Securities issuers are newsboys: The risk of setting a fixed-offer price can explain underpricing in firm-commitment and best-efforts IPOs*

Transcription

1 Securities issuers are newsboys: The risk of setting a fixed-offer price can explain underpricing in firm-commitment and best-efforts IPs Steven L. Jones Kelley School of Business, Indiana University, Indianapolis, IN John C. Yeoman Mike Cottrell School of Business, North Georgia College & State University, Dahlonega, GA Abstract We model the costs of over and underpricing in both firm-commitment and best-efforts securities offerings and solve for the optimal fixed-offer price recognizing this is the analogue of the wellknown Newsboy Problem. The result is what we call the proceeds-shortfall risk theory, which shows that it is optimal for the underwriter in a firm-commitment offering and the issuer in a bestefforts to set the fixed-offer price below the expected aftermarket price given typical levels for price uncertainty as well as the costs of over and underpricing. While we do not discount the winner s curse, or that underpriced securities can be usefully allocated to motivate information production, our theory generates underpricing based on ex ante price uncertainty, alone, without requiring asymmetric information. JEL Classification: G24 We are grateful for the comments of Heng An, Anne Anderson, la Bengtsson, Utpal Bhattacharya, Cathy Bonser-Neal, Ken Carow, Eitan Golman, Randy Heron, Craig Holden, Glen Larsen, John McConnell, Javier Navas, Rob Neal, Tod Perry, Ann E. Sherman, Mohan Tatikonda, Chuck Trzcinka, and Drew Winters, as well as seminar participants at the Indiana University Kelley School of Business Bloomington and Indianapolis (IUPUI) campuses, the Purdue University Summer Finance Conference, and the 2009 Midwest Finance Association meeting in Chicago, IL. All errors remain the responsibility of the authors. Correspondence to: Steven L. Jones, Kelley School of Business, Indiana University, 801 West Michigan Street, Indianapolis, Indiana , USA; SLJones@iupui.edu; (); (F)

2 Securities issuers are newsboys: The risk of setting a fixed-offer price can explain underpricing in firm-commitment and best-efforts IPs 1. Introduction In the classic newsboy problem, a price-taking retailer faces uncertain demand and must order a fixed-quantity of inventory to offer for sale at a given price. In the more than century-old solution to this problem, the optimal order quantity may differ from the expected quantity demanded, depending on the relative costs of an inventory shortage versus an overage. 1 Issuers and underwriters face the analogue of this problem when setting the fixed-offer price for a given quantity of securities of uncertain value. As with the newsboy s order quantity, the offer price is fixed in advance of sales, and it cannot be increased once it is posted, just as the newsboy cannot replenish inventory, and this offer price is sticky downward in that lowering it is costly, just as the newsboy bears the costs of overage. But while the newsboy s problem was solved long ago, there is no widely-accepted solution for the optimal fixed-offer price in a securities offering. Much of the literature implies, however, that in the absence of asymmetric information, the offer price should be set equal to the expected price in the aftermarket. Yet, even when asymmetric information should not be a factor, significant positive returns (i.e., underpricing) are observed on the first day of trading in all types of securities, especially in initial public offerings (IPs). 2 In this paper, we develop the proceeds-shortfall risk theory, as an analogue to the newsboy solution, and consider the implications for the underpricing of firm-commitment and best-efforts securities offerings. 1 See Silver, Pyke, and Peterson (1998) and Khouja (1999) for discussion of the newsboy problem. 2 Ritter and Welch (2002) report that the average IP return from offer price to close price, on the first day of trading, was 18% between 1980 and Muscarella and Vetsuypens (1989) find that self-underwritten investment bank IPs are underpriced by as much as other IPs where the presence of asymmetric information is likely. We examine various asymmetric-information based theories of securities underpricing in section 6. 1

3 Fixed-price securities offerings may be sold on a best-efforts or firm-commitment basis. In a firm-commitment offering, the underwriter guarantees the issuer s net proceeds. This subjects the underwriter to risk since it is costly to dispose of any securities not sold in the primary market. These potential disposal costs are usually defined as the net proceeds the underwriter paid the issuer for the shares (the offer price minus the spread) less the aftermarket price, at which the underwriter sells those securities not sold in the primary market. Yet in its most common bookbuilt form, firm-commitment offerings are rarely undersubscribed so this risk is often viewed as inconsequential. This, however, ignores the fact that book-built offerings can clear the primary market and still be overpriced relative to fair market value, as it is revealed in the aftermarket. In which case, the underwriter may bear substantial costs from providing price support. The omission of underwriter risk, from the recent literature, as a possible explanation for IP underpricing appears to be due to the dominance of book building, and the view that it alleviates this risk, in addition to the large returns observed on the first day of trading in bestefforts offerings, as noted in Tinic (1988). 3 However, financial risk arises in any situation where a decision maker bears the downside cost of committing to either a fixed quantity or price, in advance of observing demand. It follows that risk also arises in a best-efforts offering because the issuer commits to a fixed-offer price, usually several days in advance of the offering. This introduces the possibility of the withdrawal of the offering if all of the shares cannot be sold at the fixed-offer price by the end of the subscription period. In which case, the issuer s cost of withdrawal includes the opportunity costs of seeking alternative financing, or failing to fund a time-sensitive investment. The best-efforts issuer can lower the offer price, rather than withdrawing the offering; however, this is rarely done because the negatively signaling effects are potentially so large. 3 Best-efforts IPs are rare, now, compared to the 1970s and 1980s, when they made up a third of all IPs. Ritter (1987) reports an average best-efforts-ip return of 47% on the first day of trading. 2

4 In the solution to the newsboy problem, expected profit is maximized by balancing the newsboy s expected costs of over and under ordering. This same approach could offer a solution to the optimal fixed-offer price if we consider the above-mentioned costs of overpricing along with the costs of underpricing a securities offering. The latter costs arise when the initial market price is higher than the fixed-offer price; in which case, offering proceeds are left on the table because securities regulations prohibit increasing the offer price. While this is more costly for the best-efforts issuer, it can also be costly to an underwriter in terms of diminished reputation. In this paper, we show that the problems faced by newsboys and securities issuers are similar in most critical respects, and we investigate an analogous solution. This involves reversing quantity and price, and modeling the risks of over and underpricing the offered securities. We initially define these risks from the perspective of an underwriter, and then later, from that of an issuer in a best-efforts offerings. The resulting proceeds-shortfall risk theory demonstrates that it is optimal, given reasonable estimates for the costs of over and underpricing, to post a security s offer price below its expected fair value in the aftermarket. ur solution, therefore, yields an explanation for why securities offerings are underpriced, on average. While our proceeds-shortfall theory may appear to provide a radically different explanation for underpricing compared to those featured prominently in the recent literature, it is actually it has roots in some of the early theories of underwriter risk and asymmetric payoffs. The remainder of this paper is organized as follows. In section 2, the solution to the newsboy problem is described and the analogue to the underwriter s pricing problem is developed. This analogue yields the underwriter s optimal fixed-offer price given an underwriting fee, estimates for price uncertainty, the costs of over and underpricing, and an exogenously determined gross spread chosen by the issuer. Section 3 demonstrates that signaling costs make the option of lowering the fixed-offer price nearly prohibitive. Section 4 shows that underpricing is also optimal 3

5 in best-efforts offerings because it is the risk of setting a fixed-offer price that drives the result, rather than underwriter risk, per se. In section 5, we examine how our proceeds-shortfall theory complements most of the prominent theories of underpricing. Section 6 summarizes and concludes the paper. Appendix A focuses on the effect of introducing an over-allotment option, while Appendix B shows that the analogue model can be restated in terms of a profit function using terminology familiar in financial economics. 2. Applying the newsboy solution to the security underwriter s pricing problem In this section, we briefly describe the solution to the newsboy problem and then develop the analogue for a risk-neutral securities underwriter s pricing problem. While the solution pertains to an underwritten offering of any type of security, we focus on IPs of common stock, which exhibit the greatest underpricing. We assume here, in this section, that the issuing firm has already chosen the spread, before the offering is priced, so the spread is taken as a given in the underwriter s problem. Later, in section 3, we expand the problem to first determine the optimal spread and then the fixed-offer price in a Stackelberg equilibrium that includes the issuer and underwriter. Later yet, in section 5, we apply the analogue model to best-efforts offerings The solution to the newsboy problem and its application to the underwriter s pricing problem The solution to the newsboy problem is based on marginal analysis where the retailer s profit maximizing order quantity equates the expected cost of ordering too much inventory with the expected cost of not ordering enough. Specifically, FQ ( ) is the cumulative probability function for demand, c o is the marginal cost of an inventory overage, or over-ordering, and c u is the marginal cost of a stock out, or under-ordering. The optimal order quantity, Q, therefore, satisfies c F Q c F Q, where the expected cost of over-ordering, in the first term, equals the o ( ) u(1 ( )) 4

6 expected cost of under-ordering, in the second term. FQ ( ), the probability that the actual quantity demanded will be fully satisfied from the quantity ordered, Q, therefore equals cu /( cu co ), which is known as the critical ratio. It follows that the retailer s optimal order quantity equals F 1 ( c /( c c )), where F -1 is the inverse of the cumulative probability function for demand. u u o In the same manner, marginal analysis can be used to determine the offer price that maximizes an underwriter s expected profit. Now, however, c u represents the underwriter s marginal cost of underpricing the offered securities, and c o represents the underwriter s marginal cost of overpricing the securities. It follows that the underwriter s optimal offering price, P, equals F 1 ( c /( c c )), where F -1 is now the inverse of the cumulative probability function for the u u o offered securities fair market value prior to the offering, which is not revealed until the securities trade in the aftermarket. The critical ratio, therefore, represents the probability of overpricing. That is, the probability the fixed-offer price, P, is higher than the initial price realized in the aftermarket. We assume that this aftermarket price reflects the securities fair market value and that it is observed as the opening secondary market price, or shortly thereafter, before the underwriter can engage in price-support activity should the offering be overpriced. This assumption is justified based on findings of Barry and Jennings (1993) that, on average, about 90% of the initial-day returns to IPs are earned by subscribers on the opening secondary-market trade. Thus, the security underwriter s problem and our approach to solving it differ from that of the newsboy only in that the latter is given a price and must solve for an optimal order quantity before sales begin, while the underwriter has a given quantity of shares to issue and must, in advance of the offering, solve for the optimal fixed-offer price. Note that this fixed-offer price cannot be increased, per the Financial Industry Regulatory Authority s (FINRA, formerly the 5

7 NASD) Rules of Fair Practice, and it is sticky downward in that it is costly to lower this offer price because doing so erodes the underwriter s net proceeds in a firm-commitment offering. We do recognize that the quantity of shares issued can be increased, after the offering has begun, if the underwriter has an over-allotment (i.e., Green Shoe) option to purchase more shares from the issuer, usually an additional 15% within 30 days of the offer date. Schultz and Zaman (1994) and Aggarwal (2000) show that most underwriters hold this option and initially sell the additional shares, before deciding whether to exercise the option, with the intent of covering this short position by either exercising the over-allotment option if the offering is well received, thereby earning the net spread on the additional shares, or by purchasing the additional shares back in the aftermarket as a means of providing price support if the offering is not well received. In fact, Aggarwal (2000) and Lewellen (2006) show that underwriters use this aftermarket short covering as a primary means of price support. Thus, an over-allotment option provides the underwriter with a margin of safety in terms of setting the offer price. But this margin runs out if the underwriter has to repurchase more shares than the over-allotment option allows for in order to adequately support the price. In which case, the underwriter may not raise enough proceeds from the offering to cover the issuer s guarantee and is faced with unloading an inventory of shares from an offering that was not well received. Thus, the over-allotment option reduces but does not eliminate the expected costs of over and underpricing. We, therefore, model the effects of an over-allotment option by adjusting the costs under and overpricing, as we will explain shortly. This approach allows us to avoid the additional complexity of explicitly modeling the option, as is shown in the appendix The analogue to the newsboy model and the underwriter s optimal offer price To determine the underwriter s marginal costs of under and overpricing, several variables must first be defined. The underwriter s gross spread, s, is a constant percentage of the securities 6

8 offer price, P. The net proceeds available for the issuer s guarantee, therefore, equal (1 sp ) per share, and the underwriter s revenue per share equals sp, as long as the securities clear the market at the offer price, P. The gross spread includes the underwriter s direct costs, the selling concession paid to the selling group, and the management fee paid to the managing investment banks for advising the issuer and performing the due diligence. These direct costs are expressed here as a constant percentage, k, of the offer price per share. In addition, the gross spread includes the risk-neutral underwriter s fee for bearing price risk, s-k, also called the net spread. So the underwriter receives ( s k P per share if the securities clear the market at the offer price, P. ) Yeoman (2001) recognizes that in a primary equity offering, the initial share price in the secondary market, or aftermarket, equals (1 ) V (1 s) P, where is the new share ratio, defined as the number of new shares offered divided by the total number of shares the issuer has outstanding after the offering, and V is the fair market value of the shares that existed prior to the offering, sans the proceeds. Hence, V contributes to the initial market price in proportion to ( 1 ), and the net proceeds raised, (1 sp ), contribute in proportion to the new share ratio,. In debt offerings, the proceeds raised affect the value of the issuing firm, but not the value of the offered securities, and in secondary equity offerings, the issuing firm does not receive the proceeds; thus, neither the value of the issuing firm nor the value of the offered securities are affected. It follows that equals zero in a non-equity offering or a purely secondary equity offering. The determinants of the initial market price indicate that the initial secondary-market return, IR, in Eq. (1) will be negative if the offer price, P, is greater than or equal to V, since 0 s 1. (1 ) V (1 s) P IR 1 (1) P The offer price, Z P, in Eq. (2) is consistent with an initial return, IR, of zero. 7

9 Z P 1 V 1 (1 s) (2) For example, assuming the underwriter knows that V $10 values, typical of initial public equity offerings, of 0.3 per share with certainty and parameter and s 0.07, Eq. (2) yields an offer price, Z P, of $9.71, which results in an initial return of zero. 4 The underwriter s costs of underpricing are expressed here as a constant percentage,, of the amount of underpricing, which we define as the initial market price less the offer price, P, or zero, whichever is greater. The source of this cost is a loss of underwriter reputation that will potentially translate into lost revenue in the future. See, for example, Beatty and Ritter (1986). The costs of overpricing are expressed as a constant percentage,, of the amount of overpricing, which is the offer price, P, less the initial market price, or zero, whichever is greater. We assume that this initial market price reflects the shares fair market value, before the underwriter can engage in price support. Thus, when the offer is overpriced, the offer price less this initial market price reflects the true amount of overpricing, which is the relevant measure of overpricing for the underwriter because it is directly related to the cost of price support in the aftermarket. Note, however, that in a book-built IP, the empirically observed initial market price will not reflect fair market value if the underwriter was able to sellout the offering, at the offer price, only due to an implied promise to provide price support in the aftermarket. 5 There may also be litigation costs from overpricing, according to Tinic (1988), as well as Hughes and Thakor (1992). 4 Yeoman (2001) finds that the new share ratio averaged 0.32 for a sample of 1,070 IPs occurring between 1988 and Benvensite, Busaba, and Wilhelm (1996) expand on Smith s (1986) idea of price support as a means to align the interests of investors and underwriters by removing the latter s incentive to overprice, which provides more fee income. The implicit promise of price support assures investors that if the issue is overpriced, it was not intentional, and they will be insulated by the underwriter. 8

10 It follows that the underwriter s marginal cost per unit of underpricing, c u, equals s k (1 (1 s)), and the marginal cost per unit of overpricing, c o, equals s k (1 (1 s)), where the parameters are restricted so that 0, 0, and 0 k s 1. The critical ratio, c /( c c ), is, therefore, ( s k (1 (1 s))) / (( )(1 (1 s))), which u u o can be rewritten as, ( / ( )) (( s k) / (( )(1 (1 s)))). The intuition for the formulation of cu and co may be easier to follow if one first considers a purely secondary equity offering, or any non-equity offering, in which 0, so the cost of underpricing becomes a function of only s, k, and, and the cost of overpricing is a function only of s, k, and. In which case, the underwriter loses the net spread, s-k, plus for every unit of underpricing (relative to Z P from Eq. (2)) and gains the net spread, s-k, for every unit of overpricing but loses. The (1 (1 s)) term has the effect of reducing the costs associated with and for the number of new shares in a primary equity offering. The logic behind this term follows from our example, above, where 0.3, s 0.07, and V $10 yields an offer price, Z P, of $9.71, from Eq. (2), which results in an initial return of zero. If this offer price is decreased by $1, to $8.71, it is only $0.72 less than the resulting initial market price of $9.43, reflecting the (1 (1 s)) term s value of Underpricing equals $0.72, here, because the offer price of $8.71 reduced the initial market price by $0.28. Likewise, if the offer price is increased by $1, to $10.71, it is $0.72 more than the resulting initial market price of $9.99. So setting the offer price $1 above (below) Z P results in over (under) pricing the offer by a fraction of a dollar equal to (1 (1 s)). The fair market value, V, of the shares existing before the offering is, of course, uncertain prior to the offering. Thus, immediately before agreeing to purchase the offered securities from the issuer, the underwriter views V as a lognormally distributed random variable, V L, with mean, V ˆL, 9

11 representing an unbiased estimate of V, and variance, 2 L, reflecting the underwriter's uncertainty about V. Note that we have not assumed asymmetric information between the issuing firm and either the underwriter or the market. Substituting VL for V, in Eq. (2), yields Eq. (3), where P ˆ Z is an unbiased estimate of the offer price that will result in an initial market return of zero. Pˆ Z 1 Vˆ 1 (1 s) L (3) The underwriter s optimal offer price does not necessarily equal P ˆ Z, however. Solving for the profit-maximizing underwriter s optimal offer price, using our adapted-newsboy model, requires that we invert the cumulative lognormal distribution of V, which equals ˆ exp( 1 ( ) L N N N ) V, from Aitchison and Brown (1973), where ˆ, 2 N log(1 ( L / VL ) ) L is the standard deviation of V, and N 1 () is the inverse of the cumulative standard normal density function. 6 Inserting the critical ratio into N 1 () and then substituting ˆ exp( 1 ( ) L N N N ) V into Eq. (3) for V L, to account for the impact of Δ and s, identifies the solution to the underwriter s optimal offer price, P, as 1 ˆ exp( 1 s k P VL N N N ), (4) 1 (1 s) ( ) ( )(1 (1 s)) and the optimal offer price to value ratio, P / ˆ L V, as P 1 s k ˆ V 1 (1 s) ( ) ( )(1 (1 s)) L 1 2 exp( NN.5 N). (5) 6 Note that the coefficient of variation, / ˆ L V, represents a close approximation of N up to values of about 0.3, or 30%. 10

12 It follows that the underwriter s optimal offer price, P, is less than P ˆ Z, the estimate of the offer price that would yield zero return, if the critical ratio, ( / ( )) (( s k) / (( )(1 (1 s)))), is less than N(0.5 N ), so that the exponent in Eqs. (4) and (5) is less than zero. Both / ˆ L P and P V are strictly increasing in the spread, s, and decreasing in uncertainty, N, all else equal, and therefore, the expected initial return, E IR ( ), shown in Eq. (6), is strictly decreasing in the spread and increasing in uncertainty, all else equal. E IR s N s k ( ) ( )(1 (1 s)) 1 2 ( ) (1 (1 )) exp N.5N 1 (6) Furthermore, the issuer s guaranteed net proceeds per share,, will equal, I 1 ˆ s k 1 (1 s) ( ) ( )(1 (1 s)) 1 2 I (1 s) VL exp( N N.5 N ), (7) where,, is simply the product of one minus the gross spread, (1 s), and the underwriter s I optimal offer price from Eq. (4) A numerical example of the newsboy solution to the underwriter s pricing problem A simple numerical example may help with intuition, but first, we consider reasonable ranges for the values of and. The underwriter s cost of underpricing parameter,, should be well less than one since the issuer incurs the entire shortfall in net proceeds, even when the underwriter also bears costs due to reputational harm. Underwriters also benefit indirectly from underpricing by recapturing the IP-allocation profits of brokerage clients through full-commission trading. 7 Thus, a reasonable range for is well below one but more than zero. For purposes of our 7 Smith (2009) reports Frank Quattrone's technology-banking group at Credit Suisse First Boston expected to recapture 65% of a client s IP-allocation profits through full-commission trading fees. 11

13 example, which follows below, we assign a value of 0.1. Warrants and over-allotment options will decrease the costs of underpricing further; however, we reserve consideration of those for the appendix since they add considerable complexity without materially changing the results. The underwriter s cost of overpricing parameter,, will equal one if demand for the offered shares is perfectly elastic. In which case, if the offering is overpriced, none of the shares will be sold in the primary market, and the underwriter will have to unload all the shares in the secondary market at fair market value. However, as mentioned above, a book-built offering may be overpriced and still clear the primary market (i.e., be fully subscribed) if the underwriter has implied that the necessary price support will be provided in the aftermarket. So will be less than one in a bookbuilt offering since the underwriter should not have to overpay for every share to support the price. An over-allotment option would decrease by reducing the cost of aftermarket short covering since shares repurchased up to the number in the over-allotment option would not be resold, assuming those shares were issued initially. So a reasonable estimate for would be less than one but well above zero; thus, we set 0.8, for purposes of this example. The true values of and would differ across offerings, of course, and later, in the next section, we will consider the effects of alternative values. For our example, we assume 0.3 and s 0.07, from before, in addition to direct underwriter costs of k 0.04 and uncertainty about V of N 15 %. 8 At 15%, N is very closely approximated by the coefficient of variation, / Vˆ ; in which case, one standard deviation L L 8 According to Torstila (2001), the gross spread in an IP is typically divided so that the management fee is 20%, the underwriting fee is 20%, and the selling concession is 60%. If the gross spread is 7%, the underwriter fee then equals 1.4%, and the selling concession equals 4.2% of the offer price. Assuming a broker payout of 60%, given the industry standard ranges from about 50 to 60%, the underwriter s portion of the selling concession equals 1.68% (=0.6(4.2%)) of the offer price, for total underwriter compensation equal to 3.08% of the offer price. In which case, a reasonable estimate for underwriter s direct cost, k, is about 4% of the offer price. 12

14 represents a range of $8.50 to $11.50 on a stock with a mean, V ˆL, of $10. From Eq. (4), we compute the underwriter s optimal offer price, P, as $8.26; in which case, the issuer s net proceeds per share computed from Eq. (7) are 76.8% of V ˆL. The expected initial market price is then $9.30 based on (1 ) V (1 s) P, and the optimal expected initial return, E IR ( ), of 12.7% can be computed directly from Eq. (6), or from Eq. (1) by assuming that V ˆL is an unbiased estimate of V. Note also that the critical ratio, which represents the probability of the offer price, than or equal to the fair market value, is Fig. 1 depicts how given these parameter values. E( IR ) P, being greater increases in uncertainty If we assume the cost of price support is less onerous for the underwriter, and therefore, reduce the overpricing parameter so that 0.6, the underwriter s optimal offer price, P, from Eq. (4), increases but only slightly, by $0.21, to $8.47 per share. It follows that the expected initial market price is $9.36, and the optimal expected initial return, E IR ( ), is 10.5%. The issuer s net proceeds per share, (1 sp ), are, therefore, 78.8% of V ˆL, and the critical ratio, or the probability that the initial market price is less than or equal to the offer price, P, equals Fig. 2 indicates that holding the other parameter values constant, the optimal offer price, P, remains below the expected price in the aftermarket, V ˆL, as long as 0.2 or higher. 3. Potential signaling costs associated with lowering an already posted offer price We have assumed, up until now, that an underwriter can clear the primary market of shares that are potentially overpriced, relative to fair market value, by implying to key customers, most likely institutions, that price support will be provided if necessary. Presumably, price support would 13

15 allow these loyal customers to unload any overpriced shares at little or no loss. Although costly for underwriters, price support is almost certainly less costly than the alternative of lowering the offer price to clear the market. In this section, we reconsider the cost of overpricing in a regulatory environment in which aftermarket price support is prohibited, and instead, the underwriter must lower the already posted offer price to clear the primary market. The underwriter s cost of providing price support for overpriced shares is a function of the price elasticity of demand for the shares in the aftermarket. For example, if demand for the shares is perfectly elastic, then the underwriter will have to buy up all of the shares in the secondary market, presumably with no option other than to sell them later at fair market value, so the overpricing parameter,, equals one. But in the absence of price support, which effectively ensures that the primary market clears, the price elasticity of demand is irrelevant in overpriced offerings because the early investors, who initially subscribed at the original offer price, will renege once they learn the primary market did not clear. Therefore, without aftermarket support, the offer price would have to be lowered on every share offered in order to clear the primary market. This raises the question, would the revised market-clearing offer price, subsequent to the offering s failure to clear, be less than the unknown offer price that would have cleared the primary market originally? The answer is almost certainly, yes, the revised market-clearing offer price will be less. This is because lowering the offer price will affect V ˆL, the secondary market s estimate of V, since the primary market s failure to clear will send a negative signal about V. The negative market reaction reflects the fact that V is based purely on the expectations of the secondary market, and this will be revealed in the initial market price, (1 ) V (1 s) P. If the secondary market reevaluates V at a lower level than before, the subsequent market clearing price may be considerably lower than the initial V ˆL would have otherwise implied. 14

16 Consider the effect again using our previous example, where 0.3, s 0.07, uncertainty about V, 15 %, and Vˆ $10. From Eq. (3), Pˆ Z $9.71 N L so the optimal offer price to value ratio, P / ˆ L V, cannot exceed if the offering is to clear the market. That is, setting the offer price, P $9.71 results in an expected initial market price, (1 ) V (1 s) P, of $9.71, and thus, the expected initial return would equal zero. But what if the underwriter overestimated V ˆL at $10.50, and therefore felt comfortable setting the offer price, P, at $10? Note that V $10.50 and P $10 would justify an initial market price of $10.14, based on (1 ) V (1 s) P. Yet the realized initial market price would be $9.79, assuming the secondary market s initial price reflected V $10. Thus, this offering, at P $10, would not sell out unless the offer price is lowered, or the underwriter promises price support to strategic customers in return for them purchasing the remaining shares. But if aftermarket price support is prohibited, so the offer price must be lowered, it is only reasonable to assume that market participants will revise V ˆL down now that they know the market places a maximum value on V of something less than $ If, for example, the market subsequently revises V ˆL downward by one standard deviation, to $8.50, the resulting maximum possible offer price and initial market price would be $8.25 per share. It follows that the underwriter will now be required to cover a shortfall of (1 s)($10 $8.25), or $1.63 per share, because the offering was initially overpriced by $0.29 per share. In which case, the cost parameter for overpricing,, equals 5.62 (=$1.63/$0.29). Thus, the potential for the market s reevaluation of V ˆL presents a very significant deterrent to overpricing, which implies large values for, and consequently, much higher levels of optimal underpricing, 15

17 E IR ( ) than our previous analysis indicated. As we will see in the next section, the effects of these signaling costs may be even more dramatic in a best-efforts offering. 4. Determining the optimal offer price in a best-efforts offering Tinic (1988) argues that underwriter risk cannot explain underpricing in securities offerings because this would imply that underpricing should be immaterial in best-effort offerings, and Ritter (1984) documents that underpricing is actually more prevalent in best-efforts than in underwritten offerings. To evaluate this argument, we consider some institutional details of these offerings. Recall from our previous analysis of a firm-commitment offering that the underwriter guaranteed the issuing firm s net proceeds in an amount equal to (1 sp ) per share. A best-efforts offering is similar, except the offer price is published in the registration statement, usually several days or weeks before the shares are offered in the primary market, and the investment bank does not act as an underwriter, per se, since the issuer s net proceeds are not guaranteed (i.e., underwritten ). In addition, there are two alternative best-effort contracts: (1) all or none, and (2) minimum-maximum. In the former, all of the offered shares must be sold, while in the latter, a minimum number of shares must be sold and there is limit on the number that can be sold. Best-efforts offerings are usually withdrawn if the required number of shares cannot be sold at the published offer price within the subscription period, which can run several months. Investors who have already paid for withdrawn shares receive a refund, and the issuing firm, that attempted to issue the shares, receives nothing, other than responsibility for its previously agreed upon portion of the offering s direct costs. This is similar to what happens with a firm-commitment contract when the offering is withdrawn at the last stage because the underwriter and issuer cannot agree on an offer price. But once a firm-commitment offering is priced and goes to the public, the issuer s net proceeds are guaranteed, and the underwriter will sell the offered shares, one way or another. 16

18 Lowering the offer price is an option in a best-efforts offering; however, it is rarely done, probably because the signaling effects would be dramatic, as suggested in the previous section. Now, in a best-efforts contract, we define the costs of under and overpricing from the issuing firm s perspective since the investment banker is simply acting as a broker. Thus, s k from the costs of under and overpricing in a firm-commitment contract, is now replaced by 1 k in a best-efforts offering. In addition, the reputational cost of underpricing parameter,, goes to zero for the issuer. So the issuer s marginal cost per unit of underpricing, c ui, equals the constant percentage 1 k, where underpricing equals the initial market price less the offer price, or zero, whichever is greater. Hence, the issuer loses 1 k in terms of net proceeds, for every unit of underpricing relative to Z P from Eq. (2). Similarly, the marginal cost per unit of overpricing for the issuer, c oi, is expressed here as a constant percentage of the offer price, P, less Z P, or zero, whichever is greater. This cost per unit of overpricing, c oi, equals k1 i(1 (1 k)). The k 1 portion of the coi term is, of course, simply the negative of c ui, and k 1 will not be realized here if the offering is actually overpriced and thus, fails. However, since V is uncertain prior to the offering, the issuer must consider the potential for aditional proceeds, in the form of ( k 1), from setting a higher offer price. Note that an additional subscript, i, has been added to signify that these costs are from the issuer s perspective. It is not difficult to imagine that i could take on extremely high values when one considers that just a small amount of overpricing could result in a withdrawn offering and thus the loss of an opportunity to raise the funds to finance what might be a lucrative yet time-sensitive capital investment. Consistent with this, Dunbar (1998) finds that withdrawn best-efforts offerings are very costly, and Ritter reports that firms rarely try again to go public if a first attempt is 17

19 withdrawn, suggesting the reputational harm is significant. Furthermore, lowering the offer price is hardly a viable option for the reasons mentioned above. It follows that the critical ratio, c / ( c c ), in a best-efforts is (1 k) / (1 (1 k)). ui ui oi i Substituting this ratio into N 1 (), and accounting for Δ and k yields Eq. (8), the issuer s optimal offer-price to value ratio in a best-efforts offering. 1 k 2 exp( NN.5 N) i k PI 1 1 ˆ V 1 (1 k) (1 (1 )) L (8) The issuer s optimal offer price, P, in Eq. (12), is less than P ˆ Z, the estimate of the offer I price with a return of zero, if the critical ratio, (1 k) / (1 (1 k)), is less than N(0.5 ), so that the exponent in Eq. (8) is less than zero. The resulting initial market price now equals i N (1 ) (1 ) I V k P, similar to as before but with k replacing s. The realized initial return can then be calculated from Eq. (1), and if the issuer sets the offer price so as to satisfy P / ˆ I L V, as specified in Eq. (8), then the expected initial return is as shown in Eq. (9). E IR k N 1 k 1 2 ( ) (1 (1 )) exp N.5N 1 i(1 (1 k)) (9) A simple numerical example helps demonstrate the magnitude of underpricing that can be expected with reasonable parameters values. We assume that i 7, which may appear to be high; however, when one considers that even a small amount of overpricing can result in withdrawal of the offering, this may, actually, be a very modest value for i. 9 We also assume that 0.4 and k 0.10, where k is the issuer s direct costs in this best-efforts offering. Uncertainty about 18 V is 9 Note that modeling i as a constant parameter is clearly a simplifying assumption here, in analyzing the best-efforts contract, since i will certainly decrease as underpricing increases; however, the importance and implications of the cost of overpricing in a best-efforts offering can be made here without introducing the complexity necessary to model i as a function of underpricing.

20 likely to be higher in a best-efforts offering, so we assume N 40%, whereas we used 10 to 20% in our examples of a firm-commitment offering. From Eq. (8), we can compute the optimal offer price to value ratio, P / ˆ I L V, as 0.619; in which case, the issuer s net proceeds, (1 kp ) I, are expected to be 55.7% of V ˆL, and the expected initial return, E( IR ), is 33.0%, based on Eq. (9). Interestingly, this is similar to the average level Ritter observes for best-efforts offerings in the U.S. Figs. 3 and 4 indicate that the E( IR ) on a best-effort offering increases in N, and E( IR ) increases more rapidly in N as i increases. But perhaps the more important result from this analysis of the best-efforts contract is that underwriter risk, per se, is not the explanation for underpricing. 10 The more general explanation lies with the potential loss of proceeds from setting a fixed-offer price, and this risk is greater in a best-efforts contract since overpricing usually leads to withdrawal, and thus failure, of the offering. 11 We refer to this explanation for underpricing as the proceeds-shortfall risk theory. 5. A comparison of proceeds-shortfall risk with other theories of underpricing: the analogue of the newsboy solution as a unifying framework As the previous sections demonstrate, setting a fixed-offer price introduces risk, and it results in optimal expected underpricing when there are asymmetric costs, between under and overpricing, so that the critical ratio, c /( c c ), is relatively low. Similarly, we suggest that u u o many, if not most, of the existing theories for underpricing can be distilled down to some sort of cost, or benefit, of either under or overpricing. In which case, our analogue-newsboy model is 10 Sherman (1992) offers an alternative explanation for the underpricing of best-efforts offerings which relies on asymmetric information, with underpricing providing the reward to investors for investing in information production. 11 A similar point is made by Jones and Yeoman (2009) in regards to the pricing of event tickets. They show it is the potential loss of revenue from overpricing that leads to ticket rationing. 19

21 general enough to reflect the logic of these other theories by enhancing the definitions of and, accordingly. With this in mind, we review the most widely known theories of securities underpricing to determine if they are compatible with proceeds-shortfall risk in the general framework of our analogue-newsboy model. We begin by reviewing the theories that focus on underwriter risk in order to place proceeds-shortfall risk in its proper context within the literature A comparison of proceeds-shortfall risk to other theories of underwriter risk Proceeds-shortfall risk has roots in some of the earliest investigations of IP underpricing. In considering explanations for the early empirical evidence, Ibbotson (1975) noted that securities regulations prohibit fixed-offer prices from being increased, and this exposes underwriters to asymmetric, or what he called one-sided, risk. He found this explanation lacking, however, because he saw no compelling reason to set the fixed-offer price below the expected initial market price. Ibbotson was more intrigued by an explanation that arose from his questioning of whether the spread, alone, could efficiently compensate for any given level of underwriter risk. That is, could it, instead, be optimal to allow the underwriter to set the offer price below the expected initial market price, in exchange for a lower spread? Ibbotson s question is, of course, what we have addressed, here, and answered in the affirmative. That is, it is optimal, in terms of a Stackelberg equilibrium, for the issuer to allow the underwriter to set the offer price below the expected initial market price, in exchange for a lower spread. But we are not the first to address this question. Logue (1973) was the first, we are aware of, to observe that underwriters can reduce risk and curry favor with investors by underpricing a new issue. He attributed observed underpricing to a lack of competition amongst underwriters, and wondered why underwriters are willing to share this monopsony profit with investors, rather than capture it all by increasing the spread. Logue and Lindvall (1974) found empirical evidence of a trade-off between the offer price and spread in 20

22 offerings underwritten by the so-called prestigious investment banks, and they speculated on whether the limits on spreads, implied by securities regulations, might obstruct this trade off in the offerings of less prestigious underwriters and therefore exacerbate underpricing. Bear and Curley (1975) hypothesized that underwriters reflect the risk of an offering through underpricing, as well as the spread, because risk-averse buyers in the primary and secondary markets require a premium to compensate for the initial uncertainty associated with a new issue. They detect support for this hypothesis in the form of a positive relation between aftermarket returns and various measure of firm risk. Thus, they could not reject a null hypothesis of competitive underwriting, and furthermore, they suggest that underpricing has the added advantages of reducing price-support costs and making it easier to form a selling group. Affleck-Graves and Miller (1989) focus on the risks that underwriters face as a result of the procedures and regulatory restrictions on firm-commitment offerings. Specifically, they argue that selecting the spread in advance of the offer price, limiting spreads based on guidelines implied by securities regulations, guaranteeing the issuer s net proceeds, and prohibiting increases in the offer price, together, result in an asymmetric payoff that leads profit-maximizing underwriters to underprice firm-commitment offerings. They achieved this result without assuming a risk-averse underwriter because they were able to show that the guarantee reduces the underwriter s expected profit. 12 Affleck-Graves and Miller conclude that proceeds are passed along to investors via underpricing because underwriters are effectively restricted by securities regulations from raising the spread high enough to fully compensate for the risk posed by the guarantee. Although similar in some ways, our results show that underpricing is optimal even without limitations on spreads. 12 Note that Affleck-Graves and Miller limited the mathematics in their model to payoff functions and their examples apply the beta distribution to prices; thus, their model does not take advantage of option pricing analysis, although they allude to the underwriter as having granted a put to the issuer. 21

23 Tinic (1988) rejected these underwriter-guarantee based explanations for underpricing, which he categorized as the risk-averse underwriter hypothesis. He describes this hypothesis as having superficial appeal because he claims it fails to explain why issuer s do not require underwriters to just increase the spread to compensate for the risk of providing the guarantee. Thus, Tinic ignored earlier papers, mentioned above, that had attributed this to regulatory limits on spreads (Logue and Lindvall) or initial uncertainty about value (Bear and Curley). In addition, Tinic s use of the adjective, risk-averse, in describing this hypothesis, may have caused confusion since none of the relevant papers actually assumed a risk-averse underwriter, though Bear and Curley did assume the initial investors in the primary and secondary markets are risk averse. Tinic s more persuasive argument against underwriter risk, as an explanation for underpricing, was that it could not explain why underpricing is so material in best-efforts offerings. Regardless, Tinic s criticisms, along with the emergence of the asymmetric information and signaling theories, appear to have led the mainstream of this literature, with the exception of Yeoman (2001), to ignore underwriter risk, as a potential explanation for securities underpricing. Yeoman (2001) builds on Smith s (1977) contingent claims analysis of underwriting, which shows that the regulatory prohibition against raising the offer price amounts to giving a call option to potential investors, thus making the underwriter long the issuing firm s stock, short a cash payment, and short this call. Yeoman notes that the net of these positions leaves the underwriter short a put with a strike price equal to the offer price. Recognizing that the objective of a competitively-constrained underwriter is to maximize the issuer s net proceeds, he determines that the most cost-effective put for achieving this objective involves some optimal tradeoff between the spread and the offer price, which can result in expected over or underpricing. In fact, if the underwriting fee is high enough, as a percent of the gross spread, the optimal solution is to set the spread and offering price arbitrarily high and turn the process into a descending-price Dutch 22

24 auction. 13 Interestingly, this exact strategy was proposed by Ibbotson (1975) as a means of intentionally breaking the underwriting syndicate in order to circumvent the fixed-price regulations and avoid the associated one-sided risk. In addition to underwriter risk, Ibbotson proposed several other explanations for underpricing that he said, may not be very plausible but are at least consistent with empirical findings. These included asymmetric information, signaling, collusion, efficient contracting, and litigation risk. By the1980s, most of the literature was progressing along these lines and underwriter risk had fallen from favor as a potential explanation for underpricing. In the rest of this section, we consider these, and some more recent explanations, and their relation to proceeds-shortfall risk Asymmetric information and signaling Ex ante uncertainty about the issuing firm s value, V ˆL, is the source of risk in Rock (1986), just as in our model. But while investors, the issuing firm, and the investment bank in our model all face the same level of uncertainty ( V ˆL, L ), Rock assumes the existence of informed investors who have either perfect or superior information about the issuer s actual value, V, and he omits an investment banker, and thus an underwriter, from his model. Since informed investors bid only on favorably-priced offerings, uninformed investors receive just a partial allotment of these shares but a full allotment of shares in unfavorably-priced offerings. Uninformed investors, therefore, suffer the winner s curse so that a general expectation of underpricing, across all offerings, is necessary to maintain the participation of uninformed investors. 13 See Jagannathan, Jirnyi, and Sherman (2009) as well as Jones and Yeoman (2008) for an analysis of the use of auctions and why they do not dominate book-building as a mean of issuing IPs. 23