3.2.1 Closed book auction (CB)

The CB treatment involves a uniform price auction in line with the OpenIPO implemented by WR Hambrecht & Co (DeGeorge et al. Reference DeGeorge, Derrien and Womack2010). Subjects submit sealed bids, each of which for the purchase of a single asset share. Their own bids are recorded onscreen in view of constraint (1). No information is given on the bids of other subjects or the likelihood of winning during the auction. After all subjects have submitted their demand schedules, the IPO purchase price is determined given the aggregate demand. Asset-shares are placed with the submitters of the winning bids, B _k: k ≤ 18 respecting Eq. (2).

3.2.2 Open book auction (OB)

The OB treatment involves similar rules to the CB regarding bidding, price determination and the allocation of shares to the winning bidders. During the auction, however, subjects receive updated real-time information on the purchase price, B ₁₉ and all rejected bids B _k < B ₁₉. OB is a dynamic auction in which bidders can react to the submitted bids of the others. If individual valuations are independent, such dynamics must not necessarily affect the bidding and the expected IPO purchase price (Vickrey Reference Vickrey1961). Nevertheless, if bids are indications of prices in the asset market, such a revelation of the bids can help to decrease uncertainty about future prices and thus aid price discovery in the IPO. The difference between the IPO price and the aftermarket price might be reduced relative to the other treatments.

One potential adverse effect of the OB is an encouragement of early signaling and late bidding. A late-bidding effect has been documented for single-unit dynamic auctions with a fixed deadline (Roth and Ockenfels Reference Roth and Ockenfels2002; Füllbrunn and Sadrieh Reference Füllbrunn and Sadrieh2012). In a related open auction format but with a multi-unit discriminative auction for certificates of deposits such an effect has not been confirmed (Chiang and Kung Reference Chiang and Kung2005). For multi-unit uniform price auctions we are the first to investigate the late bidding effect (see the online appendix).

3.2.3 Book building (BB)

The book building-BB treatment represents a stylized book building approach involving a two-stage procedure. The first stage involves the closed-book IPO price determination rule equivalently to the CB treatment. Every subject submits a sealed demand-schedule involving up to 18 bids for multiple assets in agreement with Eq. (1). The IPO purchase price is fixed according to Eq. (2) in the first stage and is publicly announced in the second stage. Upon the announcement, investors state the number of shares they are willing to acquire at that fixed price. Shares are allocated according to a probabilistic pro-rata rule; each share request is equally considered and the winning bids are randomly drawn. The quantity demand of the second stage is individually limited to the number of bids submitted in the first stage. Thus, submission is encouraged of a maximal number of bids in the first stage. As bids in BB have no direct allocation implication, on the other side, incentives exist to low ball on bidding in the first stage to induce a lower offering price (as suggested by Ljunqvist Reference Ljungqvist and Eckbo2007). The IPO price in the BB treatment must therefore be expected to be lower than in the CB treatment.

3.2.4 Design Justification for IPO Treatments

For the design of our treatment conditions, we focus on two aspects. First, the treatment should be close to the existing real-world IPO mechanisms. Second, the treatments should be simple for implementation in the laboratory with minimal differences across treatments. The closed book auction comes very close to the standard IPO auction in the real world. Indeed, the experiment uses a smaller lot size, a shorter submission period and sets a reserve price of zero. The open book auction is a potentially interesting IPO format,Footnote ¹³ but direct revelation of price information has been rather exceptional in real world public offerings. During the IPO auction of Health Communications Network and Charos Music, the IPO underwriter, Ord Minnetts’s eCapital auction, repeatedly revealed additional bidding information, including average bid price (Jagannathen and Sherman Reference Jagannathan and Sherman2006). In related real-world auctions for bond issues WR Hambrecht & Co. typically offers real-time information on the development of the market demand curve. Finally, the book building process in our experiment with the purpose to determine a fixed offer price is simplified and transparent compared to the procedure in the real world. The book runner is usually a consortium of investment banks that elicits opinions from institutional investors to determine a range for the IPO price and the size of the capital raise. Before the first listing on the exchange, this price range is communicated to investors. Based on demand, the IPO price and size are fixed during the final days of the IPO. Hence, our implementation abstracts from many complications in real-world IPOs.

In our experiment, investors have common information about the entire procedure of the IPO and the aftermarket. They are symmetrically and transparently informed about the dividend distribution and the expected cash flows to equity. The market imperfections emphasized in the above surveyed demand side and supply side explanations of underpricing are absent. It is a justifiable theoretical benchmark if we propose that the price should equal the discounted sum of expected dividends.

Hypothesis 0

Initial public issues yield no underpricing ( $X_{\tau }^{\mathrm{IPO}}=0\forall \tau$ ) and IPO price equals fundamental value ( $x_{\tau }=0\forall \tau$ ).

However, at least two alternative explanations could justify underpricing even in our setting where symmetric and transparent information on the fundamental asset value is given: (i) uncertainty of aftermarket behavior and (ii) a market-wide impact of IPO investors’ reluctance to sell at a loss.

1. (i) Traders face strategic uncertainty about the behavior of the others, about asset pricing and their opportunities to buy and sell in the aftermarket. Therefore, it is reasonable for investors to request an uncertainty premium on IPO investment. This uncertainty premium is similar to the adverse selection problem resulting in the winner’s curse referred to above, despite the fact that information in our setting is symmetric. When subjects are inexperienced, the strategic uncertainty about the aftermarket behavior looms larger than when once experienced.

2. (ii) Underpricing may be influenced by a psychological bias akin to the disposition effect (Shefrin and Statman Reference Shefrin and Statman1985) according to which investors are reluctant to sell below their purchase price. Because in the IPO, every investor pays the same asset price, the IPO price thus could be a psychological anchor of the market. Allowing for a market-wide impact of the reluctance to sell below the purchase price, there is more upside than downside to share appreciation. Hence, we formulate the first alternative hypothesis.

Hypothesis 1

There is underpricing in each IPO mechanism and each round, $X_{\tau }^{\mathrm{IPO}}>0\forall IPO,\tau$ .

In view of (i), one may expect that learning by experience has a decreasing effect on underpricing in a repeated IPO. As subjects’ uncertainty about aftermarket behavior is reduced in the second IPO once subjects are experienced, the level of underpricing should be affected if the driver of underpricing is uncertainty. Earlier experimental evidence suggests that subjects learn between market repetitions (as most illustratively presented by Haruvy et al. Reference Haruvy, Lahav and Noussair2007) so that pricing is closer to fundamentals once subjects are experienced. We expect also for our IPO treatments that market valuation is closer to fundamentals once subjects are experienced; therefore, we anticipate a repetition effect on expected excess returns of the IPO with respect to fundamentals (2a). This effect may be reinforced by the decreased uncertainty about aftermarket trading behavior, which again may result in a decreased uncertainty premium required by the market and thus reduced underpricing (2b).

Hypothesis 2

(a) IPO-investors’ expected excess returns decrease with repetition, $x_2<x_1$ , and (b) the level of underpricing decreases with repetition $X_2^{\mathrm{IPO}}<X_1^{\mathrm{IPO}}$ .

The alternative explanation (ii) does not preclude but does not require a reduction of underpricing. A market-wide impact of the reluctance to sell below the purchase price implies some degree of persistence of underpricing. To examine whether IPO investors are reluctant to sell below their purchase price and take a loss we check the asking prices of sellers in the aftermarket. Individual investors’ reluctance to sell at a loss relative to their willingness to sell at a gain has been known as the disposition effect (Shefrin and Statman Reference Shefrin and Statman1985). In view of (ii) we state the following hypothesis.

Hypothesis 3

Aftermarket asking prices equal or exceed the IPO price.

DeGeorge et al. (Reference DeGeorge, Derrien and Womack2010) report a smaller extent of underpricing in the IPO auction mechanism than in the book building mechanism with a fixed-price offering (see also Benveniste and Busaba Reference Benveniste and Busaba1997; Zhang Reference Zhang2009; Trauten and Langer Reference Trauten and Langer2012; Bonini and Voloshyna Reference Bonini and Voloshyna2013). A lack of incentive compatibility (Ljunqvist Reference Ljungqvist and Eckbo2007) could be the reason for this difference, as low price indications are not necessarily punished. In related literature, Levin and Kagel (Reference Kagel and Levin2001) report evidence that bidding in dynamic multi-unit auctions with feedback is closer to the risk neutral equilibrium than bidding without feedback.Footnote ¹⁶ So, demand reduction may play a bigger role in the closed book format than in the open book format. Generally, the mechanism used can play a role for the pricing of offerings. Based on the referenced evidence we state the next hypothesis.

Hypothesis 4

Owing to price feedback, underpricing may be smaller in OB than in CB, and owing to incentive compatibility in CB smaller than in BB treatments, $X_{\tau }^{\mathrm{OB}}<X_{\tau }^{\mathrm{CB}}<X_{\tau }^{\mathrm{BB}}$ .

4.2.1 Observation 1: EACH IPO treatment shows significant underpricing in both rounds

Support In Table 1, the first column records the short-term returns in the BL treatment. We calculate excess returns using the average price of the first period. Returns are reported for the first and second repetitions of the experiment, when subjects are inexperienced and once-experienced, respectively. We use the one-sample Wilcoxon signed ranks test on the sample of seven independent BL observations to check whether the returns are significantly different from zero. Returns are positive and significantly different from zero for inexperienced subjects. For experienced subjects, average returns in BL are not significantly different from zero. Note the return differences between first and second repetition of BL point to differences between underpricing and expected excess return (see observation 2). Underpricing is significantly different from zero whether subjects are inexperienced or experienced as seen in columns (II)–(IV) of the table, jointly with the z-scores of the two-sample test and asterisks indicating significant differences. The results of the Mann–Whitney two-sample test as reported in columns (II)–(IV) involve seven independent observations, the test results in column (V) involve 21 independent markets. It is remarkable that underpricing is positive in each IPO, in each repetition and with respect to each reference price.Footnote ²⁰

Table 1 IPO underpricing

	(I)	(II)	(III)	(IV)	(V)
Round $\tau$	$R_{\tau }^{\mathrm{BL}}$	$X_{\tau }^{\mathrm{OB}}$	$X_{\tau }^{\mathrm{CB}}$	$X_{\tau }^{\mathrm{BB}}$	$X_{\tau }^{\mathrm{IPO}}$
1	5.5%** (2.197)	14.2%*** (2.747)	50.1%*** (2.875)	53.6%*** (2.747)	35.9%*** (2.747)
2	− 1.0%** (− 2.156)	33.9%*** (3.137)	32.3%*** (3.137)	57.1%*** (3.137)	40.7%*** (3.137)
Difference between rounds	− 6.5% (− .947)	20%** (2.028)	− 18%* (− 1.690)	3.5% (1.183)	4.8% (.156)

First-period average returns of the Baseline treatment, $R_{\tau }^{\mathrm{BL}}$ are recorded in column (I). We report in columns (II)–(IV) the realized excess returns of the IPO treatments with the average price as the reference, as defined in Eq. (2). Column (V) reports the average excess return from all IPO treatments taken into account. Round index = {1; 2} indicates subjects when inexperienced and once experienced, respectively. Significant results of the Mann–Whitney test and Wilcoxon signed ranks test are recorded in columns (II)–(V) and (I), respectively. Standard normal z-scores are recorded in parenthesis. Two-tailed significance levels are indicated by asterisks ^*** α = 1%; ^** α = 5%; ^* α = 10%

4.2.2 Observation (2a): Underpricing is not significantly reduced once experienced

Support The one-tailed Wilcoxon signed ranks test of the null hypothesis $X_1^{\mathrm{IPO}}\le X_2^{\mathrm{IPO}}$ cannot be rejected in favor of the alternative (Hypothesis 2b) of lower underpricing once experienced at any commonly used significance level when no distinction is made between treatments, i.e., based on 21 markets. Overall, as suggested by the measures recorded in Table 1 (column V), underpricing increases rather than decreases from the first to the second IPO. At the treatment level, we find underpricing to be significantly reduced in CB ( $z=-1.690$ ). This reduction, we must caution, could be a market reaction to the abnormally high level of underpricing in the first round IPO of the CB treatment. In OB and BB, in contrast, there are more independent observations for which the level of underpricing increases rather than decreases between rounds. Therefore, our data suggest persistence of underpricing between repetitions in OB and BB, and reversion in CB.

We provide further support for this observation with OLS regression results, which also show the treatment effect. In the regression, we make use of treatment dummies for the BB and CB treatments (where BB = 1 or CB = 1 in those treatments and zero otherwise), a regression dummy for experience (where experienced = 1 in the second round of the experiment and zero otherwise), and the interaction effect between experience and treatments. We report the results in Table A1 of the online appendix. Generally, we find no experience effect. Even for the CB treatment, the median and average price data suggest no significant repetition effect despite the extreme first round underpricing. That being said, the regression results indicate the treatment effect as we find reduced underpricing in CB on the basis of the bid-ask midpoint and the price at closing.

4.2.3 Observation (2b): IPO-investors’ expected excess returns are significantly positive in both repetitions but decrease once experienced

Support Table 2 records the average expected excess returns as defined in Eq. (3). As shown in column (VI), the excess return on the pre-market price in BL is significant with inexperienced subjects, but close to zero once experienced. In other words, closing prices in period zero of round 2 are almost at fundamental value. The expected excess returns on the IPO price are significantly positive in each IPO treatment and repetition [see columns (VII)–(X)]. Thus, IPO prices are significantly below fundamental value. The overall average expected excess return on the IPO price, however, declines significantly from 93 to 47% between rounds (column X). The decline in expected excess returns on IPO prices is significant based on the reported results of the Wilcoxon signed ranks test with 21 observations. The results support the testable Hypothesis 2a. At the treatment level, however, the decline in expected excess return on the IPO prices between rounds is significant only for the CB treatment, but not for the OB and BB treatments. In sum, the general support for Hypothesis 2 is weak, and Hypothesis 0 must clearly be rejected, although the second-round return in BL is close to zero.

Table 2 Expected excess return on IPO price

	(VI)	(VII)	(VIII)	(IX)	(X)
Round $\tau$	$x_{{}^{\tau }}^{\mathrm{BL}}$	$x_{{}^{\tau }}^{\mathrm{OB}}$	$x_{{}^{\tau }}^{\mathrm{CB}}$	$x_{{}^{\tau }}^{\mathrm{BB}}$	$x_{{}^{\tau }}^{\mathrm{IPO}}$
1	33%** (2.371)	31%** (2.371)	135%** (2.371)	112%** (2.366)	93%*** (4.015)
2	− 0.8% (− 0.677)	37%** (2.366)	40%** (2.366)	63%** (2.371)	47%*** (4.016)
Difference between rounds	− 34%** (− 2.366)	5.5% (0.000)	− 96%** (− 2.366)	− 49% (− 1.183)	− 46%** (− 2.450)

The average expected excess return x is the difference of price and fundamental value, as defined in Eq. (3). Round index = {1; 2} indicates subjects when inexperienced and once experienced, respectively. Wilcoxon signed ranks test results are recorded. Standard normal z-scores are in parentheses, two-tailed significance levels are indicated by asterisks ^***α = 1%; ^** α = 5%; ^* α = 10%

4.3.1 Observation 3: Investors exhibit a reluctance to sell shares in the aftermarket below the IPO price (disposition effect)

Support In Table 3 we report the total number of asking and bidding prices that we observe in the aftermarket of our IPO treatments including market orders; 15% and 12% of total orders were market orders (leading to transactions confirming outstanding limit orders) in the first and second round, respectively. We observe only a small minority of asks below the IPO price; the majority of asks are above this benchmark. As reference point we note the significantly larger fraction of bids submitted below the IPO price. Thus our data indicate a systematic imbalance vis-à-vis the IPO price on the supply side of the market. The table shows that the frequency of bids and asks is similar above the IPO price (bids slightly outnumbering asks), but apparently different below the IPO price.Footnote ²¹ We observe a total of 27 (2.21%) and 2 (0.22%) asking prices below the IPO price in 21 sessions in the first and second rounds respectively.

Table 3 Aftermarket asks and bids relative to IPO price

	Round 1	Round 2
Asks above IPO price	37.04	41.50
Asks at IPO price	0.41	0.00
Asks below IPO price	2.21	0.22
Bids above IPO price	39.74	46.64
Bids at IPO price	2.29	1.12
Bids below IPO price	18.32	10.51
Total # bids and asks	1223	894

Recorded numbers of asking prices and bids (%) include limit and market orders. Total number of valid bids and asks are in the bottom line

We provide evidence for the significance of the investors’ reluctance to sell at a loss in two ways. First, we show that sellers’ asking behavior with respect to the IPO price is significantly different from sellers’ asking behavior with respect to the benchmark from the BL, i.e., the previous closing price in the control treatment. To do so, we compare the conditional relative frequency of asks below IPO price in the IPO treatments (3.00% on average in the two rounds) with the conditional relative frequency of asks below the latest pre-period price in the baseline treatment (16.10% on average). The difference is significant; the p value of the two-tailed Mann–Whitney test is 0.047.Footnote ²² There are significantly more asks submitted below the prior closing price in the baseline treatment than asks below the IPO price in the IPO treatments. Since the expected excess return is significantly positive in both IPO rounds, we must show it is no level effect. Therefore, we report in Table A2 of the online appendix the outcomes of an OLS regression of the number/share of asks below IPO price on the IPO price-level. Hence, we observe no effect of the IPO price-level.

Second, we show by simulation between IPO markets that subjects’ after-market asks are correlated with the IPO prices. To show that sellers anchor on the IPO price, we take the 21 IPO prices and the ask data for the 21 after markets and count the number of times the asks in the aftermarket are below any of the IPO prices. If aftermarket asks were independent from IPO-prices then there should be a similar number of asks below any randomly assigned IPO price. If, instead as we find, there are fewer asks below the actual IPO price than below a randomly assigned IPO price, it shows that shareholders anchor on the IPO price. We proceed with the following simulation steps. In the first step, the 21 observed IPO prices are exchanged between sessions, that is, they are randomly assigned to the sessions (by random draw without replacement, see the illustration in Figure A1 in the online appendix), while the observed aftermarket asking prices are kept with their sessions. In the second step, for each such assignation of random-sample IPO prices with actual aftermarket asking prices we count and total over our 21 sessions the number of asks that are below the randomly assigned IPO prices. Repeating 100,000 times the steps 1 and 2 we create a random distribution of number of asks below random IPO prices. (In Figure A1, we illustrate in an example the second simulation step, and we give more details on how the simulations lead to the random distributions displayed in Fig. 1).

Fig. 1 Simulated distribution of asks below IPO price (round 1 left; round 2 right)

Figure 1 exhibits this distribution of the number of asks below the shuffled IPO prices for the first round of IPO price and aftermarket asks. Only 2 of 100,000 (0.002%) such simulations produce outcomes as extreme as, or more extreme than, the 2.21% reported for the first repetition. For the second round, 4.91% (8.30%) of the outcomes are (as extreme as, or) more extreme than the reported outcome of 0.22%.Footnote ²³ As a similarly extreme outcome as the one observed thus is unlikely to have occurred by chance, we conclude that sellers anchor on the IPO prices when they submit their asking prices or when they accept an outstanding bid.