (-1, 1), although many of the differences are slight. The greater number of positive CARs that are significant at the 5 percent level or better coupled with the sole % Positive that is significantly greater than 50 percent in Panel E may reflect a favorable certification effect that can accompany the successful completion of a common stock private placement. A tendency for issuers to wait until the terms of the private placement have been negotiated before announcing the new issue could explain why the mean CARs are significant at the 5 percent level for (-10, 0) in Panel E and at the 10 percent level in Panel B while the percentage of positive CARs is greater for this window than for all the other pre-announcement periods in every panel. The issuer’s intention to place common stock privately becomes known to investors as soon as the firm commences the offering. Prospective purchasers, as well as other market participants, can be expected to react to the firm’s attempt to sell common stock as soon as this information becomes available in the market place. If so, then the market’s reaction to the offering may already have been incorporated into the firm’s common stock price before the initial announcement occurs when the offering announcement and the completion announcement coincide.

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B.

Momentum Effect Hertzel et al. (2002) find that firms that privately place stock experience significant stock

price appreciation just prior to the offering despite poor historical operating performance. The significantly negative median CAR and % Positive significantly less than 50 percent for (-1, 0) in all five panels, and in particular the overwhelmingly negative mean and median CARs in Panels C and D, suggest that a negative reaction to the announcement occurs in more than 50 percent of the cases. One of the advantages of a PIPE as compared to a registered public offering is timing. The firm does not have to wait for the SEC to declare its registration statement effective.

However, if the firm initiates a PIPE because it believes its stock is

overpriced and investors detect the overvaluation, the market can be expected to react negatively to the announcement of the private issue. Announcing a PIPE may signal overvaluation if the firm’s stock has recently increased in price.

In that case, the market reaction to the

announcement will be the opposite of the positive reaction that prior studies have documented. The sample was partitioned into those placements for which the comparison period (-120, -21) CAR was positive (referred to as positive momentum stocks) and those for which it was negative (negative momentum stocks), and the announcement effects were tested. The results are reported in Table 4. For the full sample, all the mean CARs around the initial announcement are negative for the positive momentum stocks whereas seven of the mean CARs are positive for the negative momentum stocks. Two of the negative mean CARs for the positive momentum stocks are significant at the 5 percent level and two are significant at the 10 percent level. Four of the positive mean CARs for the negative momentum stocks are significant at the 1 percent level, one is significant at the 5 percent level, and one is significant at the 10 percent level. For all eight windows, the mean CAR is greater for the negative momentum stocks. Four of these

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differences are significant at the 1 percent level, two at the 5 percent level, and one at the 10 percent level. Similar results hold for the completion announcement for the full sample (Panel B) and for the 176 private placements with no pre announcement (Panel E). Forty-two of the 68 private placements in Panel C and 43 in Panel D involved positive momentum stocks. All but one of the mean CARs are negative for the positive momentum stocks in Panels C and D. Six of these are significant at the 10 percent level in Panel C, and two are significant at the 1 percent level, three at the 5 percent level, and one at the 10 percent level in Panel D. Four of the mean CARs are positive for the negative momentum stocks in Panel C, although none is statistically significant, and seven are positive in Panel D, although only one is statistically significant. In every window but one in these panels, the mean CAR for the negative momentum stocks is greater than the mean CAR for the positive momentum stocks. One of these differences is significant at the 1 percent level, four at the 5 percent level, and two at the 10 percent level. These results suggest that the negative mean and median CARs in Panels C and D in Table 3 are at least partly due to the relatively high proportion of positive momentum stocks. Table 4 suggests that the initial announcement signals firm management’s confidence in the firm’s prospects and its willingness to open the firm’s books to the scrutiny of outside investors, and the completion announcement conveys positive information because it signals that private investors have implicitly certified the firm by agreeing to invest after completing their due diligence, notwithstanding a previous drop in share price. However, there is a cost to announcing a common stock private placement when the firm’s stock has recently increased in price. The announcement of a private issue in that case conveys negative information because it signals possible overvaluation, as with the announcement of a public offering.

The stock

market’s reaction to private placement announcements is thus more complex than prior studies

19

have suggested. C.

PIPEs with Quick Registration of the Shares An overvalued firm can issue a PIPE, quickly register the shares for public resale, and

thereby enable the purchasers to resell the PIPE shares before the true value of the firm is revealed. I expect that a commitment to register the shares will lead to a smaller discount because investors will expect that they will be able to sell their shares sooner than the end of the Rule 144 restriction period. However, investors will also recognize the agency cost inherent in the firm’s granting of registration rights. First, I test for the impact of the commitment to register the shares on the size of the discount. Then I test the difference in signaling effect between private stock placements that are registered contemporaneously and those that are not. I expect those that are registered contemporaneously will exhibit a negative information effect, just like a public common stock new issue, and that those that are not registered as quickly will exhibit a positive, or at least less negative, announcement effect. Hertzel and Smith (1993) find that the lack of registration accounts for about two-thirds (13.5 percent) of the 20.14 percent average discount in their sample. The PIPEs market has developed since their study. PIPE investors usually require the firm to use its best efforts to register the private placement shares as quickly as possible (Morrison & Foerster, 2006). This commitment shortens the expected holding period, so long as it is credible, which should reduce the discount.18 I checked the private placement announcements and the firms’ subsequent Form 10-K reports to search for mention of a commitment to register the private placement shares. Of the 205 discounted private placements, 23 of the firms announced that they had granted the purchasers registration rights, and 127 of the firms registered the shares before the end of the Rule 144 holding period. The firm’s commitment to register the shares is only a best-efforts

20

commitment, and even then there is no assurance that the SEC will declare the registration statement effective. I also investigated how long it took firms to register the shares. Table 5 quantifies the impact on the discount of (the issuer’s commitment to) share registration. It reports that 65 of the private placements were registered within 30 days of the completion announcement, 15 were registered within the next 30 days (all within the first 15 days), 11 more within the following 30 days, and 36 thereafter but before the end of the Rule 144 holding period.19 Thus, about two-thirds of the discounted placements are registered within the Rule 144 restriction period. The discount is smaller for the 30-day registration period than for the more-than-90-day registration period except for strategic investors, although the sample sizes are too small to produce reliable results. The average discount is less than half as large, and the differences are significant at the 5 percent level, when the shares are registered within 30 days than when they are registered more than 90 days later or not at all. The differences appear to be even greater when the shares are purchased by strategic investors or related investors (such as insiders), but the small sample sizes prevent definitive conclusions for these groups. Table 6 investigates the stock market’s reaction to the announcement of a stock private placement when the firm commits to register the stock promptly. I compare the announcement effect when the firm registers the stock within 30 days to the reaction when the stock is not registered within 90 days. Seven of the mean CARs are negative when the stock is registered within 30 days but five are positive when they are not registered within 90 days. The mean and median CARs are significantly negative at the 5 percent level and the percentage of positive reactions is significantly less than 50 percent at the 5 percent level in three cases, (-5, 0), (-3, 0), and (-1, 0) when the firm registers the shares within 30 days. All eight mean CARs are smaller when the shares are registered within 30 days, although none of the differences is significant at

21

the 10 percent level. The mean difference in reaction to the commitment to register is -4.29 percent over (-10, 10) and -1.55 percent over (-5, 5).

The evidence is somewhat mixed,

however, because the difference in median CARs, while negative for all the pre-announcement periods, is insignificantly positive when the post-announcement period is included in the comparisons. But overall the results suggest that investors recognize that PIPEs have agency effects similar to a public offering when the firm precommits to register the shares promptly. V. Transfer Restrictions and Information and Ownership Concentration Effects

Transfer restrictions cause a loss of timing flexibility, which imposes a cost in the form of foregone put option value (Longstaff, 1995, 2001); Kahl, Liu, and Longstaff, 2003). Wruck (1989), Hetzel and Smith (1993), Allen and Phillips (2000), and Hertzel et al. (2002) furnish empirical evidence that information and ownership structure effects are also responsible for the private placement discount. Transfer restrictions can explain a marketability discount but not a premium. There were 39 private placements (16 percent of the sample) in which the firm sold stock at a premium. Hertzel and Smith (1993) report eight premiums greater than 10 percent in their sample, so it is a recurring phenomenon. In some cases, I found that the firm had agreed to price the new issue based on a formula consisting of recent market prices for the stock. An historical average can lead to a premium price, even when the average is discounted, if the firm’s stock has large negative momentum leading up to the offering.

This section performs a cross-sectional

regression analysis to test the relative importance of the transfer restrictions and the information/ownership effects in explaining the size of the discount in the 205 discounted private placements. I leave it to future research to determine what factors account for the premium. A.

Proxies for the Impact of Transfer Restrictions

22

Discount (day prior), the dependent variable, measures the percentage discount relative to the closing market price of the issuer’s registered stock on the trading day immediately preceding the completion announcement date, which is the market price that is usually used as the basis for pricing privately placed shares (Dresner and Kim, 2006). I also ran the regressions using Discount (10 days after) as the dependent variable to give the market time to adjust fully to the private placement announcement’s information effect.20 Longstaff (1995) models the marketability discount as a lookback put option whose value depends on stock volatility, dividend yield, time to expiration of the transfer restrictions , and the riskless interest rate.21 Volatility is the annualized standard deviation of the total return on the issuer’s common stock for the period ending on the last trading day immediately preceding the initial announcement date. Options are valued based on implied volatilities (Hull and Suo, 2002).

Since only 35 of the stocks had traded stock options, I estimated each stock’s implied

future volatility using the GARCH model (Bollerslev, 1986). I restricted the private placement sample to firms with at least three months of historical stock prices, but I used up to one year’s historical stock prices if those data were available.22 In 90 cases, the estimated implied volatility exceeded 90 percent. I rescaled estimated volatilities that exceed 90 percent to lie between 90 percent and 120 percent because option market participants discount very high volatilities estimated from historical share prices when choosing the volatility parameter.23

I interact

volatility with the length of the Rule 144 restriction period ( T ) to capture the interdependence between T and Volatility. Volatility x

T is used with T = 2 up to February 1997 and T = 1

thereafter. I used a second proxy to capture another dimension of the timing effect of the transfer restrictions (Time). Rule 144 imposed a minimum two-year restriction period prior to February

23

1997 and a minimum one-year restriction period thereafter. After the initial restriction period, the number of shares that can be sold during any three-month period is limited to the lesser of (1) the average weekly trading volume during the four calendar weeks immediately preceding the filing with the SEC of Form 144 indicating the holder’s intention to sell and (2) one percent of the number of outstanding shares. Time captures this second timing effect. Even when the firm commits to register the shares promptly, the stock’s trading volume will limit the investors’ ability to dispose of the registered shares. I use the ratio of the number of shares offered to the common stock’s trading volume during the three-month period ending on the last trading day immediately preceding the initial announcement date as a proxy for Time. Because of Rule 144’s minimum restriction period, I use the two-year Treasury yield prior to February 1997 and the one-year Treasury yield thereafter as of the pricing announcement date as the riskless interest rate (Rate). The stock’s dividend yield (Yield) is the annualized dividend yield based on the most recently declared cash dividend as of the completion announcement date and the closing price of the registered shares on the last trading day immediately preceding that date. Only 12 of the firms had declared a cash dividend within the prior 12 months. The discount should vary directly with Volatility x

T , Time, and Rate and inversely

with Yield because the greater flow of cash to investors during the restriction period reduces the degree of illiquidity.24 B.

Proxies for Information and Equity Ownership Concentration Effects I use several proxies to capture information effects and equity ownership concentration

effects. Following Hertzel and Smith (1993), Fraction measures the fraction of the firm’s common stock that is outstanding after the new issue due to the private placement. Private

24

placements take place more quickly than general cash offers, which leaves less time for due diligence. As a result, there is a danger that due diligence may be less extensive than in a general cash offer. Under the information hypothesis, larger issues require more intensive information gathering and expose investors to greater asymmetric information costs. Since they have to expend more resources to assess firm value, they require a larger discount when the offering is relatively large, which suggests a positive coefficient. Information asymmetries are likely to more severe for smaller firms because they tend to be more costly to evaluate, which implies that the size of the discount should be inversely related to firm size. Firms placing common stock privately include early-stage firms, whose prospects are especially difficult to assess. There are economies of scale in the production of information, which implies that the size of the discount should be inversely related to gross proceeds. Table 7 reports the sensitivity of Discount (day prior) and Discount (10 days after) to the market value of the firm’s equity and to the gross proceeds of the private placement. Both discounts are significantly inversely related to the market value of equity and also to gross proceeds. Gross proceeds are positively correlated.with the market value of equity with a Spearman correlation coefficient of 0.74. A smaller firm is likely to have a greater information asymmetry between the firm and investors and thus greater heterogeneity in stockholder valuations (Hodrick, 1999). The more severe information asymmetry will lead to a greater discount. Accordingly, a negative coefficient for Log (Proceeds) could reflect in part the cost of the greater information asymmetries for smaller firms, and thus support the information hypothesis, and in part information gathering economies. The decrease in the discount in Table 7 seems too large to be explained solely by information gathering economies. For example, a $1 million issue involved an average discount between 33.97 percent and 39.57 percent, which

25

amounts to between $339,700 and $395,700. A $20 million issue involved an average discount between 17.56 percent and 24.03 percent. The reduction in discount, between 16.41 percent and 15.54 percent, amounts to between $3,108,000 and $3,282,000, about 10 times the discount for a $1 million issue. Moreover, the decrease in the discount is similar for firm size and for offering size.

Thus, I would interpret a negative coefficient for Log(Proceeds) as supporting the

information hypothesis.25 The discount investors require will also depend on the level of insider ownership and the intensity of monitoring by outside shareholders. Managers of firms with low levels of insider ownership have a greater incentive to invest in unprofitable projects (Jensen and Meckling, 1976). The net proceeds from the new issue give managers more discretionary cash, which increases the risk of non-value-maximizing behavior (Jensen, 1986). Monitoring by institutional investors can mitigate this effect. The greater their percentage ownership, the stronger the incentive institutional shareholders have to protect their investment in the firm’s shares. They can achieve this objective by monitoring the use of proceeds to ensure that they are invested productively.26 I also measure the intensity of monitoring by the firm’s board of directors. Fama and Jensen (1983) argue that outside directors have an incentive to act as effective monitors because they want to protect their reputations for independence.27

I use one minus the fraction of

directors that are also managers (Direct), according to the issuer’s most recent proxy statement as of the pricing announcement date, to proxy for the intensity of monitoring by outside board members. I also considered using the percentage of shares owned by insiders (Inside), as determined from the issuer’s most recent proxy statement as of the completion announcement

26

date, to capture differences across issuers in agency costs due to differences in the degree of alignment between manager and shareholder interests.28 I use the percentage of shares owned by institutional investors (Instit), as reported by Standard & Poor’s Stock Guide, for the month ending immediately prior to the pricing announcement date, to proxy for the intensity of institutional monitoring. In regressions not reported in the paper, I found no relation between either Discount (day prior) or Discount (10days after) and Inside or Instit. Finally, I use a dummy variable to test the possible significance of exchange listing. The variable Exchange takes on the value 1 if the registered shares are listed on the NYSE or the AMEX at the time of the private placement and zero otherwise. The book-to-market ratio (Book/Market) immediately preceding the completion announcement serves as a measure of the degree of over- or undervaluation.29 On the one hand, it may proxy for the fraction of the equity market value attributable to intangible assets. The more significant are the firm’s intangible assets, the smaller the book-to-market ratio, the more difficult it is for investors to assess value, and the greater is likely to be the discount. Hertzel et al. (2002) find that firms that issue equity privately have above-average market-to-book ratios, which they attribute to investor overoptimism concerning the firm’s growth prospects. The larger (smaller) the book-to-market ratio, the greater the degree of under-(over-)valuation, and the smaller (greater) the discount.30 This suggests a negative coefficient for Book/Market. On the other hand, negative (positive) stock price momentum reduces (increases) the market value of equity and raises (lowers) Book/Market (provided book value is positive). Consistent with this observation, I find that Book/Market is negatively correlated with the comparison period CAR, although the correlation coefficient is significant at the 5 percent level only for negative momentum stocks. Negative momentum stocks presumably entail the greatest risk of post-

27

offering underperform (Hertzel et al., 2002). In addition, observe in Table 4 that negative momentum stocks tend to elicit a positive announcement effect. In light of the risk of postoffering underperformance, private placement purchasers may simply increase the discount to offset this positive announcement effect.31 This suggests that the coefficient of Book/Market will be negative if investors perceive greater risk with lower book-to-market stocks but will be positive if they perceive greater risk with negative momentum stocks.32 C. Registration Rights Because of the time required to prepare and file a registration statement with the SEC, I assume that it was planned at the time of the placement if the firm registers the shares within 45 days of the closing. I introduced the dummy variable Registered to control for the effect of a credible commitment to register the shares, which takes on the value 1 if the shares were registered within 45 days of the completion announcement and 0 otherwise. I also introduced the dummy variable Registration Rights to control for the granting of registration rights, which takes on the value 1 if the firm disclosed that it had granted mandatory, demand, or piggyback registration rights and 0 otherwise. I expect both dummies to have a negative coefficient. D.

Regression Models I ran three cross-sectional regression models to investigate the factors that are responsible

for the private placement discount.

Regression model 1 has the four transfer restriction

independent variables plus the control variables Post, Book/Market, Rights, and Registered: Model 1 Discount = a 0 + a1 Post + a 2Volatility × T + a3Time + a 4Yield + a5 Rate

+ a 6 Book / Market + a 7 Rights + a8 Re gistered

(7)

Regression model 2 has only information and ownership concentration independent variables 28

along with the control variables.

There are four information and ownership concentration

variables with Pearson correlation coefficients that are significant at the 5 percent level (Direct, Log(Proceeds), Fraction, and Exchange). The model is: Model 2 Discount = a 0 + a1 Post + a 2 Direct + a3 Log (Pr oceeds) + a 4 Fraction + a5 Exchange + a 6 Book / Market + a 7 Rights + a8 Re gistered

(8)

Regression model 3 combines both sets of independent variables plus the control variables: Model 3 Discount = a 0 + a 1 Post + a 2 Volatility × T + a 3 Time + a 4 Yield + a 5 Rate + a 6 Direct + a 7 Log (Pr oceeds)

+ a 8 Fraction + a 9 Exchange + a10 Book / Market + a11 Rights + a12 Re gistered (9) Log(Proceeds) and Volatility are negatively correlated with a Spearman correlation coefficient of -0.39, which means that the transfer restriction effects proxied by Volatility and the information effects proxied by Log(Proceeds) are not completely independent. In each case, I include the dummy variable Post, which is one for private placements that closed after February 1997 and zero otherwise, to measure any further impact from halving the Rule 144 restriction period in February 1997 that is not already captured by T . I expect a negative coefficient because the shortening of the restriction period should reduce the impact of the transfer restrictions. I include Book/Market, the ratio of the book value to the market value of the firm’s common stock just prior to the closing, to control for the pre-offering momentum effect. I expect a negative coefficient if lower Book/Market indicates greater risk due to greater information asymmetries but a positive coefficient if higher Book/Market indicates greater risk

29

of post-offering underperformance due to more negative (less positive) momentum prior to the private placement. I also include two dummy variables, Rights and Registered, to control for the effect of the commitment to register the stock. Rights is 1 if the firm granted registration rights to private placement buyers and zero otherwise, and Registered is 1 if the firm registered the stock within 45 days following the private placement and zero otherwise.

I expect both

coefficients to be negative. E.

Regression Results I examined the bivariate relationships between the discounts and the independent

variables in the cross-sectional analysis (not reported). All the variables have the predicted signs for both discount measures. Of the four transfer restriction variables, Volatility has the most significant Pearson correlation coefficient in both cases, which is consistent with the option characterization of the transferability discount; Volatility and Time have Pearson correlation coefficients that are significant at the 1 percent level in both cases; the Pearson correlation coefficients for Rate are significant at the 1 percent level in one case and at the 5 percent level in the other; and the Pearson correlation coefficient for Yield is significant at the 10 percent level in one case but not the other, which is not surprising given the small fraction of stocks in the sample that were dividend-paying at the time of the private placement. These results are consistent with Kahl, Liu, and Longstaff’s (2003) finding that the stock’s volatility and the length of the restriction period are the key drivers of the discount in their restricted stock model. Of the information and ownership concentration variables, the Pearson correlation coefficients for Fraction and Log (Proceeds) are significant at the 1 percent level in both cases, Direct and Exchange are significant at the 5 percent level in both cases. The Pearson correlation coefficients are very similar for the two discount measures

30

Table 8 contains the cross-sectional regression results.

Models 2 and 3 have 191

observations. Data were not available for Direct for 14 of the 205 firms. I ran each model separately with Discount (day prior) and Discount (10 days prior) as the dependent variable. White’s

(1980)

specification

test

indicates

heteroskedasticity,

so

I

report

White

heteroskedasticity-consistent estimators and t-statistics. The Durbin-Watson statistics indicate that the null hypothesis of zero autocorrelation can not be rejected at the 5 percent level in any of the regressions. The coefficients of Volatility × T and Time have the predicted sign in the Model 1 and Model 3 regressions and are significant at the 5 percent level or better in both models, which is consistent with the option characterization of the transferability discount. The coefficient of Rate has the wrong sign in one regression, and the coefficient of Yield has the wrong sign in all four, although none of these coefficients is statistically significant.33 All the coefficients of the information and ownership concentration variables have the predicted sign in Models 2 and 3. The coefficient of Log(Proceeds) is significant at the 1 percent level in Model 2 and at the 5 percent level in Model 3, and the coefficient of Fraction is significant at the 1 percent level in Model 2 and at the 10 percent level or better in Model 3. The coefficient of Direct is significant at the 10 percent level in the Model 3 regression for Discount (10 days after). The adjusted R2 and F statistics indicate that Model 1 and Model 2 have similar explanatory power. The slightly greater adjusted R2 and F statistics for the Model 2 regressions are consistent with the greater information effect of the initial announcement than the completion announcement reported in Table 3.

The coefficients of Volatility × T , Time, and

Log(Proceeds) are significant in the Model 3 regressions at the 5 percent level or better, the 31

coefficient of Fraction is significant at the 5 percent level in one regression and at the 10 percent level in the other, and the coefficient of Direct is significant at the 10 percent level in one regression. Model 3 explains roughly one quarter of the variation in the discount. The partial F statistics, which are significant at the 1 percent level for both measures of the discount only for the information and ownership concentration variables, indicate that the incremental contribution of these variables appears greater than the incremental contribution of the transfer restriction variables. Overall, the regression results confirm the significant explanatory power of both sets of factors. The coefficient of Post has the expected negative sign only in Model 2, but it is not statistically significant in any of the regressions. The positive coefficients in Models 1 and 3 suggest that investment bankers have not fully adjusted the discount for the halving of the Rule 144 minimum restriction period, a result that I confirm through additional testing reported later in the paper. The coefficients of Book/Market and Registered have the expected sign and are all significant at the 5 percent level or better in all six regressions. The positive coefficient for Book/Market indicates that a higher book-to-market ratio signifies greater risk of post-offering underperformance due to more negative (less positive) price momentum prior to the private placement and requires a greater discount. The negative coefficient of Registered indicates that the firm’s commitment to register the shares promptly reduces the discount investors require. F.

Effect of the Type of Investor Allen and Phillips (2000) note that firms often privately place shares with other firms

with whom they have product market or other business relationships. Such investors would be expected to have deeper knowledge of the firm’s prospects than institutional investors. They

32

should be less prone to the overoptimism about the firm’s prospects and more cognizant of the risk of future underperformance documented by Hertzel, Lemmon, Linck, and Rees (2002). Table 5 reports that the average discount is greater when shares are placed privately with strategic investors or related parties than when they are placed with (unrelated) institutional investors. I use a dummy variable (Strategic) that takes on the value 1 when the firm announces that it placed the shares with another corporation that could be identified as a strategic partner because of a marketing or development agreement of some kind. I classified the buyer as a strategic partner if a significant business relationship between the two was noted either in the offering announcement or in the issuer’s Form 10-K report for that year. I use a dummy variable (Related) that takes on the value 1 when the firm announces that it placed the shares with a related party, such as an officer, director, 5% shareholder, or a member of their family. Since the proportion of institutional ownership, and presumably the intensity of institutional monitoring, will increase when new shares are placed entirely with institutions, I use a dummy variable (Investment) that takes on the value 1 when the issuer announces that the shares were placed with institutional investors. The issuers of 93 of the 205 discounted private placements made such an announcement. I expect a positive coefficient for the dummy variable because these investors will require compensation for their monitoring services in the form of a greater discount. Table 9 tests the impact of the type of equity buyer on the size of the discount. The discount is greatest for shares placed with strategic investors and least for shares placed with (unrelated) financial institutions, although the differences are not statistically significant. The average increase in discount for strategic investors as compared to financial institutions is 4.5 percentage points, based on Discount (10 days after), and only 1.4 percentage points, based on

33

Discount (day prior). However, the sample of strategic investor private placements is very small. As a further test of buyer impact, I reran Model 3. I interacted each of Investment, Strategic, and Related with Fraction because I expect that the significance of the buyer type will also depend on the relative size of the offering (reflecting potential ownership concentration effects), and I confirmed that the results are stronger with the interaction (results not reported). I report the results in Table 10. The coefficient of Investment*Fraction has the expected sign in all four regressions. It is significant at the 5 percent level in the Discount (10 days after) regression but not at the 10 percent level in the Discount (day prior) regression. The identity of the purchasers is usually not announced until after the closing, and this information is therefore more likely to be reflected in Discount (10 days after). The coefficients of Strategic*Fraction and Related*Fraction have the expected sign in three and two of the four regressions, respectively, but none of these coefficients is significant at the 10 percent level, which may be partly due to the small sample sizes. Overall, the evidence supports the hypothesis that the discount is lower for institutional investors than for other types of private placement purchasers. VI. Average-Strike Put Option Marketability Discount Model

The regression results for Model 1 and Model 3 in Table 8 confirm that the private placement discount depends in part on the loss of timing flexibility implicit in the Rule 144 transfer restrictions, which is consistent with using an option model for the marketability discount. Longstaff (1995) proposes a lookback put option model, which assumes that the purchasers have perfect market-timing ability. This section models the marketability discount as the value of an average-strike put option. The investor is not assumed to have any special timing ability; instead, it is assumed that the investor would, in the absence of any restrictions, be

34

equally likely to sell the shares anytime during the restriction period. After developing this alternative model, I compare the predictions of the two models to the discounts observed in the sample of 205 discounted private stock placements. A.

Assumptions V(t) is the value of a share of common stock without transfer restrictions. The firm also

has restricted shares outstanding, and all the firm's shares are identical except for the transfer restrictions. Assume the following: A1.

The unrestricted shares trade continuously in a frictionless market.

A2.

Transfer restrictions prevent the investor from selling the restricted shares for a period of length T.

A3.

Any cash dividends are paid continuously during the time interval [0, T] at a rate q ≥ 0 that is proportional to V (Merton,1973).

A4.

The stock price V(t) follows a geometric diffusion process (Longstaff, 1995) dV = (µ − q )Vdt + σVdZ

(10)

where µ and σ are constants and Z is a standard Wiener process. A5.

The riskless interest rate r is constant and the same for all maturities during [0, T].

A6.

No shareholder has any special market-timing ability. The last assumption is consistent with evidence that outside investors, at least on average,

do not have any special ability to outperform the market (Barber and Odean, 2000; Carhart, 1997; Chevalier and Ellison, 1999; Graham and Harvey, 1996; Malkiel, 1995; and Odean, 1998, 1999). However, empirical evidence indicates that private information enables insiders to time the market and realize excess returns (Seyhun, 1986, 1988; Meulbroek, 1992). Longstaff’s (1995) model may be more appropriate in the presence of asymmetric information. In Section

35

VII, I investigate whether the private placement discount is greater when the firm sells shares to strategic or related investors. Suppose that a stock pays cash dividends (q > 0) and that the shareholder can sell the registered shares at t, 0 < t < T and reinvest the proceeds in the riskless asset until T. In a riskneutral world, the investor would be indifferent between selling the share immediately for V(t) and selling it forward for delivery at T with forward price e (r -q )(T- t ) V(t ) . Suppose further that the investor would want to sell the unregistered shares prior to T were it not for the resale restrictions. Since the investor lacks any special timing ability, assume that the investor would be equally likely to sell unrestricted shares at N + 1 discrete points in time and that these points are equally spaced, so that the investor considers selling at t = 0, t = T/N, t = 2T/N,…, t = NT/N = T. Under this assumption, in a risk-neutral world, the investor would be indifferent between holding a registered share and holding an unregistered share plus a series of forward contracts

all

expiring

at

1 N (r −q )T ( N- j) / N V(jT/N)] . ∑[e N + 1 j=0

T

and

having

an

average

forward

price

equal

to

If the investor’s transfer restriction risk exposure could be

perfectly hedged, or if this risk is idiosyncratic with respect to the investor’s securities portfolio, then the unregistered shares would be priced on a risk-neutral basis. As explained in Section II, the securities laws restrict the type of hedging a purchaser of restricted shares might employ. The investor bears an opportunity cost due to the transfer restrictions if

[

]

1 N (r -q )T ( N- j) / N V( jT/N ) > V(T ) ∑e N + 1 j=0

(11)

but realizes an opportunity gain if the inequality is reversed. If the investor’s transfer restriction risk exposure is idiosyncratic, then the gains and losses offset, and so the transferability discount 36

would be zero provided the investor has adequate liquidity from other sources such that the transfer restrictions do not cause the investor to miss any positive-NPV investment opportunities. In effect, the restricted share is a long forward contract for the delivery of an otherwise identical unrestricted share at T when the transfer restrictions expire. With any unhedged nonidiosyncratic risk exposure, a risk-averse investor would demand a risk premium, and the transferability discount is nonzero.

Following Longstaff (1995),

inequality (11) suggests that an upper bound on the investor’s opportunity cost can be modeled as ⎫ ⎧ 1 N ( r -q )T ( N- j) / N max ⎨0, e V( jT/N ) - V(T )⎬ ∑ ⎭ ⎩ N + 1 j=0

[

]

(12)

Expression (12) is the payoff function for an average-strike put option in which the strike price is the arithmetic average of the forward prices

[

]

1 N (r -q )T ( N- j) / N V( jT/N ) . ∑e N + 1 j=0

Expression (12) furnishes an upper bound on this opportunity cost because there are states of nature in which inequality (11) is reversed. However, even in these states the investor may miss positive-NPV investment opportunities unless adequate sources of liquidity are available. If profitable investment opportunities would be missed, then expression (12) would understate the cost of the transfer restrictions if the missed opportunities are worth more than the gains that would result when inequality (11) is reversed. How well this approach to modeling the discount for lack of free transferability explains actual discounts is an empirical question that is addressed later in the paper. One other factor needs to be considered. The transfer restrictions are costly only if the investor would sell the shares on or before T absent such restrictions. Suppose there is some likelihood p > 0 that the investor would want to hold the stock past T even without resale 37

restrictions. Again assuming that prior to T, any sale would be equally likely to occur anywhere in [0, T], the payoff function becomes ⎧⎪ ⎛ 1 N (r -q )T ( N − j) / N ⎞⎫⎪ max ⎨0, (1 - p ) ⎜⎜ e V( jT/N ) - V(T )⎟⎟⎬ ∑ ⎪⎩ ⎝ N + 1 j= 0 ⎠⎪⎭

[

]

⎧ ⎫ 1 N (r -q )T ( N − j) / N = (1 - p ) max ⎨0, e V( jT/N ) - V(T )⎬ ∑ ⎩ N + 1 j= 0 ⎭

[

]

(13)

In this case, the transferability discount equals 1 - p times the discount calculated assuming the investor would otherwise always sell sometime prior to T. B.

The Transferability Discount Model I obtain a formula for an upper bound on the value of the marketability discount by

valuing the average-strike put option whose payoff is (12). The appendix derives the following formula for the value of the discount D(T) as: ⎡ ⎛ r -q ⎞ ⎛ r -q ⎞⎤ D(T ) = V0 ⎢e (r -q )T N⎜ T + 12 v T ⎟ - N ⎜ T - 12 v T ⎟ ⎥ ⎝ v ⎠ ⎝ v ⎠⎦ ⎣

[{

v 2 = σ 2 T + ln 2 eσ

2

T

} ]- 2 ln[ e

- σ 2T - 1

σ 2T

]

-1

(14)

(15)

where N(⋅) is the cumulative standard normal distribution function. D(T) is proportional to the current share price. It increases with the length of the restriction period T when r > q, with the volatility σ, and with the riskless rate r. It varies inversely with the dividend yield q. The average strike put option model (14)-(15) is consistent with the regression results reported in the previous section for Model 1 and Model 3. The private placement discount depends on the stock’s volatility and other option parameters to the extent transfer restriction risk is priced. C.

The Discounts Implied by the Model Table 11 reports the sensitivity of the discount D(T) to the length of the restriction period

38

and the stock's volatility. In the dividend-paying case, I assume q = 0.02 because the 15-year average dividend yield on the Standard & Poor's 500 portfolio of stocks is 2.07 percent. I assume r = 0.05 for the riskless rate. For example, for a non-dividend-paying stock, D(T) increases by approximately 10 percentage points for each additional year in the restriction period when σ is 0.3. If T = 3 years, D(T) = 30.68 percent; if T = 5 years, D(T) = 52.64 percent. The discounts in Table 11 are within the range of discounts estimated by Kahl, Liu, and Longstaff (2003). They model the discount within a continuous-time portfolio choice framework and find, for example, that where the stock is restricted for five years and represents between 30 and 90 percent of the holder’s wealth, the discount is between 10.0 percent and the 85.2 percent when the stock’s volatility is 30 percent (versus 52.64 percent in Table 11 when q = 0) and is between 42.4 percent and 89.7 percent when the stock’s volatility is 60 percent (versus 76.39 percent). The discount for stocks yielding 2 percent is more than three-quarters of the discount for otherwise identical non-dividend-paying stocks. For example, with a 5-year restriction period, the discount is 52.64 percent if the stock does not pay dividends but 43.54 percent if the stock provides a 2 percent constant dividend yield.

The proportionate difference between the

discounts applicable to dividend-paying and non-dividend-paying stocks diminishes as the volatility and the length of the restriction period increase. Longstaff (1995) develops the following upper bound on the marketability discount for a non-dividend-paying restricted share under the assumption that the holder of the restricted share has perfect market-timing ability:34 2 2 ⎡ σ 2T ⎛ σ 2 T ⎞ ⎤ ⎟ + σ T exp⎛⎜ - σ T ⎞⎟ - 1⎥ D * (T ) = V0 ⎢2 + N⎜ ⎜ ⎜ 2 ⎟ 2 2π 8 ⎟⎠ ⎥ ⎢⎣ ⎝ ⎝ ⎠ ⎦

(16)

39

where exp(⋅) is the exponential function and the other variables are as defined in equations (14) – (15). Figure 1 compares the discounts calculated by applying the lookback put model and the average-strike put model, assuming the stock is non-dividend-paying and that the stock's volatility is 0.2, 0.3, or 0.4. The discount should be greater when investors possess special market-timing ability because the transfer restrictions impose a greater opportunity cost, which is evident in Figure 1. For any given restriction period, the difference increases with σ. If the restriction period is T = 0.25 year and σ = 0.3 , the difference is just over 10 percentage points (12.54 percent for perfect timing versus 2.44 percent for no special timing ability). When T = 2 years, the difference is 18.5 percentage points (38.61 percent versus 20.12 percent).

The

difference due to timing ability tends to lessen slightly as T increases. There are many reasons why the transfer of shares may be restricted. First, as mentioned, transfer may be legally constrained by the resale restrictions imposed by Rule 144 under the Securities Act of 1933. Second, selling restrictions may be imposed by contract. For example, stock lockups in connection with initial public offerings (IPOs), which are intended to resolve moral hazard and adverse selection problems, prevent company insiders from selling their shares for 180 days following the IPO (Field and Hanka, 2001). Third, many firms issue restricted stock as part of their managerial compensation plans. The restriction period ranges from 31 months to 74 months (Kole, 1997). Fourth, merger agreements often require the target firm’s insiders to take restricted stock of the acquiring firm in order to resolve asymmetric information problems and also to align their interests with those of the acquiring firm’s shareholders. While the focus of this study is the impact of the transfer restrictions under Rule 144, the model can be used to calculate discounts for other types of marketability restrictions by comparing the restrictions to those imposed by Rule 144.

40

VII. Comparison of the Lookback and Average-Strike Put Option Discount Models

A buyer of unregistered common stock may require a greater discount, as implied by Longstaff”s (1995) model, if she has asymmetric information about the firm’s prospects because in that case the resale restrictions will interfere with her ability to exploit her information advantage to time the market. I found some weak empirical support for that proposition in Section V, although the small strategic investor and related investor sample sizes may not have permitted a fair test of that proposition. Why would such an investor buy a private placement?

She might derive strategic

benefits (Allen and Phillips, 2000) or ownership concentration benefits (Wruck, 1989). If the stock is relatively illiquid, accumulating a large block could ultimately be more expensive because it is likely to drive up the market price. Entering the market to make substantial purchases could also drive up the price if other investors detect these purchases and identify the buyer as an informed investor (e.g., strategic partner or insider). Why would a public firm privately sell the shares?

The investor might require a greater discount to compensate for the

greater cost of the marketability constraint. But even with this greater discount, the firm will still benefit from placing shares privately, rather than offering them publicly, so long as inequality (4) is satisfied. Longstaff (1995) models the discount as the value of a lookback put option. The model assumes perfect market-timing ability. While this assumption may seem unrealistic, strategic investors and insiders might have valuable private information that would enable them to time the market were it not for the transferability restrictions. For such investors, the lookback put option model may be more appropriate than the average-strike put option model, which seems more appropriate for (unrelated) institutiuonal investors, who are much less likely to have any

41

private information about the firm. Table 12 compares the mean actual discount, the mean discounts calculated from the lookback put and average-strike put option models, and the mean empirical predicted discounts calculated by adjusting the actual discounts for the information, ownership concentration, and control variables in Model 3. I calculate the Empirical Predicted Discount from the actual private placement discount (Discount): Empirical Predicted Discount = Discount - (a 0 + a 1 Post + a 2Volatility × T + a 3Time + a 4Yield + a 5 Rate

+ a 6 Direct + a 7 Log (Pr oceeds) + a8 Fraction + a9 Exchange + a 10 Book / Market + a 11 Rights + a 12 Registered + a 13 Fraction * Investment + a14 Fraction * Strategic + a 15 Fraction * Related ) (17) I use the coefficients from Model 3 in Table 10 to adjust Discount (day prior) and Discount (10 days prior). Since the coefficients a 7 and a9 in equation (9) are negative but the coefficients

a 6 and a8 are positive, the Empirical Predicted Discount may understate or overstate the actual Discount. If there is a difference, I expect that it will be evident from comparing these predictions on a subsample of information-intensive private placements and a subsample of noninformation-intensive private placements. Information-intensive placements are characterized by either (a) volatility above the median and log (proceeds) below the median for the overall sample or (b) placed with strategic investors (StratInv = 1) or related investors (RelatedInv = 1). Non-information-intensive placements are characterized by (a) volatility below the median and log (proceeds) above the median and (b) Strategic= Related = 0. The mean actual discount is significantly greater for information-intensive private 42

placements than for non-information-intensive placements according to both option models. Similarly, the mean empirical predicted discount is also significantly greater for the informationintensive placements according to both models.

However, the lookback put option model

substantially overstates both the actual discounts and the empirical predicted discounts, and the overstatement is more severe for the information-intensive placements. Table 13 compares the average-strike put option model’s ability to explain the empirical predicted discounts for the information-intensive and non-information-intensive subsamples. I expect that the average-strike put option model would be more accurate in predictiing the discounts for the non-information-intensive placements.

The regression intercept is not

significantly different from zero for the regressions on the non-information-intensive subsample, and the mean-squared error is substantially smaller for this subsample than for the informationintensive subsample. The average-strike put option model fits the non-information-intensive placement discounts more closely than the information-intensive placement discounts. Table 14 compares the ability of the lookback and average-strike put option models to explain observed private placement discounts. I expect the average-strike put option model to perform relatively better (worse) than the lookback put option model in explaining the actual discounts for the non-information-intensive (information-intensive) subsample.

The mean-

squared error decreases for the lookback put option model but increases for the average-strike put option model for the information-intensive subsample as compared to the full sample. The mean-squared error for the average-strike put option model decreases substantially and is less than one-third the mean-squared error for the lookback put option model for the noninformation-intensive subsample.

The average-strike put option model fits the observed

discounts better than the lookback put option model for non-information-intensive private

43

placements. The lookback put option model’s pricing errors are less severe for informationintensive private placements; however, it still substantially overstates the discount even when the shares are placed with strategic or related investors. Table 15 repeats the tests in Table 12 on a holdout sample consisting of 27 private placements that were completed between March 1, 2005 and February 28, 2006. The averagestrike put option model discounts are more consistent than the lookback put option model discounts with both the mean actual discount and the mean empirical predicted discount for the full sample and both subsamples. The average-strike put option model slightly overstates the actual discounts and the empirically predicted discounts for non-information-intensive private placements. The evidence in Tables 12 through 15 suggests that the average-strike put option model fits observed discounts better than the lookback put option model and also that it provides reasonable estimates of the marketability discount, at least for non-information-intensive restricted stock transactions. VIII. Comparison of the Model Predicted and Empirical Predicted Discounts

I perform three additional tests of the average-strike put option marketability discount model’s ability to explain actual marketability discounts. I compare the discounts predicted by the average-strike put option model in equations (14) - (15) (Model Predicted Discount) to the Empirical Predicted Discounts from equation (17) for various stock volatilities. Next, I perform a Wilcoxon signed rank test, and then I regress the Empirical Predicted Discount on the Model Predicted Discount to investigate whether the average-strike put option model has a systematic tendency to over- or understate the discount. Table 16 compares the Empirical Predicted and Model Predicted Discounts. In Panel A, the Model Predicted Discount overstates the Empirical Predicted Discount for all volatilities

44

except volatilities under 30 percent based on Discount (day prior) for a two-year restriction period. The Model Predicted Discounts fit the Empirical Predicted Discounts (day prior) much more closely for the one-year restriction period that has applied since February 1997. For both time periods, the mean Empirical Predicted Discount (day prior) exceeds the mean Empirical Predicted Discount (10 days after) for all volatilities. With the exception of low-volatility stocks (under 45 percent), the mean Model Predicted Discount is more consistent with the mean Empirical Predicted Discount (day prior) than with the mean Empirical Predicted Discount (10 days after). The average-strike put option model fits the marketability discounts that are implicit in the pricing of private placements since 1997, but when market prices are allowed to adjust fully (over 10 days) for the accompanying information and ownership concentration effects, the model tends to overstate the discount. In Panel B, the mean Model Predicted Discount is significantly greater than the mean Empirical Predicted Discount at the 1 percent level for the two-year restriction period. The mean Model Predicted Discount is slightly less than the mean Empirical Predicted Discount (day prior) for the one-year restriction period, and 64 of the 151 differences are positive. Neither is statistically significant at the 10 percent level. However, the mean Empirical Predicted Discount (10 days after) is significantly less than the mean Model Predicted Discount, and only 40 of the 151 differences are positive, which is statistically significant. The mean and median stock price volatilities for the sample are 80 percent and 84 percent (prior to rescaling) and 86 to 88 percent (after rescaling), respectively, which are relatively high volatilities. When the stock price volatility is that high, the average-strike put option model (14) - (15) predicts discounts within the 25 to 35 percent (15 to 25 percent) range that investment bankers and appraisers customarily apply when there is a two-year (one-year) restriction period.

45

In particular, the mean Model Predicted Discount (19.04 percent), the mean Empirical Predicted Discount (day prior) (19.39 percent), and the mean Empirical Predicted Discount (10 days prior) (11.86 percent) for a one-year restriction period are all within or slightly below this range. However, when the restriction period is one year, Table 11 indicates that when q = 0, a discount in the range from 15 to 25 percent is appropriate only if the volatility is in the range from 50 to 100 percent. Above (below) this volatility range the discount should be higher (lower). I fit the regression equation

Empirical Pr edicted Discount = a 0 + a1 Model Pr edictedDiscount

(18)

in Panel C. If the Empirical Predicted Discounts perfectly track the Model Predicted Discounts, then a0 = 0 and a1 = 1. If investment bankers and business appraisers tended to apply discounts within the 25 to 35 percent range prior to February 1997 and within the 15 to 25 percent range since February 1997 with little, if any, adjustment for volatility, then I would expect a0 > 0 and a1 < 1 because then the Empirical Predicted Discounts would tend to overstate (understate) the Model Predicted Discounts for low (high) volatilities. The slope a1 would indicate how sensitive the discount is to differences in volatility and to variation in the other parameters in the model. None of the intercepts a0 is significant at the 10 percent level.

The slope a1 is

significantly different from zero at the 1 percent level in two regressions and at the 5 percent level in the other two but is not significantly different from one at the 10 percent level in any of the regressions.

Figure 2 plots the linear equations corresponding to equation (18).

The

regression line for Discount (day prior) crosses the 45 degree line at Model Predicted Discount = 20.0 percent, which falls near the midpoint of the customary 15 to 25 percent range of discounts for a one-year restriction period and corresponds to a volatility of about 80 percent when q = 0 in Table 11. Equation (18) (and thus equation (9) from which the adjustments for the information

46

and ownership concentration effects were derived) appears to fit the Model Predicted Discounts rather well since February 1997. Since the Rule 144 restriction period was halved, the discounts are still too high but the overstatement is less severe, especially for high-volatility stocks. Investment bankers and appraisers seem to have adjusted for the shortening of the Rule 144 restriction period. With the exception of relatively low-volatility (σ under 45 percent) stocks, the model (14) - (15) predicts actual discounts for lack of free transferability rather well. IX. Conclusion

The private placement discount results from the Rule 144 restrictions on transferring unregistered common stock and also from the information and equity ownership concentration effects that accompany a stock private placement. The effect of the transfer restrictions can be priced as the value of an average-strike put option. The average-strike put option model (14) (15) fits empirically observed discounts better than the lookback put option model, which substantially overstates it even when stock is privately placed with strategic or related investors. The stock market’s reaction to a private placement announcement is more complex than previous studies suggest. In contrast to the typical positive announcement effect, I find that the announcement can elicit a negative reaction if the stock has recently exhibited positive momentum or if the firm commits to register the shares promptly. In both cases, the firm appears to be using the private placement process to exploit the overpricing of its stock, and the market reacts to the overpricing signal just as it would to a public offering announcement. Indeed the ability to sell shares quickly by avoiding having to register them beforehand is one of the benefits cited by promoters of PIPEs. The average-strike put option model (14 ) - (15) calculates marketability discounts that are consistent with the range of discounts observed empirically in letter-stock private placements

47

with a one-year restriction period, although there is a tendency to overprice the discount for volatilities under 45 percent.

The observed private placement discounts appear to reflect

differences in stock price volatility as option theory and the average-strike put option model predict. The average-strike put option model can also explain the apparent inconsistency between the range of discounts found in several earlier studies, which concluded that marketability discounts of 25 to 35 percent were appropriate for the two-year Rule 144 restriction period, and studies by Wruck (1989) and Hertzel and Smith (1993), which found that this discount is only 13.5 percent.

The difference is due in part to the information and equity ownership

concentration effects that accompany a common stock private placement. This paper has explained equity private placement discounts and demonstrated that the stock’s pre-offering momentum affects the discount. What accounts for the premium at which roughly one in seven equity private placements are priced? In some cases, the firm and investors have agreed to a formula using an average of recent market prices, which can result in negative momentum stocks being priced at a premium. I leave it to future research to investigate whether other factors might also be responsible for private placement premiums.

48

Appendix

Applying the risk-neutrality transformation of Cox and Ross (1976), the stock price can be described by the geometric diffusion process dV = (r - q ) Vdt + σVdZ ,

(A.1)

and ln V(T) is normally distributed with mean ln V0 + (r - q - ½σ2)T and standard deviation σ T , where V0 is the stock price at t = 0. Similarly, the forward price F(t) = e

(r - q) (T - t)

V(t)

follows the martingale process dF = σ FdZ

(A.2)

in a risk-neutral world, and ln F(t) is normally distributed with mean ln F0 - ½ σ 2 t and standard deviation σ t where F0 = F(0 ) = V0 e ( r -q )T . In the risk-neutral framework, the strike price is the average of the risk-neutral forward prices, which I will denote A(T): A(T ) =

1 N ∑ F(t j ) N + 1 j=0

(A.3)

where tj= jT/N and the forward prices follow the martingale process (A.2). The payoff function (A.3) contains the sum of a set of correlated lognormal random variables. Although expressions exist for the moment generating function, mean, and variance of the sum of two lognormal random variables, no exact closed-form expression for the density function of the sum of a set of lognormal random variables is known. A sum of independent lognormal random variables can be closely approximated by a lognormal random variable.35

Levy (1992), Ritchken,

Sankarasubramanian, and Vijh (1993), and Turnbull and Wakeman (1991) show that the distribution of the average of a set of correlated lognormal stock prices or exchange rates can be

49

approximated by a lognormal distribution with acceptable accuracy by applying Wilkinson’s method, which matches the first and second moments. I use Wilkinson’s method to approximate the distribution of A(T). Assume that ln A(T) is normally distributed with mean α1(T) and variance v1(T)2. Since ln V(T) is also normally distributed, assume that X(T) = [ln A(T), ln V(T)] is approximately bivariate normal. An average strike put option can be characterized as the option to exchange a package of forward contracts on a share for the underlying share and evaluated by applying Margrabe’s (1978) equation (7). First, write the moment generating function for X(T) as

[

M (k 1 , k 2 ) = E * A(T) 1 V(T) k

k

2

]=e

(

α1k1 + α 2 k 2 + 1 2 v12 k12 + 2 ρv1v 2 k1k 2 + v 2 2 k 2 2

)

(A.4)

where E* denotes the expectations operator conditional on V0 and where α2 = ln V0+ (r - q ½σ2)T and v2 = σ T . Since F0 = V0 e(r-q)T, write the mean as α2 = 1n F0 - ½ σ2T = ln F0 - ½ v22. Obtain expressions for αl and v12 by substituting (kl,k2) = (1,0) and (k1,k2) = (2,0) into equation (A.4) and solving the resulting equations for:

[

α 1 = 2 ln E * [A(T )] - 1/2 1n E * A(T )2

[

]

(A.5)

]

v12 = ln E * A(T ) - 2 ln E * [A(T )] 2

(A.6)

Similar expressions for α 2 and v 22 can be obtained by substituting (k 1 , k 2 ) = (0, 1) and

(k 1 , k 2 ) = (0, 2) into equation (A.4). The covariance term, ρv1 v 2 , is obtained by substituting (k 1 , k 2 ) = (1,1) :

(

ρv1 v 2 = ln E * [A(T )V(T )] - (α1 + α 2 ) - 1 2 v1 2 + v 2 2

)

Equations (A.5)-(A.7) require expressions for E*[A(T)], E*[A(T)2], and E*[A(T)V(T)]:

50

(A.7)

⎡ 1 N ⎤ 1 N 1 N ( ) ( ) E * [A(T)] = E * ⎢ F t = E * F t = F0 = F0 = V0 e ( r -q )T ∑ ∑ ∑ j ⎥ j N + 1 N + 1 N + 1 j= 0 j= 0 j= 0 ⎣ ⎦

[

[

]

]

⎡⎛ 1 N ⎞⎤ 1 ⎞⎛ 1 N 2 ⎜ ( ) E * A(T ) = E * ⎢⎜ F t F(t j )⎟⎟⎥ = ∑ ∑ i ⎟⎜ 2 ⎠ ⎝ N + 1 j= 0 ⎢⎣⎝ N + 1 i = 0 ⎠⎥⎦ (N + 1)

[

]

since E * F(t i ) F(t j ) = F02 e σ

2

Min (i, j )T/N

N

N

i =0

j= 0

∑ ∑F

2 0

eσ

2

Min (i, j )T/N

(A.8)

(A.9)

To see this, without loss of generality, suppose

.

Min (i,j) = i. Then

[

[

]

E * F(t i ) F(t j ) = E * e1n F( t i ) e

( )

1n F t j

]

[

= F02 e ρσ

2

i j T/N

(A.10)

]

Note that ρ σ 2 i j T/N = Cov 1n F(t i ), 1n F(t j ) so that ρ σ 2 i j T/N = σ 2 iT/N = σ 2 Min(i, j)T/N

(A.11)

Substituting equation (A.11) into equation (A.10) justifies equation (A.9). After simplification, equation (A.9) becomes

[

E * A(T )

2

]

=

(N + 1)

F0 2

2

(e

2

σ T/N

(

)

⎧⎪ σ 2T +σ 2T/N 2 e σ T +σ T/N - 1 ⎫⎪ e 1 2N + ⎨ ⎬ 2 - 1 ⎪⎩ e σ T/N - 1 ⎪⎭

)

2

2

(A.12)

Finally, 2 ⎡⎛ 1 N ⎤ ⎞ F0 N ρ σ 2T ⎜ ⎟ E * [A(T )V(T )] = E * ⎢⎜ ∑ F(t j ) ⎟V(T )⎥ = N + 1 ∑ e j= 0 ⎠ ⎣⎢⎝ N + 1 j=0 ⎦⎥

[

j/N

(A.13)

]

Note that ρσ 2 T j/N = Cov 1n F(t j ) , lnV(T ) so that ρσ 2 T j/N = σ 2 jT/N

(A.14)

Substituting equation (A.14) into equation (A.13) gives

[

]

F 0 N σ 2T/N j F 0 e σ T ( N +1)/N - 1 E * [A(T )V(T )] = = 2 ∑e N + 1 j= 0 N + 1 e σ T/N - 1 2

2

2

(A.15)

Now assume that investors reevaluate their decision to hold or sell the shares

51

continually. In that case, the following continuous form expressions can be used to value the option to exchange the package of forward contracts on a share for the underlying share: E * [A(T )] = F 0

[

]

lim E * A(T ) =

N →∞

2

2F0

(A.16)

{e

2

(σ T )

2

2

lim E * [A(T )V(T )] =

N →∞

σ 2T

{e σ T F0

2

}

- σ 2T -1

(A.17)

}

(A.18)

σ 2T

2

-1

Substituting equations (A.16)-(A.18) into equations (A.5)-(A.7) and similar expressions for α 2 and v 22 gives α 1 = 1n F0 - 1 2 v 1

[{

(A.19)

2

} ] - 2 1n[ σ T ]

2

σ T 2 2 v1 = 1n 2 e - σ T - 1

2

α 2 = 1n F0 - 1 2 σ 2 T 2 2 v2 = σ T

[

2

(A.20) (A.21) (A.22)

] [ ]

(A.23)

ρv 1 v 2 = 1n e σ T - 1 - 1n σ 2 T

Apply Margrabe’s (1978) equation (7) for the value of an option to exchange one asset for another to obtain equations (14) and (15).

52

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Malkiel, Burton G., 1995, Returns from investing in equity mutual funds 1971-1991, Journal of Finance 50, 549-572. Margrabe, William, 1978, The value of an option to exchange one asset for another, Journal of Finance 33, 177-186. McConnell, John J., and Henri Servaes, 1990, Additional evidence on equity ownership and corporate value, Journal of Financial Economics 27, 595 - 612. McLaughlin, Robyn, Assem Safieddine, and Gopala K. Vasudevan, 1996, The operating performance of seasoned equity issuers: Free cash flow and post-issue performance, Financial Management 25, 41 - 53. Merton, Robert C., 1973, Theory of rational option pricing, Bell Journal of Economics and Management Science 4, 141-183. Meulbroek, Lisa K., 1992, An empirical analysis of illegal insider trading, Journal of Finance 47, 1661-1699. Morck, Randall, Andrei Shleifer, and Robert W. Vishny, 1988, Management ownership and market valuation: An empirical analysis, Journal of Financial Economics 20, 293 - 316. Morrison & Foerster LLP, 2006, PIPEs: what agents need to know, unpublished (August 4-5). Myers, Stewart C., and Nicholas S. Majluf, 1984, Corporate financing and investment decisions when the firm has information that investors do not have, Journal of Financial Economics 13, 187-221. Odean, Terrance, 1998, Are investors reluctant to realize their losses?, Journal of Finance 53, 1775-1798. Odean, Terrance, 1999, Do investors trade too much?, American Economic Review 89, 12791298.

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Pound, John, 1988, Proxy contests and the efficiency of shareholder oversight, Journal of Financial Economics 20, 237 - 266. Ritchken, Peter, L. Sankarasubramanian, and Anand M. Vijh, 1993, The valuation of path dependent contracts on the average, Management Science 39, 1202 - 1213. Rosenstein, Stuart, and Jeffrey G. Wyatt, 1990, Outside directors, board independence, and shareholder wealth, Journal of Financial Economics 26, 175 - 192. Scholes, Myron, and Joseph T. Williams, 1977, Estimating betas from nonsynchronous data, Journal of Financial Economics 5, 309-327. Securities and Exchange Commission, 1971, Institutional investor study report of the Securities and Exchange Commission (U.S. Government Printing Office, Washington, D.C.). Securities and Exchange Commission, 1997a, Revision of holding period requirements in rules 144 and 145, Release No. 33-7390 (February 20). Securities and Exchange Commission, 1997b, Revision of rule 144, rule 145 and form 144, Release No. 33-7391 (February 20). Seyhun, H. Nejat, 1986, Insiders’ profits, costs of trading, and market efficiency, Journal of Financial Economics 16 (June), 189-212. Seyhun, H. Nejat, 1988, The information content of aggregate insider trading, Journal of Business 61 (January), 1-24. Silber, William L., 1991, Discounts on restricted stock: The impact of illiquidity on stock prices, Financial Analysts Journal 47, 60 - 64. Smith, Clifford, 1986, Investment banking and the capital acquisition process, Journal of Financial Economics 15, 3 - 29.

58

Spiess, D. Katherine, and John F. Affleck-Graves, 1995, The long-run performance following seasoned equity offerings, Journal of Financial Economics 38, 243 - 267. Stulz, Rene, 1988, Managerial control of voting rights, financing policies and the market for corporate control, Journal of Financial Economics 20, 25 - 54. Turnbull, Stuart M., and Lee Macdonald Wakeman, 1991, A quick algorithm for pricing European average options, Journal of Financial and Quantitative Analysis 26, 377 - 389. Weisbach, Michael S., 1988, Outside directors and CEO turnover, Journal of Financial Economics 20, 431 - 460. White, Halbert, 1980, Heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity, Econometrica, 817-833. Wruck, Karen H., 1989, Equity ownership concentration and firm value: Evidence from private equity financings, Journal of Financial Economics 23, 3 - 28.

59

Endnotes

1

Letter stock is not registered for resale under the Securities Act of 1933 and therefore cannot be freely traded in

the public market. It must be placed privately with accredited (sophisticated) investors. It gets its name from the practice of requiring the investor to furnish an ‘investment letter’ confirming that the purchase is for investment and not for resale. This representation is one of the requirements to qualify the shares for the ‘private offering exemption’ from registration under the Securities Act of 1933 (Loss and Seligman (1995,

p. 332)). Under Rule

144, since its amendment on February 20, 1997, a holder of letter stock can not sell the shares for at least one year from the issue date except through another exempted transaction. Effecting such a transaction requires “an opinion of counsel satisfactory to the company to the effect that the proposed transaction will be exempt from registration [under the Securities Act of 1933]” (Loss and Seligman (1995)). The private purchaser would face the same resale restriction for the remainder of the one-year period (two-year period prior to the 1997 amendment). After the minimum holding period, the shares can be sold in the public market without first registering them but such sales are subject to restrictions on the volume of sales for a period of one year; they can be sold beginning three years after issue without any restrictions, provided the shareholder is not an affiliate of the firm. The SEC amended Rule 144 in 1997 to allow nonaffiliates to sell their shares after just one year, followed by the restrictions on the volume of sales just noted, and to sell them after two years without any restrictions. The SEC shortened the holding period in order to lower the cost of raising equity privately (Loss and Seligman (2000)). 2

There is also evidence from other securities markets that lack of free transferability can lead to significant price

discounts. Amihud and Mendelson (1991) and Kamara (1994) find that the yields on illiquid Treasury notes average more than 35 basis points higher than the yields on liquid Treasury bills with the same remaining maturity. Boudoukh and Whitelaw (1991) show that the yield spread between the designated benchmark Japanese Government bonds and less liquid non-benchmark Japanese Government bonds of like maturity averages more than 50 basis points. Brenner, Eldor, and Hauser (2001) find that over-the-counter currency options sell for about 21 percent less than similar exchange-traded options.

60

3

Longstaff’s model provides an upper bound on the marketability discount because it assumes that investors have

perfect market-timing ability. At least one earlier paper uses a contingent-claims approach to value the resale restriction as a put option. Alli and Thompson (1991) measure the value of marketability as the Black-Scholes (1973) value of a put option with the share price at the time of issue as the strike price. 4

The Rule 144 restriction period was shortened to one year from two after their study was published.

5

Equation (1) is obtained directly from Wruck’s (1989) Equation (A.5). This new information concerns new as well

as existing projects, which also accommodates the information effect Hertzel and Smith (1993) model. 6

PIPE offerings can take other forms, such as securities convertible into common stock, direct sale of registered

shares, and equity lines of credit (Dresner and Kim, 2006). An equity line gives investors the right to purchase additional registered shares from the firm on a formula basis (number of shares and price) at set intervals. These purchases are usually contingent on the stock’s trading volume and price being above stated thresholds. 7

Alternatively, the hedge position could consist of a portfolio of put options that correspond to the numbers of

shares that could be sold following the expiration of the resale-restriction period subject to Rule 144’s trading volume restrictions. 8

Less frequent hedging transactions might be more cost effective because of transaction costs.

9

Selling call options before the resale-restriction period expires and delivering the previously restricted shares if the

call options are exercised following the expiration of the resale-restriction period is similarly prohibited. See Securities and Exchange Commission (1997b). Only 21 of the stocks in the 244 private placements in the final sample had listed options at the time of the offering, and none of these were LEAPS. 10

The modifications to Rule 144 the SEC made on February 20, 1997 (see Securities and Exchange Commission

(1997b)) note that in some cases, market participants have used equity swaps to arbitrage the private placement discount. Securities lawyers the author contacted explained that they have advised their clients that using an equity swap to arbitrage the discount would expose them to the risk that if the SEC investigates their hedged investment in unregistered shares it might conclude that the resales were in violation of Rule 144. The use of equity swaps to

61

hedge the price risk of stocks has fallen out of favor since a 1997 tax law change deemed such transactions a ‘constructive sale’ of the hedged shares (Bettis, Bizjak, and Lemmon (2001)). 11

Almost all of the offerings dropped because of missing financial data were by firms whose shares were quoted on

the OTC Bulletin Board or in the Pink Sheets. Firms often have their shares relegated to these markets when they fail to file timely financial reports with the SEC or otherwise fail to meet the NYSE, ASE, or NASDAQ listing requirements. 12

Discount in equation (5) corresponds to one minus the Offer price/Market price ratio in Wruck’s (1989) study.

13

Hertzel and Smith’s (1993) and Wruck’s (1989) samples also include private placements that appeared to occur at

a premium. Based on discussions with investment bankers, I suspect that the calculated premia might reflect a measurement problem. If the privately offered shares are priced before the initial announcement date (as sometimes happens) and the market price subsequently decreases sufficiently, the issue will appear to be priced at a premium when the new issue price is compared to the market price just prior to the announcement. 14

Hertzel and Smith (1993) measure the discount relative to the share price 10 days after the private placement

announcement date. I measure the discount relative to the closing share price immediately prior to the pricing announcement date, which seems more appropriate for calculating the transferability discount for two reasons. First, the issuer and investors can renegotiate the offering price, size of the issue, and other terms right up to the private placement closing date, and under the securities laws, the terms of the offering must be promptly disclosed publicly once they have been finalized. Second, market participants express the discount relative to the freely traded share price, and a contemporaneous market price is most appropriate for such a comparison. 15

The securities laws do not require public disclosure until the firm has obtained definitive purchase commitments.

See Dresner and Kim (2006), chapter 5. 16

Brown and Warner (1980) describe the event-study procedures and statistical tests of significance used in this

paper. 17

The percentage of positive CARs is significantly less than 50 percent for five of the eight windows. The

percentage is only 38.52 percent for (-1, 0), which is significant at the 1 percent level.

62

18

The firm can enhance the credibility of this signal by filing a registration statement with the SEC by the private

placement closing date (Morrison & Foerster, 2006). Such an arrangement is typical with Rule 144A private placements. 19

Table 5 considers only those private placements in which shares were sold at a discount.

20

I also performed a third set of regressions to test whether information about the offering that comes into the

market before the completion announcement date, either because the issuer announces the offering before it is priced (about 1 case in 4) or because of the issuer’s marketing efforts, might affect the magnitude of the discount. The regressions using the discount calculated based on the closing market price 10 days prior to the offering date yielded results that are similar to but statistically weaker than the results reported in the paper. Details are available upon request from the author. 21

I explain in Section VI why it may be more appropriate in some cases to model transfer restrictions as an average-

strike put option. 22

The implied volatility obtained from publicly traded options would be preferable to an historical volatility but

only 21 of the stocks in the sample had exchange-traded options around the time of the private placements and none of these were LEAPS. 23

I rescaled the estimated volatility linearly by mapping volatilities between 90 percent and 540 percent (the

maximum estimated volatility) to between 90 percent and 120 percent. The 120 percent upper limit is arbitrary. When I varied it between 100 percent and 150 percent and reran the regressions, I obtained qualitatively similar results to those reported in the paper. Details are available form the author. 24

The discount might also tend to vary inversely with Rate to the extent the nonmarketable stock’s higher total

return (the riskless rate in a risk-neutral world) partially compensates for the opportunities missed due to the stock’s marketability restrictions. This compensation reduces the portion of the opportunity cost that must be covered by the discount. 25

Log (1 + sales), one plus the latest fiscal year’s total sales measured in millions, could also be used to proxy for

the greater information costs and greater difficulty in assessing the prospects of early-stage companies where

63

revenue is typically small. I add one to avoid taking the logarithm of zero. In my sample, 33 of the firms had sales under $1 million and seven had zero sales in the latest fiscal year. I also reran the regressions with Log (1 + sales) to proxy for the greater information asymmetry costs and greater difficulty in assessing the prospects of smaller firms. I obtained results similar to those reported for the regressions including Log (proceeds). However, because of the strong positive correlation between sales and gross proceeds, Log (1+sales) will also partly reflect any economies of scale in information gathering. 26

McConnell and Servaes (1990) document a significant positive relationship between firm value and the

percentage of institutional ownership, and Brous and Kini (1994) find a significant positive relationship between announcement-period abnormal stock returns and the level of institutional ownership. See also Brickley, Lease, and Smith (1988) and Jarrell and Poulsen (1987). These findings are consistent with the efficient-monitoring hypothesis (Pound (1988)): Higher levels of institutional ownership lead to more effective monitoring by outside investors, including the use of proceeds from the new issue. 27

Brickley, Coles, and Terry (1994) find significantly positive abnormal returns among poison-pill-adopting firms

when outside directors comprise a majority on the board, but significantly negative returns when outside directors are a minority. Brickley and James (1987), Byrd and Hickman (1992), Rosenstein and Wyatt (1990), and Weisbach (1988) furnish additional empirical evidence of the link between the proportion of outside directors and shareholder wealth. 28

The effect of insider ownership is complex. Wruck (1989) finds that changes in firm value around the date of the

private sale of common stock are positively related to changes in ownership concentration when concentration is high (insiders own 25 percent or more of the common stock after the sale) or low (insiders own 5 percent or less) but that the relationship is negative when ownership concentration is moderate (insiders own between 5 percent and 25 percent).

She concludes that within this middle range, increased ownership concentration promotes

entrenchment of managers. McConnell and Servaes (1990) find that the relationship between firm value and the percentage of insider ownership is positive for increases in the percentage of insider ownership until this percentage reaches approximately 40 percent to 50 percent, at which point the relationship becomes slightly negative, which is

64

consistent with Stulz (1988). Morck, Shleifer, and Vishny (1988) also note the tendency for higher levels of management ownership to promote managerial entrenchment. However, Hertzel and Smith (1993) do not detect a statistically significant relationship between the discount and either ownership concentration or the change in ownership concentration (see their Table VI). I did not find a significant relationship in my overall sample or in sub-samples based on less than 5 percent, between 5 and 25 percent, or greater than 25 percent insider ownership. 29

The book-to-market ratio is used instead of the market-to-book ratio because it is better behaved when there are

near-zero equity market values, as there are in my sample. 30

Lehn, Netter, and Poulsen (1990) use the market-to-book ratio as a proxy for Tobin’s q; McLaughlin, Safieddine,

and Vasudevan (1996) interpret Tobin’s q as a proxy for the firm’s growth opportunities (Tobin’s q > 1 signifying a high-growth firm); and Spiess and Affleck-Graves (1995) find that high-growth firms tend to be more prone to overvaluation than low-growth, mature firms. 31

Consistent with this conjecture, the Spearman correlation coefficient between Book/Market and Discount (10

days after) was 0.118 with a p-value of 0.066 whereas the Spearman coefficient for Discount (day prior) was 0.019 with a p-value of 0.77. 32

The costs of information gathering and the degree of difficulty in assessing the issuer’s value are also likely to be

greater, the weaker the issuer’s financial condition. Book/Market may also proxy for the financial condition of the issuer at the time of the offering. 33

Only 12 of the firms had declared a cash dividend within the 12 months immediately preceding the private

placement. 34

This ability could be due to valuable private information regarding the issuing company's future prospects. Such

shareholders would presumably time their sales of unrestricted shares so as to maximize the sales proceeds. Thus, Longstaff’s (1995) model can also be interpreted to apply to insiders with valuable private information, such as senior executives. Many publicly traded companies prohibit their executives from buying or selling shares except during limited periods, as for example, a brief period commencing a few days following an earnings announcement. Longstaff's model could be used to measure the impact of such blackout period restrictions.

65

35

For empirical evidence, see Levy (1992) and the references therein. Beaulieu, Abu-Dayya, and McLane (1995)

(BAM) describe four methods for analytically approximating the cumulative distribution function of a random variable that is the sum of n i.i.d. lognormal random variables and compare these approximations to a numerical simulation of the actual distribution. They do not find that any one approximation dominates the other.

66

Marketability Discounts With and Without Special Timing Ability 100 % 90

Percentage Discount

80 70 60 50 40 30 20 10 0

0

.25

.50

.75

1

2

3

4

Length of Restriction Period Upper Bound Without (σ = 0.2) Upper Bound Without (σ = 0.3) Upper Bound Without (σ = 0.4)

Upper Bound With (σ = 0.2) Upper Bound With (σ = 0.3) Upper Bound With (σ = 0.4)

Figure 1. Comparison of the Marketability Discounts for Investors With and Without Special Timing Ability. The figure compares the upper bound on the marketability discount implied by Longstaff’s (1995) model, which assumes perfect timing ability (Upper Bound With), and the upper bound on the discount obtained from equations (14) and (15), which assumes no special timing ability (Upper Bound Without), when σ = 0.2, σ = 0.3, σ = 0.4. Since Longstaff’s model assumes a non-dividend-paying stock, q is set to zero in equation (14).

5

Panel A. T = 2 Years 1.00

Empirical Predicted Discount

0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Model Predicted Discount Discount (t - 1)

Discount (t + 10)

Empirical = Predicted

Panel B. T = 1 Year 1.00

Empirical Predicted Discount

0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Model Predicted Discount Discount (t - 1)

Discount (t + 10)

Empirical = Predicted

Figure 2. Empirical Predicted Discount Versus Model Predicted Discount. Panel A of this figure plots the linear equations corresponding to Panel C.1 in Table 16, and Panel B plots the linear equations corresponding to Panel C.2 in Table 16.

Table 1 Sample Descriptive Statistics The letter stock sample consists of 244 private placements by NYSE, AMEX, NASDAQ, and OTC firms between April 1, 1991 and February 1, 2005. Market value was obtained from Bloomberg L.P. and is measured as the closing price on the day immediately preceding the announcement for NYSE, AMEX, and NASDAQ-quoted stocks and as the average of the closing bid and ask prices for OTC stocks whose shares are not quoted in NASDAQ. The number of shares outstanding prior to the offering and the issuer’s assets, sales, net income, and cash flow as of the latest fiscal year-end were obtained from Compustat. The gross proceeds and number of shares issued were obtained from Bloomberg. The percentage discount was calculated from equations (14) and (15) using the closing prices on the day prior to the offering date and 10 trading days after the offering date, respectively. Panel A: Listing Information By Exchange: All Observations Discounts Only

NYSE 13 9

AMEX 19 17

NASDAQ NMa 130 109

NASDAQ SCb 21 16

OTC 36 33

Pink Sheets 25 21

Total 244 205

Maximum $2,460.96 18,170.30 1,986.74 161.36 356.88

Standard Deviation $336.47 1,230.47 190.85 46.07 24.39

Panel B: Chronological Distribution Year 1991 1992 1993 1994 1995 1996 1997c 1997d 1998 1999 2000 2001 2002 2003 2004 2005 Total

All Observations 1 8 14 8 8 8 5 2 10 17 32 31 27 32 33 8 244

Discounts Only 0 7 14 8 8 8 4 2 7 14 24 26 24 24 28 7 205

Panel C: Descriptive Statistics for the Issuers

Market value of equity (millions) Total assetse (millions) Total salese(millions) e Net income (millions) Cash flow from operationse (millions) a

N 244 244 244 244 244

Mean $186.01 216.16 65.33 -11.73 2.30

Median $86.75 41.82 13.18 -4.44 0.10

Minimum $0.06 0.24 0.00 -543.30 -33.36

Nasdaq National Market Nasdaq Small Cap Market c Prior to February 20, 1997 when the SEC modified Rule 144 by shortening the resale-restriction period. d Includes private placements after February 20, 1997. e For the latest fiscal year immediately preceding the offering. b

Table 2 Description of the Private Equity Placements The letter stock sample consists of 244 private placements by NYSE, AMEX, NASDAQ, and OTC firms between April 1, 1991 and February 1, 2005. Market value was obtained from Bloomberg L.P. and is measured as the closing price on the day immediately preceding the announcement for NYSE, AMEX, and NASDAQ-quoted stocks and as the average of the closing bid and ask prices for OTC stocks whose shares are not quoted in NASDAQ. The number of shares outstanding prior to the offering and the issuer’s assets, sales, net income, and cash flow as of the latest fiscal year-end were obtained from Compustat. The gross proceeds and number of shares issued were obtained from Bloomberg. The percentage discount was calculated from equations [ ] and [ ] using the closing prices on the day prior to the offering date and 10 trading days after the offering date, respectively. Panel A: Gross Proceeds and Fraction Issued Pre Feb 1997 N Gross proceeds b (millions) c

Fraction issued (%)

Mean

a

Post Feb 1997

Standard Minimum Maximum Deviation

Median

Mean

Comparative Statistics

Standard Minimum Maximum Deviation

Median

t-statistic

z-statistic F- statistic

244

12.87

8.56

0.01

98.08

16.18

17.12

8.92

0.01

144.00

25.45

-1.03

-1.47

0.40

244

15%

12%

0%

70%

13%

13%

11%

0.1%

173%

16%

0.63

0.72

0.69

Panel B: Average Percentage Discount for the Full Sample g Pre Feb 1997a Time Period:

Comparative Statistics

Post Feb 1997

Standard Median Minimum Maximum Deviation 20.00 -26.00 68.00 19.40

Dayt-1d

N 244

Mean 21.00

Dayt+10e

244

21.61

23.48

-104.16

77.08

27.21

18.70

16.87

-126.21

85.68

27.19

0.74

0.68

1.00

f

244

0.01

-0.85

-18.15

18.55

7.57

-1.72

-1.52

-175.81

68.43

19.27

0.92

1.96

0.98

H & S Discount AAR

Mean 15.94

Standard Median Minimum Maximum Deviation 12.00 -79.00 85.00 25.43

t-statistic z-statistic F- statistic 0.81 1.55 0.68

Panel C: Average Percentage Discount for Shares Placed at a Discount g Pre Feb 1997a Time Period:

Post Feb 1997

Standard Median Minimum Maximum Deviation 20.00 4.00 68.00 16.63

Dayt-1d

N 205

Mean 24.98

Dayt+10e

202

27.92

25.07

1.67

77.08

18.99

27.17

24.16

0.77

85.68

19.21

0.66

0.33

1.46

f

103

7.03

4.86

1.11

18.55

5.62

10.20

6.41

0.19

68.43

12.29

0.75

1.96

4.79

H & S Discount AAR

Mean 22.47

Comparative Statistics

Standard Median Minimum Maximum Deviation 16.00 0.00 85.00 20.04

a

Prior to February 20, 1997 when the SEC modified Rule 144 by shortening the resale-restriction period.

b

Before deducting the private placement agent's fee and other expenses of the offering.

c

Calculated as the number of shares placed divided by the sum of the number of shares placed and the number outstanding prior to the offering.

d

Calculated from equation (1)

e

Calculated from equation (2)

f

Indicates Hertzel and Simth's (1993) Discount-Adjusted Abnormal Return.

g

Negative value indicates a premium.

t-statistic z-statistic F- statistic 1.36 0.86 0.69

Table 3 Cumulative Abnormal Returns Around the Announcements of Private Placements of Restricted Stock (page 1 of 2) Mean and median cumulative abnormal returns (CARs) are calculated using a market model and the Scholes-Williams (1977) procedure to estimate beta. % Positive is the percentage of positive CARs. The sample includes 244 private placements of letter stock that took place in the U.S. between April 1, 1991 and February 1, 2005. The initial announcement date (the earlier of the offering announcement date, when one occurs, and the completion announcement date) is day 0 in Panels A, C, and E, and the completion announcement date is day 0 is Panels B and D. There were 68 private placements in which the announcement of the offering (or the intention to offer) preceded the completion announcement giving the pricing and other terms of the offering, and 176 private placements for which the two announcements coincided. In all five panels, the comparison period extends from 120 trading days through 21 trading days prior to the initial announcement date. The tstatistic for the difference of means test for the Mean CAR, the z-statistic for the Wilcoxon signed rank test for the median CAR, and the z-statistic for % Positive are given in parentheses.

Panel A: Initial Announcementd Period Relative to the Announcement Day (Day 0) N Overall Results Mean CAR

(-10,0)

(-5,0)

(-3,0)

(-1,0)

(-1,1)

(-3,3)

(-5,5)

(-10,10)

244 1.92

t-statistic Median CAR z-statistic % Positive z-statistic

0.14

-0.24

-0.71

0.71

1.85

2.29 c

5.87

(1.23)

(0.13)

(-0.31)

(-1.12)

(0.85)

(1.49 )

(1.63 )

(2.53a)

-0.94

-1.18

-1.07

-1.22

-1.42

-1.19

0.35

1.90

(-0.220)

(-0.894)

(-1.246)

(-1.739 )

(-0.396)

(-0.135)

(0.103)

(1.800b)

47.54

44.26

42.62

38.52

42.62

45.90

51.23

53.69

(0.384)

(1.152)

(-0.768)

b

(-1.793 )

b

(-2.305 )

b

c

a

(-3.585 )

b

(-2.305 )

c

(-1.280 )

Panel B: Completion Announcementd Period Relative to the Announcement Day (Day 0) N Overall Results Mean CAR

(-10,0)

(-5,0)

(-3,0)

(-1,0)

(-1,1)

(-3,3)

(-5,5)

(-10,10)

244 2.00 c

0.43

-0.22

-0.74

0.69

1.63

1.96 c

5.48

(1.29 ) -0.61

(0.43) -1.20

(-0.28) -1.25

(-1.20) -1.40

(0.82) -1.71

(1.32 ) -1.83

(1.39 ) -0.82

(2.38a) 0.46

z-statistic % Positive

(-0.198) 48.36

(-0.669) 45.49

(-1.224) 39.34

(-1.769b) 36.89

(-0.410) 41.80

(-0.187) 43.85

(-0.163) 47.54

(0.017) 50.82

z-statistic

(-0.512)

(-1.408c)

(-3.329a)

(-4.097a)

(-2.561a)

(-1.921b)

(-0.768)

(0.256)

t-statistic Median CAR

c

Panel C: Offering Announcement that Precedes a Completion Announcementf Period Relative to the Announcement Day (Day 0) N Overall Results Mean CAR t-statistic Median CAR z-statistic % Positive z-statistic

(-10,0)

(-5,0)

(-3,0)

(-1,0)

(-1,1)

(-3,3)

(-5,5)

(-10,10)

68 -2.50

-2.17 c

-1.70 c

-0.75

-0.19

-1.24

-1.26

-2.48

(-1.22)

(-1.48 )

(-1.52 )

(-1.01)

(-0.22)

(-0.85)

(-0.64)

(-0.84)

-2.22 (-1.778b)

-1.35 (-1.860b)

-2.10 (-1.872b)

-1.27 (-1.689b)

-0.60 (-1.174)

-1.26 (-1.604c)

0.02 (1.477c)

-0.54 (-1.600c)

44.12

38.24

39.71

39.71

47.06

42.65

50.00

50.00

(-0.970)

(-1.940b)

(-1.698b)

(-1.698b)

(-0.490)

(-1.213)

(0.000)

(0.000)

Table 3 Cumulative Abnormal Returns Around the Announcements of Private Placements of Restricted Stock (page 2 of 2) Panel D: Completion Announcement that Follows an Offering Announcementf Period Relative to the Announcement Day (Day 0) N Overall Results Mean CAR

(-10,0)

(-5,0)

(-3,0)

(-1,0)

(-1,1)

(-3,3)

(-5,5)

(-10,10)

68

t-statistic Median CAR

-2.23

-1.10

-1.63

-0.87

-0.25

-2.02

-2.45

-3.86

(-1.16)

(-0.77)

(-1.36c)

(-1.41c)

(-0.28)

(-1.43c)

(-1.26)

(-1.39c)

-0.94

-1.36

-2.40

-1.89

-1.72

-2.78

-1.94

-4.82

b

(-1.752 )

z-statistic % Positive z-statistic

c

(-1.557 )

b

(-1.825 )

b

(-1.840 )

(-1.221)

b

(-1.847 )

b

(-1.792 )

(-1.836b)

47.06

42.65

27.94

33.82

44.12

35.29

36.76

39.71

(-0.485)

(-1.213)

(-3.638a)

(-2.668a)

(-0.970)

(-2.425a)

(-2.183b)

(-1.698b)

(-5,5)

(-10,10)

Panel E: No Pre Announcemente Period Relative to the Announcement Day (Day 0) N Overall Results Mean CAR

(-5,0)

(-3,0)

(-1,0)

(-1,1)

(-3,3)

176 3.63

1.02

0.33

-0.69

1.05

3.04

3.66

9.09

(1.81b) -0.47

(0.79) -1.17

(0.34) -0.97

(-0.84) -1.17

(0.95) -1.71

(1.88b) -1.05

(2.05b) 0.69

(3.06a) 2.83

z-statistic % Positive

(-0.071) 48.86

(-0.427) 46.59

(-0.732) 43.75

(-1.598c) 38.07

(-0.340) 40.91

(-0.060) 47.16

(0.040) 51.70

(0.002) 55.11

z-statistic

(-0.302)

(-0.905)

(-1.658b)

(-3.166a)

(-2.412a)

(-0.754)

(0.452)

(1.357c)

t-statistic Median CAR

a,b,c

(-10,0)

denote significance (based on a one-tailed test) at the 1%, 5%, and 10% levels, respectively.

d

The initial announcement of the private placement. Of the 244 announcements, 68 specified an intention to offer common stock privately, and the other 176 indicated specific pricing terms to which investors had agreed.

e

There were 176 private placements for which the initial announcement coincided with the completion announcement.

f

There were 68 private placements for which the completion announcement followed a separate offering announcement.

Table 4 Cumulative Abnormal Returns Around the Announcements of Private Placements for Positive Momentum and Negative Momentum Stocks (Page 1 of 2) Mean and median cumulative abnormal returns (CARs) are calculated using a market model and the Scholes-Williams (1977) procedure to estimate beta. % Positive is the percentage of positive CARs. The sample includes 244 private placements of letter stock that took place in the U.S. between April 1, 1991 and February 1, 2005. The initial announcement date (the earlier of the offering announcement date, when one occurs, and the completion announcement date) is day 0 in Panels A, C, and E, and the completion announcement date is day 0 is Panels B and D. There were 68 private placements in which the announcement of the offering (or the intention to offer) preceded the completion announcement giving the pricing and other terms of the offering, and 176 private placements for which the two announcements coincided. In all five panels, the comparison period extends from 120 trading days through 21 trading days prior to the initial announcement date. The tstatistic for the difference of means test for the Mean CAR, the z-statistic for the Wilcoxon signed rank test for the median CAR, and the z-statistic for % Positive are given in parentheses. Panel A: Initial Announcementd Period Relative to the Announcement Day (Day 0) N Positive Momentum Mean CAR t-statistic Negative Momentum Mean CAR

(-10,0)

(-5,0)

(-3,0)

(-1,0)

(-1,1)

(-3,3)

(-5,5)

(-10,10)

-1.90

-1.46

-1.51

-0.95

-0.43

-2.09

-2.19

-2.96

b

c

b

c

139 (-1.15)

(-1.22)

(-1.85 )

(-1.32 )

(-0.41)

(-1.85 )

(-1.42 )

(-1.23)

6.97

2.25

1.45

-0.39

2.21

7.07

8.22

17.55

a

c

b

a

a

105 (2.44 ) 0.0039

t-statistic P-Value (Pos v. Neg)

(1.29 ) 0.0403

(1.05) 0.0331

(-0.35) 0.3352

(1.67 ) 0.0574

(2.98 ) 0.0003

(3.37 ) 0.0002

(4.30a) 90 Days Not Registered Total

≤ 30 Days Discount (day prior) Discount (10 days after) > 90 Days Discount (day prior) Discount (10 days after)

Panel A: Number of Days to Registration by Type of Investor Institutional Strategic Related Other 37 2 1 25 9 0 1 5 6 0 0 5 14 3 2 17 27 7 19 25 93 12 23 77

Total 65 15 11 36 78 205

Panel B: Average Discount Strategic Related N=2 N=1 27.35 12.13 16.36 8.08

Other N = 25 15.73 13.62

Total N = 65 11.53 11.55

Other N = 17 24.49 23.31

Total N = 36 26.40 23.58

Institutional N = 37 16.38 15.04 Institutional N = 14 19.87 17.27

Strategic N=3 20.30 30.25

Related N=2 32.82 28.63

Panel C: Difference in Average Discount Between Registration within 30 Days and More than 90 Days Institutional Strategic Related Other Total

b

Discount (day prior)

3.49

-7.05

20.69

8.76b

14.87b

Discount (10 days after)

2.23

13.89

20.55

9.69

12.03b

denotes significance at the 5% level.

Table 6 Cumulative Abnormal Returns Around the Initial Announcement of Private Placements of Restricted Stock Mean and median cumulative abnormal returns (CARs) are calculated using a market model and the Scholes-Williams (1977) procedure to estimate beta. % Positive is the percentage of positive CARs. The sample includes 244 private placements of letter stock that took place in the U.S. between April 1, 1991 and February 1, 2005. The initial announcement date (the earlier of the offering announcement date, when one occurs, and the completion announcement date) is day 0 in Panels A and C. The comparison period extends from 120 trading days through 21 trading days prior to the initial announcement date. The t-statistic for the difference of means test for the Mean CAR, the zstatistic for the Wilcoxon signed rank test for the median CAR, and the z-statistic for % Positive are given in parentheses.

Overall Results Mean CAR

Panel A: Stock Registered within 30 Days Period Relative to the Announcement Day (Day 0) N (-10,0) (-5,0) (-3,0) (-1,0) (-1,1) (-3,3) (-5,5) 65 -1.50 -2.90 -2.19 -1.65 -1.03 -1.07 -1.21

0.24

t-statistic Median CAR

(-0.69) -1.95

(-2.04b) -2.13

(-2.03b) -2.04

(-2.08b) -1.41

(-1.11) -1.74

(-0.63) -1.36

(-0.56) 0.36

(0.07) -1.26

z-statistic % Positive

(-0.97) 45.31

(-2.02b) 35.94

(-2.22b) 35.94

(-2.10b) 35.94

(-1.27) 43.75

(-0.15) 43.75

(0.00) 53.13

(0.15) 48.44

z-statistic

(-0.75)

(-2.25b)

(-2.25b)

(-2.25b)

(-1.00)

(-1.00)

(0.50)

(-0.25)

Overall Results Mean CAR t-statistic Median CAR z-statistic % Positive z-statistic

Panel B: Stock not Registered within 90 Days Period Relative to the Announcement Day (Day 0) N (-10,0) (-5,0) (-3,0) (-1,0) (-1,1) (-3,3) (-5,5) 114 1.14 0.02 -0.43 -0.33 -0.53 0.01 0.34 (0.35) (0.01) (-0.34) (-0.34) (-0.56) (0.01) (0.15) -0.88 -1.16 -1.10 -0.99 -1.94 -3.61 -0.88 (-0.05) (-0.23) (-0.46) (-0.86) (-1.28) (-0.27) (-0.24) 50.00 44.44 41.67 44.44 44.44 41.67 44.44 (0.00) (-0.67) (-1.00) (-0.667) (-0.667) (-1.00) (-0.67)

Panel C: Test of Differences in Mean and Median Period Relative to the Announcement Day (Day 0) (-10,0) (-5,0) (-3,0) (-1,0) (-1,1) (-3,3) (-5,5) -2.64 -2.92 -1.76 -1.32 -0.50 -1.08 -1.55 Difference in Mean (Reg. v. Not Reg.) t-statistic (-0.70) (-1.26) (-1.02) (-1.03) (-0.35) (-0.42) (-0.46) Difference in Median (Reg. v. Not Reg) z-statistic a,b,c

(-10,10)

(-10,10) 4.54 (1.07) -3.60 (-0.31) 47.22 (-0.33)

(-10,10) -4.29 (-0.77)

-1.07

-0.97

-0.94

-0.42

0.21

2.24

1.24

2.33

(-0.38)

(-0.84)

(-0.70)

(-0.34)

(0.32)

(0.39)

(0.25)

(0.35)

denote significance (based on a two-tailed test) at the 1%, 5%, and 10% levels, respectively.

Table 7 Relationship Between Private Placement Discount and Firm Size and Placement Gross Proceeds The table shows the relationship between the gross proceeds of the private placement and the market value of the firm's equity on the one hand and Discount (day prior) and Discount (10 days after) on the other. The private placement discount decreases for larger firms and for larger private placements.

Discount (day prior) Size Range

N

Mean

Market Value of Equity (Millions)

≤ $10.0 10.0 - 25.0 25.0 - 75.0 75.0 - 100.0 > 100.0

26 20 50 14 99

28.15 31.20 24.52 20.29 19.66

Gross Proceeds

≤ $1.0 1.0 - 5.0 5.0 - 10.0 10.0 - 20.0 > 20.0

29 54 29 38 59

33.97 24.98 24.55 19.21 17.56

Spearman Coefficient (p-Value)

Discount (10 days after) Spearman Coefficeint (p-Value)

N

Mean

-0.118 (0.0880)

25 18 48 16 95

34.43 36.57 29.89 26.00 22.65

-0.218 (0.0018)

-0.208 (0.0025)

27 52 31 40 52

39.57 30.61 25.07 20.88 24.03

-0.227 (0.0011)

Table 8 Cross-Sectional Regression Results Regression model 1 is

(7)

Discount (day prior) = a0 + a1 Post + a2 Volatility * T + a3 Yield + a4 Time + a5 Rate

which includes only the four transfer restriction variables. Regression model 2 is Discount (day prior) = a0 + a1 Post + a2 Log(proceeds) + a3 Fraction + a4 Direct + a5 Exchange

(8)

which includes only information and ownership concentration variables. Regression model 3 is (9)

Discount (day prior) = a0 + a1 Post + a2 Volatility * T + a3 Yield + a4 Time + a5 Rate + a6 Log(proceeds) + a7Fraction + a8 Direct + a9 Exchange

which includes the four transfer restriction variables plus four information and ownership concentration variables, Log(proceeds), Fraction, Direct, and Exchange. I include Book/Market, Registration Rights, and Registered Stock as control variables in each model. Discount(day prior) measures the percentage discount relative to the closing market price of the issuer’s registered common stock on the trading day immediately preceding the pricing announcement date. Post is one for those issuers whose offering occurred after [January 1998]. Volatility is the annualized standard deviation of the total return of the issuer’s common stock as estimated by the GARCH model. Volatilities above 90% were rescaled to between 90% and 120%. Volatility is interacted with

T where T is the length of the

Rule 144 lockup period (T=2 prior to February 1997 and T=1 thereafter). Yield is the annualized dividend yield based on the latest quarterly cash dividend. Time is the ratio of the number of shares offered to the common stock’s trading volume during the three-month period ending on the last trading day immediately preceding the initial announcement date. Rate is the interest rate on one-year (post-February 1997 offerings) or two-year (pre-February 1997 offerings) Treasury notes as of the pricing announcement date. Log(proceeds) is the log of the gross proceeds of the offering. Fraction is the number of shares placed divided by the sum of the number of shares placed and the number outstanding prior to the offering. Direct is one minus the fraction of directors that are also managers. Exchange is one for those companies listed on the NYSE, American Stock Exchange, Nasdaq National Market or Nasdaq Small Cap Market and is zero otherwise. Book/Market is the book value of equity divided by the market value of equity. Registration Rights is one for those offerings that provide for Piggyback and/or Demand Rights and is zero otherwise. Registered Stock is one for those stocks that the firm registered within 45 days of the offer date. I also run the three models using Discount (10 days after) as the dependent variable. The regressions are fitted using ordinary least squares. The sample includes 205 U.S. private placements between April 1, 1991 and February 1, 2005. Fourteen observations had to be dropped from the regressions that include the variable Direct because the fourteen firms’ historical proxy statements could not be obtained. The predicted sign is provided next to each variable. All t-statistics (in parentheses below coefficients) are calculated using heteroskedasticity-consistent standard errors. In addition to the F statistic for each regression, the Partial F statistic is reported when the information and equity ownership concentration variables Direct, Log(proceeds), Fraction, and Exchange are added to Model 1 (Partial F(In/Own)) and when the transfer restriction variables are added to Model 2 (Partial F(Transfer)).

Table 8 Cross-Sectional Regression Results

Dependent Variable Number of Observations Intercept

Post (-)

Volatility * T (+)

Model 1 Discount Discount (day prior) (10 days after)

Model 3

Discount (10 days after)

Discount (day prior)

Discount (10 days after)

191

191

191

205

205

191

-0.307 (-0.0482)

8.612 (1.0779)

62.477

64.647

(5.1467 a)

(4.3976 a)

24.673 (1.5350)

(1.8277 c)

2.835 (0.9095)

3.732 (0.9060)

-3.255 (-1.2750)

-1.344 (-0.3981)

1.324 (0.4222)

1.419 (0.3513)

0.248

0.195

0.188

0.141

a

(4.8816 ) Time (+)

Model 2 Discount (day prior)

a

a

(3.2525 )

(3.4525 )

36.527

(2.1986 b)

0.065

0.078

0.039

0.049

(7.9654 a)

(8.1028 a)

(2.2218 b)

(2.4893 b)

Yield (-)

0.266 (1.3298)

0.239 (1.0370)

0.266 (1.3953)

0.246 (1.1319)

Rate (+)

0.136 (0.1838)

-0.714 (-0.7790)

0.676 (0.8932)

0.113 (0.1278)

9.600 (1.5788)

(1.6584 c)

Direct (+)

6.008 (0.9450)

Log (proceeds) (-)

Fraction (+)

Exchange (-)

-2.609

-3.320

-1.857

-2.614

(-3.1976 a)

(-2.0347 b)

(-2.4699 b)

49.402

59.028

29.782

39.481

(3.5039 a)

(3.8225 a)

(1.8044 c)

(2.2873 b)

-8.067

-3.557 (-0.8130)

-4.265 (-1.1194)

-0.483 (-0.1106)

(-2.0497 )

Registration Rightsd (-)

13.589

(-2.8584 a)

b

Book to Market (+)

10.885 (1.3707)

0.097

0.326

0.134

0.384

0.111

0.364

(2.7375 a)

(2.2951 b)

(3.5032 a)

(2.2006 b)

(2.8013 a)

(2.0106 b)

-0.694 (-0.2571)

-5.598 (-1.5733)

0.428 (0.1284)

-2.532 (-0.6932)

0.693 (0.2353)

-2.436 (-0.7280)

-6.637

-8.633

-5.619

-6.498

-4.871

-6.333

(-2.8697 a)

(-2.8533 a)

(-2.2241 b)

(-2.1021 b)

(-1.9926 b)

(-1.9968 b)

R2

0.2489

0.2273

0.2428

0.2526

0.3108

0.2802

Adjusted R2

0.2182

0.1957

0.2095

0.2198

0.2644

0.2317

MSE

269.019

429.130

275.394

404.676

250.654

389.741

F-value

8.12a

7.21a

7.30a

7.69a

6.69a

5.77a

White's Test

2.38a

3.75a

1.25

6.23a

2.69a

4.22a

Durbin-Watson Statistic

2.07

2.10

2.10

2.09

2.22

2.15

Partial F(In/Own)f

6.93a

8.27a

Partial F(Transfer)g

4.39a

1.71

Registered Stocke (-)

a,b,c

denote significance at the 1%, 5%, and 10% levels, respectively.

d

Registration Rights are defined as piggyback and/or demand registration rights.

e

The firm registered the stock within 45 days following the offer date.

f

The Partial F statistic from adding the information variables Direct, Log(proceeds), Fraction, and Exchange to Model 1.

g

The Partial F statistic from adding the transfer restriction variables Post, Volatility, Time, Yield, and Rate to Model 2.

Table 9 Impact of the Type of Private Equity Buyer on the Size of the Discount This table shows the impact of the type of private equity buyer on the size of the average discount and compares the average actual discount to the discounts predicted by the average-strike and lookback put option models for different trypes of private equity buyers. The Financial Investors category includes those stocks where the issuer announced that the shares were placed with institutional investors. The Strategic Investors category includes those stocks where the issuer announced that the shares were sold to another corporation that could be identified as a strategic partner The Insiders category includes those stocks where the issuer announced that the shares were sold to someone related to the issuer. The t-statistic is given in parenthesis below each difference in means.

N

Full Sample

Financial Investors

Strategic Investors

Insiders

Other Investors

205

93

12

23

77

Strategic v. Financial (t-statistic1)

Insiders v. Financial (t-statistic1)

Panel A: Average-Strke Put and Lookback Put Model Discounts Average Discounts: Average-Strike Put Option Model

22.493

21.961

24.973

22.190

22.840

3.012 (1.1684)

0.229 (0.1119)

Lookback Put Option Model

81.153

82.436

79.874

83.670

79.050

-2.561 (-0.3893)

1.234 (0.2418)

1.414 (0.2304)

-1.632 (-0.3532)

4.511 (0.4692)

2.279 (0.1263)

Difference

-58.660

-60.475

-54.902

-61.480

-56.210

(-33.3864a)

(-25.8006a)

(-7.2060a)

(-10.7058a)

(-17.9931a)

Panel B: Discounts (day prior) Average Actual Discount

Average-Strike Put Option Model Average Discount - Average Actual Discount

Lookback Put Option Model Average Discount - Average Actual Discount

22.423

21.671

23.086

20.039

23.940

0.070 (0.0472)

0.290 (0.1291)

1.887 (0.2928)

2.151 (0.4690)

-1.100 (-0.4681)

58.729

60.764 a

(28.5050 )

56.789 a

(20.1173 )

a

(6.2039 )

63.630 a

(9.6398 )

55.110 a

(16.4358 )

Panel C: Discounts (10 days after) Average Actual Discount Average-Strike Put Option Model Average Discount - Average Actual Discount

Lookback Put Option Model Average Discount - Average Actual Discount

a,b,c 1

denote significance at the 1%, 5%, and 10% levels, respectively.

t-tests based on two-tailed test.

23.787

20.003

24.514

22.282

24.668

-1.294 (-0.7322)

1.958 (0.1291)

0.458 (0.0793)

-0.092 (-0.0170)

-1.828 (-0.7065)

57.365

62.432

55.360

61.387

54.382

(25.2316a)

(20.1773a)

(6.3646a)

(8.5067a)

(15.4341a)

Table 10 Importance of the Type of Equity Private Placement Buyer Base Model is Discount (day prior) = a0 +a1 Post + a2 Volatility * T + a3 Time + a4 Yield + a5 Rate + a6 Direct +

(9)

a7 Log(Proceeds) + a8Fraction + a9 Exchange + a10 Book/Market + a11 Rights + a12 Registered which includes the four transfer restriction variables plus four information and ownership concentration variables, Log(Proceeds), Fraction, Direct, and Exchange. I include Post, Book/Market, Registration Rights, and Registered Stock as control variables in each model. Discount(day prior) measures the percentage discount relative to the closing market price of the issuer’s registered common stock on the trading day immediately preceding the pricing announcement date. Volatility is the annualized standard deviation of the total return of the issuer’s common stock as estimated by the GARCH model. Volatilities above 90% were rescaled to between 90% and 120%. Yield is the annualized dividend yield based on the latest quarterly cash dividend. Time is the ratio of the number of shares offered to the common stock’s trading volume during the three-month period ending on the last trading day immediately preceding the initial announcement date. Rate is the interest rate on one-year (post-February 1997 offerings) or two-year (pre-February 1997 offerings) Treasury notes as of the pricing announcement date. Log(Proceeds) is the log of the gross proceeds of the offering. Fraction is the number of shares placed divided by the sum of the number of shares placed and the number outstanding prior to the offering. Direct is one minus the fraction of directors that are also managers. Exchange is one for those companies listed on the NYSE, American Stock Exchange, Nasdaq National Market or Nasdaq Small Cap Market and is zero otherwise. Book/Market is the book value of equity divided by the market value of equity. Registration Rights is one for those offerings that provide for Piggyback and/or Demand Rights and is zero otherwise. Registered Stock is one for those stocks that the firm registered within 45 days of the offer date. The Investment, Strategic, and Related variables are added to the Base Model as independent variables in three separate regressions. Investment is one for those stocks where the issuer announced that the shares were placed with institutional investors. Strategic is one for those stocks where the issuer announced that the shares were sold to another corporation that could be identified as a strategic partner. Related is one for those stocks where the issuer announced that the shares were sold to someone related to the issuer. I also run the three models using Discount (10 days after) as the dependent variable. The regressions are fitted using ordinary least squares. The sample includes 205 U.S. private placements between April 1, 1991 and February 1, 2005. Fourteen observations had to be dropped from the regressions that include the variable Direct because the fourteen firms’ historical proxy statements could not be obtained. The predicted sign is provided next to each variable. All t-statistics (in parentheses below coefficients) are calculated using heteroskedasticity-consistent standard errors.

Table 10 Importance of the Type of Equity Private Placement Buyer Dependent Variable

Number of Observations Intercept

Post (-)

Volatility * T (+)

Time (+)

Discount (day prior)

Discount (10 days after)

Base Model 191

with Investment 191

with Strategic 191

with Related 191

All Buyers 191

Base Model 191

with Investment 191

with Strategic 191

24.673 (1.5350)

20.823 (1.2846)

24.678 (1.5280)

26.300 (1.5676)

22.420 (1.3333)

36.527 (1.8277 )

27.365 (1.4017)

(1.8223 )

c

(1.6682 )

26.426 (1.3282)

1.324 (0.4222)

2.331 (0.7400)

1.350 (0.4277)

1.345 (0.4254)

2.576 (0.8200)

1.419 (0.3513)

3.815 (0.9241)

1.425 (0.3505)

1.385 (0.3449)

3.754 (0.9010)

c

36.528

with Related 191 33.935 c

All Buyers 191

0.188

0.194

0.191

0.186

0.191

0.141

0.153

0.141

0.145

0.152

(3.4525a)

(3.5330a)

(3.4679a)

(3.3536a)

(3.4024a)

(2.1986b)

(2.4053b)

(2.2043b)

(2.2389b)

(2.3533b)

0.039

0.044

0.039

0.037

0.042

0.049

0.060

0.049

0.052

0.061

(2.2218 )

b

(2.1323 )

b

(2.2560 )

b

(2.0799 )

b

(1.9648 )

c

(2.4893 )

b

(2.1988 )

b

(2.4920 )

b

(2.6569 )

a

(2.2183 )

Yield (-)

0.266 (1.3953)

0.239 (1.2496)

0.271 (1.4168)

0.269 (1.3868)

0.239 (1.2150)

0.246 (1.1319)

0.183 (0.8473)

0.247 (1.1301)

0.240 (1.1004)

0.175 (0.7965)

Rate (+)

0.676 (0.8932)

0.719 (0.9490)

0.651 (0.8564)

0.661 (0.8751)

0.705 (0.9376)

0.113 (0.1278)

0.215 (0.2432)

0.108 (0.1219)

0.137 (0.1530)

0.254 (0.2872)

Direct (+)

9.600 (1.5788)

10.296

9.483 (1.5407)

9.097 (1.4292)

9.692 (1.5171)

13.589

15.245

15.685

(1.6584c)

(1.9470c)

13.563 (1.6414)

14.391

(1.6986c)

(1.7546c)

(1.9688c)

Log (proceeds) (-)

Fraction (+)

-1.857

-1.720

-1.868

-1.899

-1.754

-2.614

-2.288

-2.617

-2.547

-2.250

(-2.0347b)

(-1.8614c)

(-2.0295b)

(-2.0537b)

(-1.8634c)

(-2.4699b)

(-2.2055b)

(-2.4592b)

(-2.3970b)

(-2.1491b)

29.782 c

Exchange (-)

Book to Market (+)

Registration Rightsd (-)

Registered Stocke (-)

b

36.006 b

29.412 c

30.868 c

38.920 b

39.481 b

54.294

39.398

a

b

37.751

53.981

(1.8044 )

(2.2051 )

(1.7863 )

(1.8647 )

(2.4554 )

(2.2873 )

(3.1662 )

(2.2767 )

(2.1717 )

b

(3.1448 )

a

-4.265 (-1.1194)

-4.260 (-1.1188)

-4.168 (-1.0856)

-4.630 (-1.2186)

-4.797 (-1.2617)

-0.483 (-0.1106)

-0.472 (-0.1091)

-0.462 (-0.1057)

0.099 (0.0228)

-0.366 (-0.0858)

0.111

0.105

0.110

0.114

0.108

0.364

0.349

0.364

0.359

0.349

(2.8013a)

(2.5918b)

(2.7533a)

(2.8469a)

(2.5866b)

(2.0106b)

(2.0775b)

(2.0058b)

(1.9818b)

(2.0555b)

0.693 (0.2353)

0.867 (0.2947)

0.731 (0.2481)

0.929 (0.3131)

1.255 (0.4249)

-2.436 (-0.7280)

-2.023 (-0.6113)

-2.427 (-0.7251)

-2.811 (-0.8185)

-2.216 (-0.6511)

-4.871

-4.868

-4.783

-4.870

-4.863

-6.333

-6.327

-6.313

-6.333

-6.435

(-1.9926b)

(-1.9782b)

(-1.9410c)

(-1.9928b)

(-1.9563c)

(-1.9968b)

(-2.0006b)

(-1.9782b)

(-2.0013b)

(-2.0112b)

Investment*Fraction (-)

-16.231

-19.674

(-1.0780)

(-1.3337)

Strategic*Fraction (+)

13.106 (0.2318)

Related*Fraction (+)

-38.633

-31.427 (-0.7712)

b

(-2.2139 )

0.572 (0.0099) -21.194 (-0.5302)

-38.370

b

(-2.1199 ) 2.945 (0.0557)

-16.012 (-0.3004) 33.766 (0.7214)

12.966 (0.2646)

R

0.3108

0.3154

0.3113

0.3125

0.3189

0.2802

0.2976

0.2802

0.2830

0.2985

Adjusted R2

0.2644

0.2651

0.2607

0.2620

0.2605

0.2317

0.2460

0.2274

0.2304

0.2384

MSE

250.654

248.992

250.501

250.051

247.740

389.741

380.327

389.733

388.212

379.846

6.69a

6.27a

6.15a

6.19a

5.46a

5.77a

5.77a

5.30a

5.38a

4.96a

0.59

0.05

0.21

0.34

2.18

0.00

0.35

0.75

2.36a

2.59a

2.96a

2.64a

3.10a

3.97a

4.31a

2.71a

2

F-value Incremental F White's Test a,b,c

2.69

a

denote significance at the 1%, 5%, and 10% levels, respectively. Registration Rights are defined as piggyback and/or demand registration rights. e The firm registered the stock within 45 days following the offer date. d

4.22a

Table 11 Marketability Discounts Equations (14) and (15) are used to calculate the percentage marketability discount for both non-dividend-paying stocks (q = 0) and for stocks that provide a 2% constant percentage dividend yield (q = .02). The range of marketability restriction periods is between 3 months and 5 years, and the range of stock price volatilities is between σ = 0.1 and σ = 0.8. The riskless rate is r = 0.05. Panel A: q = 0 Restriction Period

σ = 0.1

σ = 0.2

σ = 0.3

σ = 0.4

σ = 0.5

σ = 0.6

σ = 0.7

σ = 0.8

3 months

1.41%

1.89%

2.44%

2.99%

3.55%

4.11%

4.67%

5.23%

6 months

2.84

3.81

4.90

6.01

7.12

8.22

9.31

10.38

9 months

4.29

5.75

7.38

9.04

10.69

12.32

13.91

15.45

1 year

5.76

7.71

9.88

12.09

14.27

16.40

18.45

20.42

2 years

11.81

15.76

20.12

24.43

28.56

32.42

35.97

39.15

3 years

18.16

24.18

30.68

36.93

42.69

47.83

52.25

55.93

4 years

24.83

32.95

41.52

49.52

56.56

62.49

67.25

70.88

5 years

31.84

42.08

52.64

62.13

70.09

76.39

81.07

84.32

Panel B: q = 0.02 Restriction Period

σ = 0.1

σ = 0.2

σ = 0.3

σ = 0.4

σ = 0.5

σ = 0.6

σ = 0.7

σ = 0.8

3 months

1.03%

1.57%

2.13%

2.70%

3.27%

3.83%

4.39%

4.95%

6 months

2.07

3.15

4.27

5.40

6.52

7.63

8.72

9.79

9 months

3.11

4.74

6.42

8.11

9.77

11.40

12.98

14.52

1 year

4.17

6.34

8.58

10.81

13.00

15.12

17.17

19.12

2 years

8.46

12.82

17.27

21.58

25.68

29.50

33.00

36.14

3 years

12.87

19.45

26.02

32.22

37.89

42.92

47.24

50.84

4 years

17.41

26.20

34.79

42.64

49.50

55.25

59.86

63.37

5 years

22.08

33.06

43.54

52.77

60.45

66.51

71.00

74.11

Table 12 Test of the Predictive Accuracy of the Average-Strike and Lookback Put Option Models The Mean Actual Discount is calculated from the percentage discount relative to the closing market price of the issuer’s registered common stock on the trading day immediately preceding the pricing announcement date. The Mean Empirical Predicted Discount is calculated by adjusting the actual discounts for the information, ownership concentration, and control variables in Model 3, as shown in equation (17). The Mean Model Predicted Discount is calculated from the lookback put option model in Longstaff (1995) and from the average-strike put option model in equations (14) - (15). Information-intensive placements are characterized by either (a) volatility above the median and log (proceeds) below the median for the overall sample or (b) placed with strategic investors or related investors. Non-informationintensive placements are characterized by (a) volatility below the median and log (proceeds) above the median and (b) not placed with strategic investors or related investors. 58 placements were neither information-intensive nor non-information intensive. Non-Information-Intensive Full Sample Subsample Information-Intensive Subsample 191 78 55 Number of Observations Panel A: Tests Based on the Actual Discount 22.89%

Mean Actual Discount

30.21%

13.62%

Mean Model Predicted Discountd

Mean Differencee

Mean Model Predicted d Discount

Mean Differencee

Mean Model Predicted d Discount

Mean Differencee

Average-Strike Put Option Model

22.59%

0.30%

25.81%

4.40%

19.52%

-5.90%

Lookback Put Option Model

80.94%

c

-58.05% a (-32.9183 )

(-4.2857a)

(1.8196 )

(0.2304) 91.01%

-60.80% (-21.7480a)

68.31%

-54.69% (-20.8740a)

Panel B: Tests Based on the Empirical Predicted Discount 19.56%

Mean Empirical Predicted Discount

Average-Strike Put Option Model

23.57%

Mean Model Predicted Discountd

Mean Differencef

Mean Model Predicted d Discount

Mean Differencef

Mean Model Predicted d Discount

Mean Differencef

22.59%

-3.03%

25.81%

-2.24%

19.52%

-5.70%

b

(-2.5378 ) Lookback Put Option Model

a,b,c

13.83%

80.94%

-61.38% a (-34.8138 )

(-3.9934a)

(-1.0349) 91.01%

-67.44% (-24.9089a)

68.31%

-54.48% (-20.9190a)

denote significance at the 1%, 5%, and 10% levels, respectively.

d

Model Predicted Discount is calculated from the lookback put option model in Longstaff (1995) and from the average-strike put option model in equations (14) - (15)

e

Mean Actual Discount minus Mean Model Predicted Discount.

f

Mean Empirical Predicted Discount minus Mean Model Predicted Discount.

Table 13 Test of the Predictive Accuracy of the Average-Strike Put Option Model of the Discount Empirical Predicted Discount is calculated by adjusting the actual discounts for the information, ownership concentration, and control variables in Model 3, as shown in equation (17). Model Predicted Discount is calculated from the average-strike put option model in equations (14) - (15). AAR is Hertzel and Smith’s Discount-Adjusted Abnormal Return. Direct is one minus the fraction of directors that are also managers. Log(proceeds) is the log of the gross proceeds of the offering. Fraction is the number of shares placed divided by the sum of the number of shares placed and the number outstanding prior to the offering. Exchange is one for those companies listed on the NYSE, American Stock Exchange, Nasdaq National Market or Nasdaq Small Cap Market and is zero otherwise. Book/Market is the book value of equity divided by the market value of equity. Registration Rights is one for those offerings that provide for Piggyback and/or Demand Registration Rights and is zero otherwise. Registered Stock is one for those stocks that the firm registered within 45 days of the offer date. Related is one for those stocks where the issuer announced that the shares were sold to someone related to the issuer. Strategic is one for those stocks where the issuer announced that the shares were sold to another corporation that could be identified as a strategic partner. I also tested the average-strike put option model’s accuracy in predicting Discount (10 days after). The regressions are fitted using ordinary least squares. The sample includes 205 U.S. private placements between April 1, 1991 and February 1, 2005. Fourteen observations had to be dropped from the regressions that include the variable Direct because the fourteen firms’ historical proxy statements could not be obtained. All t-statistics (in parentheses below coefficients) are calculated using heteroskedasticity-consistent standard errors. Informationintensive placements are characterized by either (a) volatility above the median and log (proceeds) below the median for the overall sample or (b) placed with strategic investors or related investors. Non-information-intensive placements are characterized by (a) volatility below the median and log (proceeds) above the median and (b) not placed with strategic investors or related investors. 58 placements were neither information-intensive nor non-information-intensive.

Table 13 Test of the Predictive Accuracy of the Average-Strike Put Option Model of the Discount Dependent Variable

Empirical Predicted Discount (day prior) - Model Predicted Discount

Empirical Predicted Discount (10 days after)Model Predicted Discount

Information-Intensive Subsample

Non-InformationIntensive Subsample

Information-Intensive Subsample

Non-InformationIntensive Subsample

78

55

78

55

-47.803

(-2.2074 )

-11.858 (-0.2191)

(-2.4937 )

-13.806 (-0.2596)

AAR

0.011 (0.0463)

0.168 (1.3628)

0.008 (0.0354)

0.167 (1.3884)

Direct

21.729

15.763 (1.2607)

-20.259

(1.7323 )

-14.413 (-1.3979)

(-1.9998c)

Log (proceeds)

1.487 (1.0873)

0.043 (0.0145)

1.994 (1.4665)

0.401 (0.1378)

Fraction

10.573 (0.6265)

-25.439 (-1.4871)

-2.682 (-0.1614)

-40.565 (-2.4568b)

-0.411 (-0.0835)

15.526 (5.0755 a)

-4.913 (-1.0037)

(3.5323 a)

-0.095

-0.185

Number of Observations Intercept

-42.609 b

c

Exchange

Book to Market

0.148 (2.8060 )

0.061 (0.8970)

6.275 (1.1434)

0.764 (0.1903)

-9.381 (-1.6583)

7.444

a

Registration Rights

Registered Stock

Investment*Fraction

67.451 (3.1973 a)

b

c

10.780

(-1.8677 )

(-2.8057a)

9.743

3.802 (0.9620)

c

(1.7889 )

(2.3252 )

-7.686 (-1.3728)

19.357 (1.2527)

84.157

37.236

(4.0281 a)

(2.4768 b)

b

Strategic*Fraction

-35.538 (-0.4606)

-19.450 (-0.2553)

Related*Fraction

16.928 (0.4118)

-29.143 (-0.7098)

8.590 (2.7336 a)

R2

0.1932

0.3543

0.2655

0.5188

Adjusted R2

0.0588

0.2252

0.1431

0.4225

MSE

337.927

82.994

333.615

79.667

Durbin-Watson Statistic

2.30

1.39

2.31

1.44

F-value

1.44

2.74b

2.17b

5.39a

a,b,c

denote significance at the 1%, 5%, and 10% levels, respectively.

Table 14 Comparison of the Predictive Accuracy of the Average-Strike and Lookback Put Option Models The Mean Actual Discount is calculated from the percentage discount relative to the closing market price of the issuer’s registered common stock on the trading day immediately preceding the pricing announcement date. AAR is Hertzel and Smith’s Discount-Adjusted Abnormal Return. Direct is one minus the fraction of directors that are also managers. Log(proceeds) is the log of the gross proceeds of the offering. Fraction is the number of shares placed divided by the sum of the number of shares placed and the number outstanding prior to the offering. Exchange is one for those companies listed on the NYSE, American Stock Exchange, Nasdaq National Market or Nasdaq Small Cap Market and is zero otherwise. Book/Market is the book value of equity divided by the market value of equity. Registration Rights is one for those offerings that provide for Piggyback and/or Demand Rights and is zero otherwise. Registered Stock is one for those stocks that the firm registered within 45 days of the offer date. Related is one for those stocks where the issuer announced that the share were sold to someone related to the issuer. Strategic is one for those stocks where the issuer announced that the shares were sold to another corporation that could be identified as a strategic partner. The regressions are fitted using ordinary least squares. The sample includes 205 U.S. private placements between April 1, 1991 and February 1, 2005. Fourteen observations had to be dropped from the regressions that include the variable Direct because the fourteen firms’ historical proxy statements could not be obtained. All t-statistics (in parentheses below coefficients) are calculated using heteroskedasticity-consistent standard errors. Information-intensive placements are characterized by either (a) volatility above the median and log (proceeds) below the median for the overall sample or (b) placed with strategic investors or related investors. Non-information-intensive placements are characterized by (a) volatility below the median and log (proceeds) above the median and (b) not placed with strategic investors or related investors. 58 placements were neither information-intensive nor non-information-intensive.

Information-Intensive Subsample

Full Sample Dependent Variable

Non-Information-Intensive Subsample

Actual Discount - Average-Strike Put Option Model Predicted Discountd

Actual Discount - Lookback Put Option Model Predicted Discounte

Actual Discount - Average-Strike Put Option Model Predicted Discountd

Actual Discount - Lookback Put Option Model Predicted Discounte

Actual Discount - Average-Strike Put Option Model Predicted Discountd

Actual Discount - Lookback Put Option Model Predicted Discounte

191

191

78

78

55

55

22.257 (1.5920)

-56.702

-18.249 (-0.9342)

-113.813

(-3.0908a)

(-4.9039a)

3.503 (0.0585)

-89.342 (-0.7691)

AAR (+)

0.002 (0.0132)

-0.049 (-0.3589)

0.015 (0.0645)

-0.071 (-0.3096)

0.162 (1.2513)

0.031 (0.1223)

Direct (+)

10.708 (1.5837)

17.758

32.021

46.510

(1.8536c)

(2.6606a)

(3.1065a)

-7.524 (-0.6939)

-2.472 (-0.1196)

-1.412 (-1.1390)

-0.295 (-0.2175)

0.592 (0.3742)

-1.226 (-0.3693)

0.439 (0.0701) 30.435 (0.7170)

Number of Observations Intercept

Log (proceeds) (-)

-1.980 (-2.0011b)

Fraction (+)

Exchange (-)

Book to Market (+) Registration Rightsf (-) g Registered Stock (-)

Strategic*Fraction (+)

36.138

29.940

44.303

66.504

(2.7217a)

(1.6706c)

(2.4657b)

(3.7649a)

25.110 (1.3101)

-4.092 (-1.0009)

6.683 (1.3309)

-4.786 (-0.9616)

3.557 (0.6014)

12.287

21.196

(3.4653a)

(2.6069b)

0.150

0.107 (1.5899)

0.261

0.206

0.187

0.252

(3.6300a)

(4.5126a)

(4.9615a)

(2.4618b)

(1.9788c)

3.022 (0.9124)

3.994 (0.8981)

7.602 (1.3472)

14.749 (2.0315b)

3.470 (0.7617)

6.415 (0.8873)

-4.015 (-1.4577)

-3.323 (-0.8141)

-14.792

-16.253

(-2.5843b)

(-2.2590b)

3.574 (0.9333)

5.048 (0.7485)

0.573

23.589

-32.287

1.794

(0.0091)

(0.3700)

(-0.4153)

(0.0268)

-1.986 (-0.1248)

-28.392 (-1.3702)

54.146 (2.4714b)

14.997 (0.6091)

0.1284

0.0605

0.3140

0.3131

0.2258

0.1760

Adjusted R

0.0799

0.0083

0.2116

0.2106

0.0912

0.0327

MSE

289.887

555.180

333.668

444.684

105.104

332.608

3.07a

3.05

1.68

1.23

Related*Fraction (+)

R

2 2

1.16 2.65a denote significance at the 1%, 5%, and 10% levels, respectively. d Average-Strike Put Option Model Predicted Discount is calculated from equations (14) - (15). e Lookback Put Option Model Predicted Discount is calculated from the lookback put option model in Longstaff (1995). f Registration Rights are defined as piggyback and/or demand registration rights. g The firm registered the stock within 45 days following the offer date. F-value

a,b,c

a

Table 15 Test of the Predictive Accuracy of the Average-Strike Put and Lookback Put Option Models on the Holdout Sample The Mean Actual Discount is calculated from the percentage discount relative to the closing market price of the issuer’s registered common stock on the trading day immediately preceding the pricing announcement date. The Mean Empirical Predicted Discount is calculated by adjusting the actual discounts for the information, ownership concentration, and control variables in Model 3, as shown in equation (17). The Mean Model Predicted Discount is calculated from the lookback put option model in Longstaff (1995) and from the average-strike put option model in equations (14) - (15). The holdout sample consists of 27 placements that occured in 2005 and 2006 that were not included in the sample of 205 placements used to fit Model 2 and calculate the Empirical Predicted Discount. Three placements were neither information-intensive nor non-information intensive.

Number of Observations

Full Sample 27

Information-Intensive Subsample 6

Non-Information-Intensive 18

Panel A: Tests Based on the Actual Discount 11.73%

Mean Actual Discount

Average-Strike Put Option Model

21.03%

Mean Model Predicted d Discount

Mean e Difference

Mean Model Predicted d Discount

Mean e Difference

Mean Model Predicted d Discount

Mean e Difference

15.74%

-4.01%

21.80%

-0.77%

12.80%

-2.64%

a

(-4.0190 ) Lookback Put Option Model

10.16%

58.78%

-47.05% (-10.8095a)

(-3.0137a)

(-0.0973) 82.46%

-61.42% (-4.7250a)

45.13%

-34.98% (-8.9084a)

Panel B: Tests Based on the Empirical Predicted Discount 10.97%

Mean Empirical Predicted Discount

Average-Strike Put Option Model

1.98%

Mean Model Predicted Discountd

Mean f Difference

Mean Model Predicted d Discount

Mean f Difference

Mean Model Predicted d Discount

Mean f Difference

15.74%

-4.77%

21.80%

-19.82%

12.80%

-1.26%

b

(-2.5059 ) Lookback Put Option Model a,b,c

11.54%

58.78%

-47.80% (-9.8578a)

(-0.1406) 82.46%

-80.47% (-3.7680a)

(-0.9715) 45.13%

-33.60% (-9.3542a)

denote significance at the 1%, 5%, and 10% levels, respectively.

d

Model Predicted Discount is calculated from the lookback put option model in Longstaff (1995) and from the average-strike put option model in equations (14) - (15).

e

Mean Actual Discount minus Mean Model Predicted Discount.

f

Mean Empirical Predicted Discount minus Mean Model Predicted Discount.

Table 16 Empirical Predicted Discount Versus Model Predicted Discount for Different Volatilities The Mean Empirical Predicted Discount is calculated by adjusting the actual discounts for the information, ownership concentration, and control variables in Model 3, as shown in equation (17). The Mean Model Predicted Discount is calculated from the average-strike put option model in equations (14) - (15). Panel A.1 applies to those offerings which were announced prior to February 1997 and Panel A.2 applies to those offerings which were announced after February 1997. Panels B.1 and B.2 provide the difference in means of the Model Predicted Discount and the Empirical Predicted Discount, as well as the Wilcoxon Signed Rank Test z-statistic which is used to test whether the median difference in means is significantly different from zero. Panels C.1 and C.2 provide the results of fitting the regression equation (18): Empirical Predicted Discount = a 0 +a1Model Predicted Discount. The t-statistics for the null hypotheses that a1 is equal to zero and that a1 is equal to one are shown below the estimates for a1. Panel A.1: T = 2 Years

a

Volatility Range (%) 0.0 - 29.9 30.0 - 44.9 45.0 - 59.9 60.0 - 74.9 75.0 - 89.9 90.0 - 104.9 105.0 - 120.0 Average:

Mean Model Predicted Discountb (T = 2) 16.86 % 30.29 34.71 40.30 43.23 47.61 35.98 %

Mean Empirical Predicted Discount (day prior) 16.71 % 15.59 16.90 26.88 37.78 29.20 23.63 %

Mean Empirical Predicted Discount (10 days after) 10.23 % 9.99 13.65 21.02 35.44 18.84 18.85 %

Total:

N 3 0 9 9 9 8 2 40

Total:

N 2 13 15 31 28 30 32 151

Panel A.2: T = 1 Year

Volatility Rangea (%) 0.0 - 29.9 30.0 - 44.9 45.0 - 59.9 60.0 - 74.9 75.0 - 89.9 90.0 - 104.9 105.0 - 120.0 Average:

Mean Model b Predicted Discount (T = 1) 2.46 % 7.23 13.29 16.86 20.12 21.54 26.41 19.04 %

Mean Empirical Predicted Discount (day prior) 9.88 % 13.84 10.31 16.11 19.45 15.68 28.68 19.39 %

a

Volatilities above 90% were rescaled to between 90% and 120%.

b

Model Predicted Discount is calculated from equations (14) - (15).

Mean Empirical Predicted Discount (10 days after) 1.08 % 5.24 3.24 9.20 12.37 9.25 23.84 11.86 %

Table 16 Panel B.1: Difference of Means and Wilcoxon Signed Rank Test Results (T = 2)

Discount (day prior)

Discount (10 days after)

Mean Model d Predicted Discount (T = 2) 35.98 %

Mean Empirical Predicted Discount 23.63 %

Difference of e Means -12.36 % a (5.1826 )

35.98

18.85

-17.14 a (6.1769 )

Number of Positive Differences 5

Wilcoxon Signed Rank Test Z-statisticf (4.7246a)

4

(4.7246 )

40

Number of Positive Differences 64

Wilcoxon Signed Rank Test Z-statisticf (1.2251)

N 151

40

(5.0334a)

151

a

N 40

Panel B.2: Difference of Means and Wilcoxon Signed Rank Test Results (T = 1)

Discount (day prior)

Discount (10 days after)

Mean Model d Predicted Discount (T = 1) 19.04 %

Mean Empirical Predicted Discount 19.39 %

Difference of e Means 0.35 % (0.3920)

19.04

11.86

-7.18 (4.5290a)

a,b,c

denote significance at the 1%, 5%, and 10% levels, respectively. Model Predicted Discount is calculated from equations (14) - (15). e Mean Actual Discount minus Mean Model Predicted Discount. d

f

The Wilcoxon signed rank test is used to test the null hypothesis that the population median equals zero. It assumes that the distribution of the population is symmetric. The Wilcoxon signed rank test statistic is computed based on the rank sum and the numbers of observations that are either above or below the median. The interpretation of the p-value is the same as for the t-test. If the p-value is significant, we conclude that the median of the variable in question is significantly different from zero. Here the variable tested is the Empirical Predicted Discount minus the Model Predicted Discount.

Table 16 Panel C.1: Regression Results (T = 2) Dependent Variable

Empirical Predicted Discount (day prior)

Empirical Predicted Discount (10 days after)

Number of Observations

40

40

a0 t-statistic for a0

-2.963 (-0.2430)

-10.988 (-0.8212)

a1 t-statistic for a1: H0 : a1 = 0 Ha : a1 > 0 H0 : a1 = 1 Ha : a1 ≠ 1

0.739

0.829

(2.2815b) (-0.8059)

(2.2668b) (-0.4671)

0.2028 0.1819

0.1719 0.1501

9.67a 1.89

7.89a 1.90

R2 Adjusted R2 F-value D.W.

Panel C.2: Regression Results (T = 1) Dependent Variable

Empirical Predicted Discount (day prior)

Empirical Predicted Discount (10 days after)

Number of Observations

151

151

a0 t-statistic for a0

3.025 (0.6145)

-6.136 (-1.2036)

a1 t-statistic for a1: H0 : a1 = 0 Ha : a1 > 0 H0 : a1 = 1 Ha : a1 ≠ 1

0.810

0.945

(3.0161a) (-0.8059)

(3.4312a) (-0.1993)

0.0786 0.0724

0.0945 0.0884

12.70a 2.23

15.55a 2.28

R2 Adjusted R2 F-value D.W. a,b,c

denote significance at the 1%, 5%, and 10% levels, respectively.