## 1 Introduction

The pricing behavior of initial public offerings (IPOs) has been one of the great mysteries of modern corporate finance. IPOs feature two seemingly antithetical pricing phenomena: First, in the short-run, IPO stocks appear to be underpriced; namely, first-day post-IPO returns have averaged 18.6% (Ritter 1998), indicating that firms and their underwriters are on average deliberately pricing IPO firms below their fundamental value. Second, empirical evidence suggests that in the medium-to-long-run, IPOs underperform; specifically, IPOs achieve negative abnormal results relative to their peers, indicating that firms and their underwriters may be deliberately overpricing IPOs. Although many attempts have been made to rationalize these two patterns individually, the coexistence of these two contradictory phenomena–which I hereafter refer to as the "IPO Puzzle"–has long confounded researchers.

Two major behavioral theories explaining the IPO Puzzle have recently been gaining acceptance: The first, disagreement theory, uses the existence of disagreement and short-sales constraints in the days and months immediately following IPOs to argue that during IPOs, investors with low valuations are priced out of the market, causing short-term post-IPO prices to reflect only the valuations of optimistic investors (Miller 1977). The second, information cascades theory, suggests that gradual information dispersion and momentum are commonplace among IPOs and are the cause of the short-run bubbles that form immediately after IPOs (Welch 1992).[1]

This paper therefore has two goals: First, I seek to combine the intuitions of Miller's disagreement theory and Welch's information cascades theory in a theoretical framework to illustrate the pricing implications of temporary disagreement and short-sales constraints, given the existence of gradual information diffusion–here, through momentum traders. Second, I seek to study for the first time the effect of aggregate, non-idiosyncratic disagreement on post-IPO price-volume dynamics and see Miller's intuitions stand empirically.

To achieve these ends, this paper is organized as follows: In Section 2, I review literature pertaining to the IPO Puzzle, herding in markets, and disagreement in order to motivate this research. In Section 3, I develop a simple model in which I incorporate momentum traders into the classic A-B disagreement framework. I use the intuitions from my model to motivate Sections 4 and 5, in which I describe my dataset and empirical methodology, respectively. In Sections 6 and 7, I present and discuss my empirical results. Finally, in Section 8, I summarize the major conclusions of my study and introduce a number of avenues for future work.

## 2 Background

### 2.1 The IPO puzzle

Historically, two main empirical idiosyncrasies of IPOs have drawn the attention of academics: (1) exceptionally high returns immediately following IPOs, and (2) long-run underperformance of IPOs (Ritter 1998). The key unanswered question is therefore how both short-term underpricing and long-term underperformance can coexist for IPOs. I consider attempts by researchers to explain each phenomenon in turn.

#### 2.1.1 Short-run underpricing

A wide body of empirical work has shown that the distribution of first-day returns to IPO stocks is highly right-skewed (Ibbotson 1975; Ritter 1984, 1998; Loughran and Ritter 2004): between 1980 and 2012, mean proceeds-weighted first-day returns have been approximately 18.6% (Ritter 2013). This phenomenon has been replicated in every country with a stock market, with historical average first-day returns ranging from 4.2% in Russia to 264.5% in Saudi Arabia (Loughran et al. 1994).

**Asymmetric information models.** Asymmetric information models presume that issuing firms, underwriters, or investors know more about the firm's true value than the other two. The most famous of these is Rock's (1986) winner's curse model, which argues that the best-informed, privileged investors crowd out unprivileged investors also during underpriced issues and abstain from investing during overpriced issues. When they abstain, they trigger negative conditional expected returns on the IPO, causing unprivileged investors to also abstain from investing. As such, firms underprice IPOs to ensure that privileged and unprivileged investors participate in the market.[2]

**Institutional incentives.** Institutional incentives models suggest that companies underprice themselves to reduce the likelihood of post-IPO lawsuits, prevent price drops following an IPO, generate additional revenue from greater brand awareness, or reduce managers' personal tax burdens (Tinic 1988; Hughes and Thakor 1992; Ruud 1993; Demers and Lewellen 2003; Rydqvist 1997).[3]

**Control theories.** The two major control theories actually conflict directly with each other: Brennan and Franks (1997) argue that underpricing helps to increase managerial control and agency costs by reducing the risk of a single shareholder taking control of a company. By contrast, Stoughton and Zechner (1998) argue that underpricing helps to increase monitoring and thus reduce agency costs and misaligned incentives.

**Behavioral models.** The three rational-choice-based groups of theories suffer from one major flaw: incentive-driven underpricing is an exceptionally costly means for firms to convey information to investors. It seems especially unlikely that a high-quality firm would incur an opportunity cost of over 10% of its overall value to help communicate its true value to investors (Ritter 2011).[4] Behavioral models, by contrast, allow for the existence of irrationality in firms and markets. As a note, behavioral theories are the newest, least-developed, and fastest-growing theories of IPO underpricing (Ljungqvist 2007).

Prospect theory models build on Kahneman and Tversky (1979) and Thaler (1985) and argue that managers of issuing firms both underweight the opportunity cost of underpricing and overweight the direct cost of underwriter spreads (Loughran and Ritter 2002). Welch's famous information cascades model (1992) claims that later investors use other investors' purchasing decisions rather than their own private signals to guide their purchasing decisions. This triggers the formation of "cascades," many of which are untethered from the firm's fundamental value. Finally, proponents of disagreement models argue that as issuing firms seek to extract as much surplus from high disagreement investors as possible, they limit asset float immediately following IPOs, causing IPO offer prices to exceed firms' fundamental value. Miller (1977) and Ljungqvist et al. (2003) therefore predict short-run overperformance and long-run underperformance of IPOs, as in the long run, investors learn the true value of the firm. The appeal of a number of the behavioral IPO theories over rationality-based theories is that they can explain both first-day IPO underpricing and long-term post-IPO underperformance.

### 2.1.2 Long-run underperformance

An equally interesting but far more empirically contentious phenomenon concerns the long-run returns of IPOs. As a result of the exceptional methodological complexity of the empirical debate pertaining to long-run post-IPO returns, I draw the following two conclusions from existing literature and point the reader to reviews by Ritter (1998), Jenkinson and Ljungqvist (2001), Ritter and Welch (2002), Yong (2007), and Ritter (2011) for further reading. First, evidence from U.S. and Chinese financial markets indicates that IPOs underperform in the long run (Yong 2007). Second, the extent of IPO underperformance will be up for debate as long as there are multiple accepted measures of risk-adjusted performance (Ritter and Welch 2002).

I turn to the two major explanations given for long-run IPO underperformance. Originally proposed by Ritter (1991) and Loughran and Ritter (1995), the window of opportunity hypothesis holds that firms attempt to time IPOs to take advantage of positive swings in investor sentiment when IPOs themselves are overvalued (Ritter 1998).[5] Of greater interest to this paper is the concept that short-sales constrained investors with heterogenous expectations cause the formation of price bubbles. This theory has its roots in Miller (1977) and is predicated on the intuition that IPOs are environments with high disagreement and short-sales constraints as a result of the limited float available post-IPO.

The review above has demonstrated that behavioral explanations to the IPO Puzzle may be superior to their rational-markets counterparts. Accordingly, I address the precepts of both herding and disagreement finance and discuss recent work tying each to IPOs.

### 2.2 Herding and markets

#### 2.2.1 Information diffusion

The most famous study of the effect of information diffusion is by Huberman and Regev (2002), who study EntreMed. After the *New York Times* carried a front-page article about the company in 1998, EntreMed's share price rose from a 12 Friday close to an 85 Monday open, consistently closing above 30 in the subsequent three weeks. Even though the Sunday *New York Times* article provided no new information, it induced a permanent price increase for EntreMed.

The EntreMed example illustrates the power of gradual information diffusion, a phenomenon described famously in Bikhchandani et al. (1992). Investors receive noisy signals of the technology's true value and revise their beliefs using Bayesian updating, given previous investors' investment decisions. The result of the model is fascinating: early movers exert exceptional amounts of influence on late movers. Moreover, when there are sufficiently many prior confirmatory actions, Bayesian updating rationally requires unconditionally throwing away individuals' signals, initiating an information cascade.

#### 2.2.2 Momentum

Closely related to the concept of information cascades is the concept of medium-term momentum in markets, a phenomenon described famously by Jegadeesh and Titman (1993). On the empirical side, Lee and Swaminathan (2000) show that stocks with high past turnover generally had higher and more persistent momentum. Hong et al. (2012) demonstrate that arbitrageurs can amplify the effects of good news if investors have a disproportionate number of short positions on the stock *ex ante*.[6] Theoretical attempts to rationalize momentum include Hong and Stein (1999) and Hong et al. (2011), who use epidemiological models to explain momentum and information diffusion, and the aforementioned studies on information cascades.[7]

#### 2.2.3 Turnover

Also related to the above literature is the widely documented relationship between turnover and price bubbles. Piqueira (2004) demonstrates that between 1993 and 2002, turnover was negatively related to long-run returns, when controlling for liquidity. Similar results have also been found in Baker and Stein (2004), Datar et al. (1998), Chen et al. (2002), and Brennan et al. (1998).[8]

Approaches to this apparent violation of the Milgrom and Stokey (1982) No-Trade Axiom include the disagreement approach, which focuses on speculative motives that can create volume regardless of whether price moves exist. Given the growing acceptance of disagreement approaches to the IPO Puzzle, I turn my attention to the effect of disagreement on speculation in markets.

### 2.3 Disagreement and speculation

#### 2.3.1 Sources of disagreement

**Gradual information diffusion.** Although the EntreMed example from Huberman and Regev (2002) is often cited by behavioral economists, the existence of gradual information diffusion can be fully consistent with models of rational decision-making; namely, specialists may face lower information acquisition costs than generalists. In the case of EntreMed, generalists failed to deduce information from the trading patterns of specialists following stories before the front-page *New York Times *article; instead, they only traded when spoon-fed information (Hong and Stein 2007).

This theory is especially relevant in the case of IPOs, which feature extremely limited publicly available information, and therefore highly asymmetrical information. As information about companies typically spreads gradually, it is likely that gradual information diffusion may be driving disagreement during and immediately following IPOs.

**Limited attention. **Limited attention theory suggests that individuals pay attention to only a small fraction of information available to them. Empirical studies of limited attention include Klibanoff et al. (1998), who find that closed-end country fund prices react far more to changes in fundamentals when news pertaining to that country appears in the *New York Times*, and underreact otherwise. Conversely, DellaVigna and Pollet (2005) find that stocks with Friday earnings announcements have substantially slower stock prices responses, and 10% lower volume, as investors are distracted temporarily over weekends.[9]

**Heterogenous priors. **The heterogenous priors school of thought suggests that investors can *still* disagree about asset valuations if they utilize different economic models for interpreting information (Harris and Raviv 1993; Kandel and Pearson 1995).[10]

Regardless of the channel by which disagreement exists, it can only create speculative bubbles if it exists in the context of short-sales constraints (Miller 1977).

#### 2.3.2 Short-sales constraints and speculation

Short-sales constraints are a regular occurrence in markets: many investors lack the ability to short. Short-sales constraints can additionally come in the form of unavailable proxies for shorting, government bans on short-sales (Bris et al. 2007), and even limited asset float, as is often the case with IPOs. Miller (1977) argues that if short-sales constrained investors disagree sufficiently about the intrinsic value of an asset, pessimistic investors can effectively be shut out of the market, causing the price of an asset to reflect only the views of optimists. Miller argues that disagreement can explain low returns on value stocks, IPOs, and high-beta stocks. One major implication of Miller's canonical model is that as the magnitude of disagreement rises, so does overpricing. This conclusion is supported by a simple static A-B model from Chen et al. (2002), as well as empirical evidence in Diether et al. (2002) and Chen et al. (2002).[11]

Two pieces of Hong and Sraer's (2011b) empirical work are of great interest to this paper. First is the inversion of the securities market line predicted in high aggregate disagreement periods, a result that inspires me to study for the first time the effect of aggregate disagreement on IPOs. Second, and more importantly, is the monthly time series of aggregate disagreement used by Hong and Sraer. As a proxy for aggregate disagreement, the authors use the beta-weighted average of the dispersion of analyst forecasts of the long-term growth rate (c.f. Yu (2011)). I use this same measure as my primary explanatory variable during this paper.

#### 2.3.3 Disagreement and IPOs

Although the disagreement approach to the IPO Puzzle has existed since Miller (1977), empirical research studying the effect of disagreement on IPO returns is surprisingly scant.

Houge et al. (2001) study IPOs between 1993 and 1996, and use three proxies for disagreement–the flipping ratio, time of first trade, and opening bid-ask spread. Houge et al. find that all three measures of disagreement have the ability to predict low long-run IPO returns when controlling for issue quality. Similarly, Loughran and Marietta-Westberg (2005) use turnover as a proxy for disagreement, and unsurprisingly find a negative relationship between long-run return and turnover.

No paper has attempted to directly study the effect of disagreement on IPOs. Each of the aforementioned papers uses a noisy measure of disagreement that can reflect a number of market factors that may not be directly related to actual market disagreement. Moreover, idiosyncratic measures of disagreement often are influenced by a firm's risk profile, introducing further omitted variables bias and error-in-variables bias into these studies. Accordingly, I opt for more direct proxies of disagreement used in Hong and Sraer (2011b) and Yu (2011).

## 3 Model

### 3.1 Setup

I seek to show that temporary disagreement in a setting with temporary short-sales constraints and momentum traders–both of which often exist immediately following IPOs–can lead to a short-term bubble *and* long-term underperformance below fundamental value. To illustrate this, I use a simple adaptation of the static A-B model used in Chen et al. (2002), Hong and Stein (2003), Hong et al. (2006), Hong and Stein (2007), Hong and Sraer (2011a), and Hong and Sraer (2011b).

Consider a single asset in supply \(Q > 0\), and assume for simplicity that the risk-free rate is zero. There are four dates: \(t = 0\), 1, 2, and 3. The asset pays a terminal dividend \(D = V+\epsilon_v\) at \(t = 3\), where \(\epsilon_v \sim \mathcal{N}(0,1)\).

In this model, there are three types of investors: \(A\), \(B\), and \(M\). Investors of type \(A\) and \(B\) trade the asset at \(t=0\), 1, and 2. Each period, investors of type \(A\) and \(B\) maximize the following CARA function:

\begin{equation}

E[W] - \frac{1}{2\eta}[\textit{var(W)}]

\end{equation}

where \(W\) is wealth and \(\eta\) is the risk-bearing capacity of each group. I denote \(D_t^{(i)}\) as type \(i\in{A,B}\) investor's belief of the terminal dividend at time \(t\), and \(x_t^{(i)}\) to be the time \(t\) demand of type \(i\) investors.

At \(t=0\), type \(A\) and \(B\) investors have homogenous priors about \(D\):

\begin{equation}

D_0^{(A)} = D_0^{(B)} = V + \epsilon_v

\end{equation}

where \(\epsilon_v \sim \mathcal{N}(0,1).\)

At \(t=1\), investors of type \(A\) and \(B\) receive a disruptive signal \(\lambda\) and \(-\lambda\) about the fundamental value of the asset, respectively, where \(0 <\lambda < \frac{3Q}{\eta }\). I interpret \(\lambda\) and \(-\lambda\) as the positive bias of investor type \(A\) and the negative bias of investor type \(B\)–namely, their disagreement.

No investors know that this disruptive signal will exist at \(t=0\). At \(t=1\), the disruption \(\lambda\) is a private signal to both investors of type \(A\) and \(B\); moreover, each investor naively believes that the other investor has the old belief \(D_1^{(i)} = V\), and does not dynamically infer the other investor's belief based on prices until after markets have cleared at \(t=1\). This disruption transforms the beliefs of investors of type \(A\) and \(B\) into the following:

\begin{align}

D_1^{(A)} &= V + \lambda + \epsilon_v + \epsilon_{\lambda} & D_1^{(B)} = V - \lambda + \epsilon_v - \epsilon_{\lambda}

\end{align}

where \(\epsilon_\lambda \sim \mathcal{N}(0, \sigma_\lambda^2)\) represents the additional perceived variance by type \(A\) and \(B\) investors as a result of \(\lambda\). For the purposes of this model, assume \(0<\sigma_\lambda< \sigma_v = 1\).

At \(t = 2\), disagreement between type \(A\) and \(B\) investors disappears, restoring their beliefs about the dividend to the following:

\begin{equation}

D_2^{(A)} = D_2^{(B)} = V + \epsilon_v

\end{equation}

Note that at \(t=2\), type \(A\) and \(B\) investors believe that other non-type \(M\) investors also hold the same belief about the asset's terminal dividend.[12]

I let \(\Sigma_t^{(i)}\) be type \(i\in{A,B}\) investor's beliefs about the variance of the returns between time \(t\) and \(t+1\). For simplicity, I assume \(\Sigma_0^{(i)} = 1\), and \(\Sigma_1^{(i)} = \Sigma \in (1,2)\) (because of the symmetric but distorted beliefs of the investors), and \(\Sigma_2^{(i)} = 1\).

Investors of type \(M\) represents momentum traders. Momentum traders only trade the asset at \(t = 1\) and 2. Like type \(A\) and \(B\) investors, type \(M\) investors receive the same terminal dividend \(D\) for holding the asset at \(t=3\). Their demands are the following:

\begin{align}

x_1^{(M)} &= \eta (P_1 - P_0) & x_2^{(M)} = \eta (P_2 - P_1)

\end{align}

It is important to understand why momentum traders exist in my model. Momentum traders can consist of a number of individuals: First, non-institutional traders often react to IPOs based on initial price movements. Second, momentum traders can reflect growing numbers of investors learning about the IPO, in a manner similar to the information diffusion documented in the EntreMed case (Huberman and Regev 2002). Finally, and perhaps most importantly, it is conceivable that traders dynamically and profitably trade based on momentum.[13]

Hereafter, I assume that type \(A\) and \(B\) investors are fully short-sale constrained at \(t = 0\) and 1, as is often initially the case for IPOs, and that no investor is short-sale constrained at \(t = 2\). Investors also know they will not be short-sale constrained at \(t=2\). Moreover, I assume momentum traders are never short-sale constrained.[14]

### 3.2 Solution

**Lemma 1.** The stock holdings and price at \(t=0\) are given by the following:

\begin{align}

x_0^{(M)} = 0, \,\,\,\,\, x_0^{(A)} = x_0^{(B)} = \frac{Q}{2}, \,\,\,\,\, P_0 = V - \frac{9\tilde{Q}}{8} \label{eq:pricet0}

\end{align}

where \(\tilde{Q} = \frac{Q}{\eta}\).

**Lemma 2.** The stock holdings and price at \(t=1\) are given by the following two cases:**Case 1:** \(\lambda > \frac{3\Sigma \tilde{Q}}{4(4 - \Sigma)}\)

\begin{align}

&x_1^{(M)} = \frac{\eta \lambda}{2-\Sigma} + \frac{Q(5-4\Sigma)}{4(2-\Sigma)}, \,\,\,\,\, x_1^{(A)} = \frac{-\eta \lambda}{2-\Sigma} + \frac{3Q}{4(2-\Sigma)}, \,\,\,\,\, \nonumber \\

&P_1 = V + \frac{\lambda}{2-\Sigma} - \frac{\tilde{Q}(8-\Sigma)}{8(2-\Sigma)}

\end{align} **Case 2:** \(\lambda \le \frac{3\Sigma \tilde{Q}}{4(4 - \Sigma)}\)

\begin{align}

&x_1^{(M)} = \frac{Q(5-2\Sigma)}{2(4 - \Sigma)}, \,\,\,\,\,

x_1^{(A)} = \frac{\eta \lambda}{\Sigma} + \frac{3Q}{4(4 - \Sigma)}, \,\,\,\,\, \nonumber \\

&x_1^{(B)} = \frac{- \eta \lambda}{\Sigma} + \frac{3Q}{4(4 - \Sigma)}, \,\,\,\,\, P_1 = V - \frac{\tilde{Q}(16-\Sigma)}{8(4 - \Sigma)} \label{eq:pricet1-case2}

\end{align}

**Lemma 3.** The stock holdings and price at \(t=2\) are given by the following two cases:**Case 1:** \(\lambda > \frac{3\Sigma \tilde{Q}}{4(4 - \Sigma)}\)

\begin{align}

&x_2^{(M)} = \frac{-2\eta \lambda}{2-\Sigma} - \frac{Q(8-6\Sigma)}{8(2-\Sigma)}, \,\,\,\,\, x_2^{(A)} = x_2^{(B)} = \frac{\eta \lambda}{2-\Sigma} + \frac{Q(8-7\Sigma)}{8(2-\Sigma)}, \,\,\,\,\, \nonumber \\

&P_2 = V - \frac{\lambda}{2-\Sigma} - \frac{\tilde{Q}(8-7\Sigma)}{8(2-\Sigma)}

\end{align}**Case 2:** \(\lambda \le \frac{3\Sigma \tilde{Q}}{4(4 - \Sigma)}\)

\begin{align}

&x_2^{(M)} = \frac{6Q\Sigma}{8(4 - \Sigma)},\,\,\,\,\, x_2^{(A)} = x_2^{(B)} = \frac{Q(16-7 \Sigma)}{8(4 - \Sigma)},\,\,\,\,\, \nonumber \\

&P_2 = V - \frac{\tilde{Q}(16-7 \Sigma)}{8(4 - \Sigma)}

\end{align}

*Proof. *I begin by solving for demand and price at \(t = 2\). Given CARA preferences, investor demands are given by the following:

\begin{align}

x_2^{(A)} = \max[\eta (D_2^{(A)} - P_2), 0] \\

&= \max[\eta (D_2^{(B)} - P_2), 0] = x_2^{(B)}

\end{align}

I impose the market-clearing condition, \(x_2^{(A)} + x_2^{(B)} + x_2^{(M)} = Q\), and have the following:

\begin{align}

Q &= 2\eta (E[D_2^{(A)}] - P_2) + \eta [P_2 - P_1] \nonumber \\

P_2 &= 2E[D_2^{(A)}] - P_1 - \tilde{Q} = 2V - P_1 - \tilde{Q} \label{eq:time2price}

\end{align}

I pause here to solve for each investor type's \(t=1\) expectation of the \(t=2\) price. For type \(A\) and \(B\) investors, I have: \(E_1^{(A)}[P_2] = 2V + \lambda - P_1 - \tilde{Q}\) and \(E_1^{(B)}[P_2] = 2V - \lambda - P_1 - \tilde{Q}\).

I now turn to the \(t = 1\) equilibrium. Type \(A\) and \(B\) investors seek to maximize their one-period return. As such, given their mean-variance preferences, \(t=0\) demands are given by the following:

\begin{align}

&x_1^{(A)} = \max \left[ \frac{\eta (2V + \lambda - 2P_1 - \tilde{Q})}{\Sigma}, 0 \right] \nonumber \\

& x_1^{(B)} = \max \left[ \frac{\eta (2V - \lambda - 2P_1 - \tilde{Q})}{\Sigma}, 0 \right]

\end{align}

I once again impose the market-clearing condition, \(Q = x_1^{(A)} + x_1^{(B)} + x_1^{(M)}\) i.e. \(Q = \max \left[ \frac{\eta (2V + \lambda - 2P_1 - \tilde{Q})}{\Sigma}, 0 \right] + \max \left[ \frac{\eta (2V - \lambda - 2P_1 - \tilde{Q})}{\Sigma}, 0 \right] + \eta [P_1 - P_0]\), and am left with three cases: (1) \(P_1 \ge \frac{2V + \lambda - \tilde{Q}}{2}\), (2) \(\frac{2V + \lambda - \tilde{Q}}{2} > P_1 \ge \frac{2V - \lambda - \tilde{Q}}{2}\), and (3) \(P_1 < \frac{2V - \lambda - \tilde{Q}}{2}\).

In case (1), as only momentum traders participate, I trivially have:

\begin{equation} \label{eq:full-binding-ss-t1}

P_1 = \tilde{Q} + P_0,\,\,\,\,\, x_1^{(A)} = x_1^{(B)} = 0,\,\,\,\,\, x_1^{(M)} = Q

\end{equation}

In case (2), type \(B\) investors are short-sale constrained, while type \(A\) investors are long:

\begin{align}

Q &= \frac{\eta (2V + \lambda - 2P_1 - \tilde{Q})}{\Sigma} + \eta [P_1 - P_0] \nonumber \\

P_1 &= \frac{2V + \lambda - (1+\Sigma) \tilde{Q} - \Sigma P_0}{2-\Sigma}

\end{align}

And in case (3), I have:

\begin{align}

Q &= \frac{\eta (2V + \lambda - 2P_1 - \tilde{Q})}{\Sigma} + \frac{\eta (2V - \lambda - 2P_1 - \tilde{Q})}{\Sigma} + \eta [P_1 - P_0] \nonumber \\

P_1 &= \frac{4V - (2+\Sigma)\tilde{Q} - \Sigma P_0}{4 - \Sigma} \label{eq:eq:no-ss-t1}

\end{align}

I now consider the \(t = 0\) equilibrium. Here, I have a symmetric equilibrium, with demand \(x_0^{(A)} = \max \left[\eta (E_0^{(A)}[P_1]-P_0), 0 \right] = x_0^{(B)} = \frac{Q}{2}\). Therefore, I have the following:

\begin{equation} \label{eq:unclosed-sol-t0}

P_0 = E_0^{(A)}[P_1]-\frac{\tilde{Q}}{2}

\end{equation}

I pause again to solve for the investors' \(t=0\) expectation of the \(t=1\) price. At \(t=0\), type \(A\) and \(B\) investors believe that short-sales constraints will bind if \(P_1 > \frac{2V-\tilde{Q}}{2}\). In the case of binding short-sales constraints, the demand curve is the same as that of Equation 14. At \(t=0\), type \(A\) and \(B\) investors can solve Equations 14 and 17 to show that short-sales constraints will not bind at \(t=1\) given their \(t=0\) priors.

Additionally, at \(t=0\) the expected market clearing condition at \(t=1\) is:

\begin{align}

Q &= \eta (2V - 2P_1 - \tilde{Q}) + \eta (2V - 2P_1 - \tilde{Q}) + \eta (P_1 - P_0) \nonumber \\

P_1 &= \frac{4V - 3\tilde{Q} - P_0}{3} \label{eq:expt1sol}

\end{align}

Solving Equations 17 and 18 gives me Lemma 1. I then plug Equation 6 into Equations 14-16, and observe that type A investors cannot be priced out by momentum traders, to obtain Lemma 3. I then use Lemma 2 and Equation 12 to obtain Lemma 3.

I focus on Case 1 in Lemmas 2 and 3. In each expression, the first term \(V\) represents the expected value of the terminal dividend, the second term (\(\frac{\lambda}{2-\Sigma}\) in Lemma 2 and \(-\frac{\lambda}{2-\Sigma}\) in Lemma 3) represents the effect of \(t=1\) disagreement, and the third term represents the combined effect of risk aversion and the existence of momentum traders. Of interest is the disagreement term: disagreement at \(t=1\) contributes not only to short-term overperformance but also to underperformance at \(t=2\). The implication of Lemmas 2 and 3 is therefore the following:\\

**Proposition 1. ***In a universe with sufficiently high short-term disagreement \(\lambda\), short-term short-sales constraints, and momentum traders, the extent of the short-term overperformance and long-term underperformance increases with \(\lambda\).*

### 3.3 Empirical implications

I pause briefly to consider the results I would expect in my empirical work given Proposition 1. First, Proposition 1 suggests that the effect of disagreement should be positive initially following an IPO, especially given the existence of momentum traders.

Second, extrapolating this model to a continuous-time environment, I would expect an increasingly positive effect of disagreement on returns in the first months following an IPO, as gradual information diffusion and momentum effects magnify the effect of initial disagreement.

Third, Proposition 1 suggests that medium-to-long-term prices should be negatively impacted by disagreement, as momentum traders exacerbate the effect of prices returning to their fundamental value after disagreement disappears, causing prices to swing below the IPO firm's fundamental value.

Fourth, combining Proposition 1 with the work of Harrison and Kreps (1978), Scheinkman and Xiong (2003), and Hong et al. (2006), I would expect disagreement to have a positive effect on turnover in the first months following an IPO.

I use these predictions to motivate the empirical analysis that follows, and return to all four of these predictions in Section 7.

## 4 Data

I used two datasets for this study: the aggregate dataset, which consists of IPO time-series data aggregated by month, and the firm-level dataset, which consists of data for individual firms performing IPOs.

### 4.1 The aggregate dataset

The aggregate dataset consists of monthly data from December 1981 through January 2010. Monthly data for the number of IPOs, the average first-day return for IPOs, and percentage of IPOs priced above the midpoint of the original file-price range are from Ibbotson et al. (2013), through Professor Jay Ritter's online IPO database. All three measures exclude closed-end funds, real estate investment trusts, acquisition companies, IPOs with offer prices below 5, American depositary receipts, limited partnerships, savings and loan associations, and any IPOs excluded from the Center for Research in Security Prices database (CRSP). The percentage of IPOs priced above the midpoint of the original file price range also excludes IPOs with starting file-price range midpoints below 8.

Similarly, monthly data for the number of SEOs are from Ritter (2004), also through Professor Jay Ritter's online IPO database. In this dataset, SEOs are defined as non-IPO share issuances including at least some shares offered by the company performing the SEO. As such, pure secondaries–as well as SEOs for utilities, non-CRSP-listed companies, and NASDAQ-listed ADRs–are excluded from this dataset.

Aggregate disagreement is from Hong and Sraer (2013), thanks to the generosity of Professors Harrison Hong and David Sraer. The measure of aggregate disagreement used by Hong and Sraer is the monthly beta-weighted average of the dispersion in analysts' forecasts of the long-term growth rate. Note that beta-weighting of analysts' forecasts creates a proxy for aggregate disagreement by underweighting high-beta assets. For more information about this measure, see Hong and Sraer (2011b) and Yu (2011).

Smoothed aggregate disagreement is computed using STATA's exponential smoothing algorithm on the aggregate disagreement data series. I compute smoothed aggregate disagreement to reflect the multi-month horizons during which firms decide whether to launch an IPO, as well as the expanded period during which underwriters must prepare firms before they are ready to issue shares publicly.

There are two important notes to consider when analyzing aggregate disagreement. First, aggregate disagreement exhibits random walk-like behavior: Dickey-Fuller tests fail to reject the null of a unit root, and simple autoregressions of aggregate disagreement on lagged aggregate disagreement have significant (p < 0.001) coefficients of 0.98, 0.95, 0.89, 0.83, 0.76, 0.70, 0.63, 0.57, and 0.50 when regressed against the first, third, sixth, ninth, twelfth, fifteenth, eighteenth, twenty-first, and twenty-fourth aggregate disagreement lags, respectively, and \(r^2\) values of 0.9626, 0.8963, 0.7971, 0.6813, 0.5604, 0.4656, 0.3770, 0.3018, and 0.2317, respectively. As such, present disagreement is a very strong predictor of future aggregate disagreement. Second, aggregate disagreement exhibits exceptionally bizarre behavior of aggregate disagreement during the 2000-2002 post-dot-com/September 11th era. As such, I create dummies for years 2000-2002, and cross them with aggregate disagreement, to control for potential structural breaks in my model.

Monthly data for the Fama-French and broad market factors–SMB, HML, market risk premium, and risk-free rate–are from French (2013), through Professor Ken French's website. Monthly data for monthly broad-market price/earnings and dividend/price ratio are from Shiller (2006), through Professor Robert Shiller's website.

Cross-correlations of all of the right-hand side variables in the aggregate dataset are summarized in Table 1. Note here the relatively high correlation between aggregate disagreement and the price/earnings ratio, as well as the high negative correlation between aggregate disagreement and the dividend/price ratio. This underscores the fact that multicollinearity may be disrupting my regressions. I use these intuitions extensively as I motivate my empirical models.

### 4.2 The firm-level dataset

The firm-level dataset consists of forward abnormal returns and turnover data for IPOs between 1996 and 2006. The firm-level dataset consists of three main pieces. The foundational piece is a list of IPOs, IPO prices, and IPO dates from January 1996 to December 2006 (Kenney and Patton 2010), obtained through the generosity of Professors Don Patton and Martin Kenney. This list excludes mutual funds, real estate investment trusts, blank-check companies, asset acquisitions, foreign F-1 filers, small business IPOs (with the exception of internet firms), spin-offs, and all non de-novo issues.

The second piece includes price and SIC industry group data from Compustat (2013), as well as turnover data from CRSP (2013).[15] I compute forward abnormal returns for the end of the calendar month during which the IPO took place, as well as the end of calendar months 1-24 after the IPO took place (forward returns \(N\) months after IPO), by subtracting the CRSP value-weighted index from forward \(N\)-month return. Note here that computational and dataset limitations force me to use end-of-month price data instead of daily price data. Although this does create a small amount of left-hand-side measurement error, it does not detract substantially from my analysis.

Forward turnover is computed by dividing volume by the number of publicly traded shares (both from CRSP), and like forward returns is computed for all IPOs in the Patton dataset. As many firms have only partially available shares outstanding and volume data, all firms without CRSP data are excluded from my dataset. I also exclude from my turnover dataset any firm that does not have volume or shares outstanding data by the sixth complete month following the IPO, to help reduce sample bias.

I compute SIC division using SIC industry group data from Compustat, with the classification system from the Occupational Safety and Health Administration (2013). This enables me to perform fixed-effects regressions with reasonable numbers of groups, while reducing the effect of the error inherent in the SIC group classification process.

The third piece to the firm-level dataset is the set of right-hand-side variables from the aggregate dataset; data from the aggregate dataset are paired with firm-level data by matching the month and year of data from the aggregate dataset with the month and year of the IPO.

I conclude with one final note: when possible, studies should attempt to utilize aggregated time-series data, to avoid the frequency bias addressed in Schultz (2003). The aggregate dataset uses a large enough time period to allow for aggregation; however, the firm-level dataset only uses 1996-2006, a time period far too small to allow for aggregation. I address this limitation to my study further in the Sections 7 and 8.

## 5 Methodology

For the purposes of this section, I distinguish between public-side models, in which the primary left-hand-side variables are first-day returns, forward abnormal returns, and forward turnover; and private-side models, in which the primary left-hand-side variables are the number of IPOs, number of SEOs, and percent of IPOs priced above the file-price range midpoint in a given month.[16] Note that all of the data in the firm-level dataset are entirely public-side data.[17]

Given my analytical motivations, I focus first and primarily on public-side models, and turn later to private-side models.

### 5.1 Public-side models

#### 5.1.1 Average first-day returns

One of the core questions of this thesis is the effect of aggregate disagreement on initial IPO returns. I begin therefore begin my analysis using the aggregate dataset, and start with Equation 19:

\begin{align}

AVG\_FIRST\_DAY\_RET_{t} &= \beta_0 + \beta_1 AGG\_DISP_{t} + u_{t}

\end{align}

where \(AVG\_FIRST\_DAY\_RET_{t}\) is the average first-day return for IPOs at time \(t\) and \(AGG\_DISP_{t}\) is the aggregate disagreement at time \(t\).[18]

As the Durbin's alternative test allows me to reject soundly the null of no serial correlation in Equation 19, I turn to the Prais-Winsten GLS estimation method in Prais and Winsten (1954) for the following regressions on \(AVG\_FIRST\_DAY\_RET_{t}\).[19]To further refine the above model, I introduce a number of controls, as in Hong and Sraer (2011b) and Loughran and Ritter (1995):

\begin{align}

AVG\_FIRST\_DAY\_RET_{t} &= \beta_0 + \beta_1 AGG\_DISP_{t} \nonumber \\

& + \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} \nonumber \\

&+ \beta_3 Rf_{t} + \beta_4 Rm\_Rf_{t} + u_{t} \

\end{align}

where \(I_{t\in[2000,2002]}*AGG\_DISP_{t}\) is 0 if \(t \notin [2000,2002]\) and is \(AGG\_DISP\) if \(t \in [2000,2002]\), \(Rf_{t}\) is the risk-free rate at time \(t\), and \(Rm\_Rf_{t}\) is the market risk premium at time \(t\). I also add further controls, as in Loughran and Ritter (1995):

\begin{align}

AVG\_FIRST\_DAY\_RET_{t} &= \beta_0 + \beta_1 AGG\_DISP_{t} \nonumber \\

&+ \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} \nonumber \\

&+ \beta_3 Rf_{t}+ \beta_4 Rm\_Rf_{t} + \beta_5 SMB_{t} \nonumber \\

&+ \beta_6 HML_{t} + u_{t}

\end{align}

where \(SMB_{t}\) and \(HML_{t}\) are the small (market capitalization) minus big and high (book-to-market ratio) minus low Fama-French factors at time \(t\). Furthermore, given the relationship between aggregate disagreement and both the price/equity and dividend/price ratios, I add controls for each, as in Hong and Sraer (2011b) and Yu (2011):

\begin{align}

AVG\_FIRST\_DAY\_RET_{t} &= \beta_0 + \beta_1 AGG\_DISP_{t} \nonumber \\

&+ \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} + \beta_3 Rf_{t} \nonumber \\

&+ \beta_4 Rm\_Rf_{t} + \beta_5 SMB_{t} \nonumber \\

&+ \beta_6 HML_{t} + \beta_7 PE_{t} + \beta_8 DP_{t} + u_{t}

\end{align}

where \(PE_{t}\) and \(DP_{t}\) are the market average price/equity and dividend/price ratios at time \(t\), respectively. Note: given the potential for multicollinearity in Equation 22, I compute the uncentered variance inflation factor (VIF) after each regression to measure the degree of multicollinearity introduced in each regression.

I also repeat the same regressions for the smoothed aggregate disagreement measure, replacing \(AGG\_DISP_{t}\) and \(I_{t\in[2000,2002]}*AGG\_DISP_{t}\) with \(SM\_AGG\_DISP_{t}\) and \(I_{t\in[2000,2002]}*SM\_AGG\_DISP_{t}\), respectively, where \(SM\_AGG\_DISP_{t}\) is the exponentially-smoothed aggregate disagreement measure at time \(t\).

Additionally, I study the possibility of using the square of aggregate disagreement, both standard and smoothed, in all of my models. As I find no interesting results while performing this analysis, I omit these results for the sake of parsimony.

#### 5.1.2 Forward abnormal returns and turnover

I investigate two main relationships when working with the firm-level dataset: the effect of aggregate disagreement on forward abnormal returns for IPO stocks, and the effect of aggregate disagreement on forward turnover for IPO stocks. I address each in turn, noting that I use very similar techniques for both analyses.

My baseline model (results not presented) for the firm-level regression of forward \(n\)-month abnormal returns on aggregate disagreement is the following:

\begin{align}

FWD\_RET^{(t+n)}_{i} &= \beta_0 + \beta_1 AGG\_DISP_{t} + u_{it}

\end{align}

where \(FWD\_RET^{(t+n)}_{i}\) is the \(n\)-month forward post-IPO abnormal return for firm \(i\), and \(t\) is the time of IPO. Note that \(n\) ranges from 0 (the end of the calendar month of the IPO) to 24. Adding in controls as before gives me the following model (results not presented):

\begin{align}

FWD\_TURN^{(t+n)}_{i} &= \beta_0 + \beta_1 AGG\_DISP_{t} \nonumber \\

&+ \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} + \beta_3 Rf_{t} \nonumber \\

&+ \beta_4 Rm\_Rf_{t}+ \beta_5 SMB_{t} + \beta_6 HML_{t} \nonumber \\

&+ \beta_7 PE_{t} + \beta_8 DP_{t} + \sum_{k=0}^N \lambda_k INDCL^{(k)}_i + u_{t}

\end{align}

However, given that industry sector is potentially correlated with the error term in Equation 24, I turn to fixed-effects regression techniques to help bring this error into my models. As such, my primary model is the following:

\begin{align}

FWD\_RET^{(t+n)}_{i} &= \beta_0 + \beta_1 AGG\_DISP_{t} \nonumber \\

&+ \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} \nonumber \\

&+ \beta_3 Rf_{t}+ \beta_4 Rm\_Rf_{t} + \beta_5 SMB_{t} + \beta_6 HML_{t} \nonumber \\

&+ \beta_7 PE_{t} + \beta_8 DP_{t} + \sum_{k=0}^N \lambda_k INDCL^{k} + u_{t}

\end{align}

where \(INDCL^{(k)}_i\) is an indicator variable for the \(k^{th}\) SIC industry group, equaling 1 if firm \(i\) has been classified as part of sector \(k\). I also consider the effect of removing \(PE_{t}\) and \(DP_{t}\), given their high multicollinearity, using the following model:

\begin{align}

FWD\_RET^{(t+n)}_{i} &= \beta_0 + \beta_1 AGG\_DISP_{t} \nonumber \\

&+ \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} + \beta_3 Rf_{t} \nonumber \\

&+ \beta_4 Rm\_Rf_{t}+ \beta_5 SMB_{t} + \beta_6 HML_{t} \nonumber \\

&+ \sum_{k=0}^N \lambda_k INDCL^{(k)}_i + u_{t} \label{eqn:fwdret-famafr}

\end{align}

In both of the above regressions, I perform Hausman tests to determine whether there is omitted-variables bias as a result of industry classification. In all cases, I reject the null that the random-effects and fixed-effects models are both equally acceptable, and thus focus on my fixed-effects regression results.

My analysis for forward turnover follows the same approach. I begin with the following baseline model:

\begin{align}

FWD\_TURN^{(t+n)}_{i} &= \beta_0 + \beta_1 AGG\_DISP_{t} + u_{it} \label{eqn:fwdturn-base}

\end{align}

where \(FWD\_TURN^{(t+n)}_{i}\) is the \(n\)-month forward post-IPO turnover for firm \(i\), and \(t\) is the time of the IPO. Adding in controls and using the same fixed-effects model as before gives me the following model:

\begin{align}

FWD\_TURN^{(t+n)}_{i} &= \beta_0 + \beta_1 AGG\_DISP_{t} \nonumber \\

&+ \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} + \beta_3 Rf_{t} \nonumber \\

&+ \beta_4 Rm\_Rf_{t}+ \beta_5 SMB_{t} + \beta_6 HML_{t} \nonumber \\

&+ \beta_7 PE_{t} + \beta_8 DP_{t} + \sum_{k=0}^N \lambda_k INDCL^{(k)}_i + u_{t}

\end{align}

Once again, I reject the null of acceptability of random-effects results, and therefore in all cases use fixed-effects regressions. Once again, given the potential for multicollinearity, I remove the price/equity and dividend/price ratios in the following model:

\begin{align}

FWD\_TURN^{(t+n)}_{i} &= \beta_0 + \beta_1 AGG\_DISP_{t} \nonumber \\

&+ \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} + \beta_3 Rf_{t} \nonumber \\

&+ \beta_4 Rm\_Rf_{t}+ \beta_5 SMB_{t} + \beta_6 HML_{t} \nonumber \\

&+ \sum_{k=0}^N \lambda_k INDCL^{(k)}_i + u_{t}

\end{align}

Of note is one major issue I face when performing regressions on forward turnover: CRSP lacks data on publicly traded shares for a large number of firms in the immediate months following the IPO. As a result, as I note in Section 4, I limit my dataset to firms that have volume and publicly traded shares data by the sixth month, doing so with the caveat that my analysis of turnover may be incomplete.

### 5.2 Private-side models

After analyzing the effects of aggregate disagreement on first-day returns, forward abnormal returns, and forward turnover, I turn my focus to whether the behavior observed in the public-side models is driven by private decision-making by firms–specifically, whether firms consider aggregate disagreement when deciding to undertake and price an IPO–as a potential alternative to Proposition 1.

I begin by studying the number of IPOs in a given month, beginning with the following base-line model:

\begin{align}

NUM\_IPOS_{t} &= \beta_0 + \beta_1 AGG\_DISP_{t} + u_{t}

\end{align}

where \(NUM\_IPOS_{t}\) is the number of IPOs launched in month \(t\). I then expand the model, as before, with the following three models:

\begin{align}

NUM\_IPOS_{t} &= \beta_0 + \beta_1 AGG\_DISP_{t} + \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} \nonumber \\

&+ \beta_3 Rf_{t} + \beta_4 Rm\_Rf_{t} + u_{t} \\

\

NUM\_IPOS_{t} &= \beta_0 + \beta_1 AGG\_DISP_{t} + \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} \nonumber \\

&+ \beta_3 Rf_{t} + \beta_4 Rm\_Rf_{t} + \beta_5 SMB_{t} \nonumber \\

&+ \beta_6 HML_{t} + u_{t} \\

\

NUM\_IPOS_{t} &= \beta_0 + \beta_1 AGG\_DISP_{t} \nonumber \\

&+ \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} + \beta_3 Rf_{t} \nonumber \\

&+ \beta_4 Rm\_Rf_{t} + \beta_5 SMB_{t} + \beta_6 HML_{t} + \beta_7 PE_{t} \nonumber \\

&+ \beta_8 DP_{t} + u_{t}

\end{align}

I repeat the same analysis with \(NUM\_SEOS_{t}\), the number of SEOs in month \(t\):

\begin{align}

NUM\_SEOS_{t} &= \beta_0 + \beta_1 AGG\_DISP_{t} + u_{t} \\

NUM\_SEOS_{t} &= \beta_0 + \beta_1 AGG\_DISP_{t} \nonumber \\

&+ \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} + \beta_3 Rf_{t} \nonumber \\

&+ \beta_4 Rm\_Rf_{t} + u_{t} \label{eqn:seos-capm} \\

NUM\_SEOS_{t} &= \beta_0 + \beta_1 AGG\_DISP_{t} \nonumber \\

&+ \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} + \beta_3 Rf_{t} \nonumber \\

&+ \beta_4 Rm\_Rf_{t} + \beta_5 SMB_{t} + \beta_6 HML_{t} + u_{t}

\end{align}

\begin{align}

NUM\_SEOS_{t} &= \beta_0 + \beta_1 AGG\_DISP_{t} \nonumber \\

&+ \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} + \beta_3 Rf_{t} \nonumber \\

&+ \beta_4 Rm\_Rf_{t} + \beta_5 SMB_{t} + \beta_6 HML_{t} + \beta_7 PE_{t} \nonumber \\

&+ \beta_8 DP_{t} + u_{t} \label{eqn:seos-pedp}

\end{align}

I also use the same modeling methodology with \(PCT\_ABV\_MED\_{t}\), the percent of IPOs priced above the median of the file-price range in month \(t\):

\begin{align}

PCT\_ABV\_MED_{t} &= \beta_0 + \beta_1 AGG\_DISP_{t} + u_{t} \\

PCT\_ABV\_MED_{t} &= \beta_0 + \beta_1 AGG\_DISP_{t} \nonumber \\

&+ \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} + \beta_3 Rf_{t} \nonumber \\

&+ \beta_4 Rm\_Rf_{t} + u_{t} \label{eqn:pam-capm} \\

PCT\_ABV\_MED_{t} &= \beta_0 + \beta_1 AGG\_DISP_{t} \nonumber \\

&+ \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} + \beta_3 Rf_{t} \nonumber \\

&+ \beta_4 Rm\_Rf_{t} + \beta_5 SMB_{t} + \beta_6 HML_{t} + u_{t} \\

PCT\_ABV\_MED_{t} &= \beta_0 + \beta_1 AGG\_DISP_{t} \nonumber \\

&+ \beta_2 I_{t\in[2000,2002]}*AGG\_DISP_{t} + \beta_3 Rf_{t} \nonumber \\

&+ \beta_4 Rm\_Rf_{t} + \beta_5 SMB_{t} + \beta_6 HML_{t} + \beta_7 PE_{t} \nonumber \\

&+ \beta_8 DP_{t} + u_{t}

\end{align}

In Equations 30-41, I perform Durbin's alternative test, and soundly reject the null of no serial correlation. As such, in all of the above models, as before, I use the Prais-Winsten GLS estimation method in lieu of OLS.

### 5.3 Empirical predictions

Given Proposition 1, I expect the following results for the above empirical models: (1) a significant, positive relationship for the models in Equations 19-22; (2) an initially significant, positive (for low \(i\)) and subsequently negative (for high \(i\)) relationship for the models in Equations 25 and 26; (3) an initially significant, positive relationship for the models in Equations 28 and 29; and (4) no material relationship for the public-side models. I return to these predictions repeatedly in the following sections.

## 6 Results

### 6.1 Public-Side Models

#### 6.1.1 Average first-day returns

The results of my Prais-Winsten regressions for average first-day returns are summarized in Table 2. Here, I turn my focus to the coefficient on aggregate disagreement. As expected, I obtain positive, significant coefficients on aggregate disagreement for each of the four regressions, indicating that high-disagreement periods likely have bigger first-day IPO returns, a result consistent with both disagreement theory and Proposition 1.[20]

Moreover, I observe that a one standard deviation increase in aggregate disagreement (i.e. an increase of 0.897) leads to a 0.192, 0.392, 0.383, and 0.279 standard deviation increase in day-one returns in each of the four models, respectively. This, along with \(r^2\) values of 0.003, 0.047, 0.081, and 0.145, respectively, indicate that although the model unsurprisingly does not explain most of the variance in first-day IPO returns, aggregate disagreement is moderately economically significant as an explanatory variable for average first-day returns.

As a note, similar but marginally less statistically and economically significant results were obtained for regressions using smoothed aggregate disagreement as an explanatory variable.

Of note in Table 2 is the decrease in the scale and significance of the coefficient on aggregate disagreement after controlling for market average price/earnings and dividend/price ratios. This is unsurprising: aggregate disagreement has a correlation of 0.403 with the price/earnings ratio, and -0.472 with the dividend/price ratio. This, however, suggests that multicollinearity (and thus overly large standard errors) might be introduced into the model by price/equity and dividend/price–in fact, the VIF value for aggregate dispersion grows from 4.29 to 13.44 between models 3 and 4 in Table 2. As such, it is somewhat unclear whether the drop in statistical and economic significance between models 3 and 4 in Table 2 is the result of omitted variables bias or multicollinearity.

#### 6.1.2 Forward abnormal returns

The results of my regressions on forward abnormal returns are summarized in Tables 3-7. Interestingly, I observe highly statistically significant, positive coefficients on aggregate disagreement (at the 0.1% level except month 13) from months 0-13 post-IPO. Between month 14 and 18, I fail to reject the null that the coefficients on aggregate disagreement equal zero. From month 19 through at least month 24, I observe highly statistically significant (at the 0.1% level except month 19) negative coefficients on aggregate disagreement.

The coefficients on aggregate disagreement from Tables 3-7 are summarized in Figure 2. Interestingly, an increase in aggregate disagreement has an increasingly positive effect on forward abnormal returns in the first three months following an IPO, a decreasingly positive effect on forward abnormal returns after month three, and an increasingly negative effect on forward abnormal returns after month 18. I discuss this further in Section 7.

The regressions in Tables 3-7 explain only a moderate fraction of the variance in forward abnormal returns, with \(r^2\) values ranging from 0.050 to 0.159. Still, the economic significance of the coefficient on aggregate disagreement is substantial: a one standard deviation change in aggregate disagreement causes a 0.62 standard deviation increase in two-month forward abnormal returns, and causes similarly large changes in forward abnormal returns in other months.

One concern in Tables 3-7 is multicollinearity: with price/equity and dividend/price in the regressions, VIF for aggregate disagreement is over 80 in all 25 regressions. Therefore, I perform the same regressions excluding both ratios. Interestingly, although all VIF values fall below 15, the economic and statistical significance of the coefficients on aggregate disagreement change only marginally. As such, I omit the results of these regressions.

The results using smoothed aggregate disagreement as the explanatory variable mirrored the results using simple aggregate disagreement closely. Therefore, I omit summary tables from this paper.

#### 6.1.3 Forward turnover

In my study of the effect of aggregate disagreement on forward turnover, I begin my analysis with regressions excluding price/equity and dividend/price controls. The results of my fixed-effects firm-level regression models of forward turnover are summarized in Tables 8-12. As before, the coefficients on aggregate disagreement from these tables are summarized in Figure 3.

Interestingly, the coefficients on aggregate disagreement for months 0-4 are significant, positive, and increasing, indicating that higher disagreement has an increasingly positive effect on forward turnover. This result is consistent with the behavior of speculative bubbles in Hong et al. (2006), and suggests that there may be a momentum effect magnifying the effect of disagreement immediately post-IPO. Moreover, I cannot reject the null that the coefficients on aggregate disagreement from months 6-24 equal zero. This is consistent with the disappearance of the speculative bubble after the first months following the IPO.

Of interest are a few features of the above tables. First, the regressions capture very little of the variance in forward turnover, with a maximum \(r^2\) of 0.048. Still, however, at the four-month point, a one standard deviation increase in aggregate disagreement can increase four-month forward post-IPO turnover by 0.37 standard deviations. Second, the standard error in all of my regressions is fairly high relative to my returns regressions, and is likely driven by the relatively smaller sample size used in these regressions.

I also consider models controlling for the market-wide price/equity and dividend/price ratio. However, as these regressions have exceptionally high VIF values (in all cases greater than 80), and different results from those of Tables 8-12, I omit them in this paper.

Although the predictive quality of this model is effectively unchanged when controlling for the price/equity and dividend/price ratios, I do note that the coefficients on aggregate disagreement for the months immediately following the IPO unsurprisingly fall slightly. However, the overall patterns (initially positive, and then subsequently insignificant coefficients) remain unchanged. I discuss this pattern in greater detail in Section 7.

As a note, as the regressions using smoothed aggregate disagreement as an explanatory variable (both with and without price/equity and dividend/price controls) produce similar results to the regressions featuring simple disagreement, I exclude tabular summaries of these regressions.

### 6.2 Private-side models

Although the results above suggest that short-run IPO underpricing and long-run IPO underperformance may be partially explained by a speculative motive, I explore the possibility that firms and their underwriters consider aggregate disagreement when deciding (1) whether to initiate an IPO, and (2) the appropriate IPO price. Accordingly, I consider three monthly measures–the number of IPOs, number of SEOs, and the percent of IPOs priced above the median of the file price range.

#### 6.2.1 Number of IPOs and SEOs

I begin my analysis of private-side decision-making with Table 13, which presents the results of my Prais-Winsten GLS regressions of the number of IPOs on aggregate disagreement.

In all cases, I fail to reject the null that the coefficient on aggregate disagreement is equal to zero (and in fact fail to do so for most of the terms in the regression). Given the low predictive value of the regressions (\(r^2 \le 0.031\)), and the across-the-board economically and statistically insignificant coefficients on aggregate disagreement, it is likely that there exists no meaningful relationship between disagreement and the number of IPOs in a time period, also indicating that aggregate disagreement likely does not affect a firm's decision to undertake an IPO.

I obtain fairly similar results when performing similar regressions on the number of SEOs in a given month, the results of which are summarized in Table 14.[21] Here again I universally fail to reject the null that the coefficient on aggregate disagreement is equal to zero, and once again have low predictive quality to my regression models (\(r^2 < 0.06\)). Given the low economic and statistical significance of the coefficients, the likely implication of these regressions is that a firm and its underwriters' decision to issue shares–either initially or for follow-on offerings–is not influenced by aggregate disagreement.

#### 6.2.2 Percent of IPOs priced above file-price-range median

In the previous section, I consider the possibility that a firm's choice to go forward with an IPO is influenced by aggregate disagreement. In this section, I consider whether a firm's IPO price is influenced by aggregate disagreement given the decision to undertake an IPO.

As a proxy for firms' pricing decision-making, I use the percent of IPO prices priced above the median of the file-price range. Although the measure is undoubtedly an imperfect proxy for pricing decision-making, it does reflect the firm's decision after surveying potential buyers, as well as the broad market. Moreover, this pricing decision occurs after the firm and its underwriters have objectively set the valuation range for the company issuing shares.

The results of my analysis of the effect of aggregate disagreement on the percent of IPO prices above the median of the file-price range are summarized in Table 15. Once again, I fail to reject the null that the coefficients on aggregate disagreement are equal to zero. Although these models capture slightly more variance than the models for the number of IPOs and SEOs (\(r^2 \in [0.042, 0.140]\)), the coefficients on aggregate disagreement are still highly economically insignificant, indicating that the relationship between aggregate disagreement and pricing is negligible.

As such, I cannot conclude that firms and their underwriters are, given knowledge of aggregate disagreement, changing their share issuance decisions. Furthermore, I cannot conclude that firms are altering share offer prices as a result of varying levels of disagreement. As I will further explore in the following section, these results all suggest that a speculative motive more likely drives the strong effect disagreement has on IPO pricing and turnover.

## 7 Discussion

I begin by recalling the conclusions of Section 3, and specifically Proposition 1, which suggest that short-term overperformance and long-term underperformance both increase with increasing disagreement, given temporary short-sales constraints, sufficiently high temporary disagreement, and momentum traders.

My model suggests that (1) increasing aggregate disagreement during the day of the IPO should have a positive effect on first-day returns; (2) forward abnormal returns in the months immediately following the IPO should rise with day-of-IPO aggregate disagreement; and (3) day-of-IPO aggregate disagreement should affect long-run post-IPO negatively. Moreover, the combination of the results of my model and the work of Scheinkman and Xiong (2003), Hong et al. (2006), and Hong and Sraer (2011b) suggest that (4) turnover immediately following IPOs should rise with increasing disagreement.

My empirical results appear to support the above hypotheses. First, my work with first-day IPO returns suggests that a one standard-deviation change in time-of-IPO aggregate disagreement increases average monthly first-day returns by 7.8%, indicating that increasing time-of-IPO aggregate disagreement leads to increased overpricing immediately following the IPO.

Second, my results also offer preliminary evidence that time-of-IPO aggregate disagreement affects long-term post-IPO returns. Specifically, I observed that aggregate disagreement has an increasingly positive effect on forward abnormal returns in the first three months following an IPO. Although the high serial correlation in the aggregate disagreement time series makes it challenging to parse whether the positive effect of disagreement on short-term post-IPO returns is the result of the combination of time-of-IPO disagreement and momentum or the persistence of aggregate disagreement, the increasing effect of aggregate disagreement suggests that there is a momentum effect interacting with the disagreement effect. That said, the fact that aggregate disagreement has a positive effect on forward abnormal returns for the first twelve months post-IPO is harder to interpret–this effect can be credibly attributed to both momentum and the persistence of the aggregate disagreement time series.

Third, my results indicate that disagreement has a decidedly negative effect on medium-to-long-term post-IPO returns. Specifically, disagreement appears to have a significant, negative relationship on medium-to-long-term (1-2 year) post-IPO returns. It follows, then, that momentum traders exacerbate the effect of mean-reversion as simple investors receive signals from nature about the true, fundamental value of IPO stocks.

Especially important to the analysis here is the fact that I utilized aggregate disagreement as my proxy for disagreement, instead of idiosyncratic disagreement. Had I used idiosyncratic disagreement as my proxy, it would have been difficult to distill whether the negative long-term effect of disagreement on returns is the result of disagreement itself or the perceived riskiness of the IPO stock. Since I use aggregate disagreement, this objection does not hold.

Fourth, my empirical evidence on forward post-IPO turnover seems to be consistent with the theory that momentum traders exacerbate the effect of disagreement, and thereby cause increased turnover in the months immediately following the IPO. Specifically, in the first four months following an IPO, disagreement appears to have a significant, increasingly positive effect on turnover, a result consistent with the price-bubble behavior observed in this paper, as well as the results of Hong et al. (2006). Furthermore, disagreement appears to have no significant, positive effect on long-term post-IPO turnover, a result consistent with the disappearance of post-IPO price bubble behavior after the first months following an IPO.

My empirical work has given me evidence that the interaction between aggregate disagreement and momentum traders, through market-driven channels, has a strong effect on post-IPO price-volume dynamics. However, one equally interesting finding is the implication that aggregate disagreement dynamics do *not* have a place at the table in private decision-makers' IPO decision-making processes. Specifically, I failed to find any significant relationship between aggregate disagreement and the number of IPOs and SEOs launched in a given month. The absence of this relationship is surprising, especially given the dramatic effect aggregate disagreement has on post-IPO pricing. This offers preliminary evidence that there may be flaws in overall firm and underwriter-level IPO decision-making.

I also consider the possibility that firms' pricing decisions have a significant relationship with aggregate disagreement, by studying the percent of IPOs priced above the file-price range median. Here again, I fail to find a significant relationship, an especially interesting result given the enormous opportunity cost firms face when IPOs are underpriced. I believe that this paradoxical behavior should undoubtedly be the explored further by researchers.

I conclude with the following observation: this paper has been the first to show that *aggregate*, non-idiosyncratic disagreement affects post-IPO price-volume dynamics. Given that measures of idiosyncratic disagreement naturally are confounded by a firm's risk profile, and that all prior studies of the effect of disagreement on IPOs have focused on noisy measures of idiosyncratic disagreement, this paper offers the first conclusive evidence that disagreement can explain both short-term IPO underpricing and long-term IPO underperformance.

## 8 Conclusions and future work

In this paper, I demonstrate that the existence of short-term disagreement and short-sales constraints in an environment with momentum traders can have significant short- and long-term implications for post-IPO price-volume dynamics. Consistent with literature and my theoretical model, I provide new conclusive econometric evidence that aggregate disagreement has an increasingly positive effect on early post-IPO returns, and an increasingly negative effect on medium-to-long-term post-IPO returns. Moreover, I find that post-IPO volume dynamics act consistently with my empirical post-IPO pricing results, and surprisingly fail to find any strong relationship between disagreement and firm- and underwriter-level decision-making.

This study suggests a number of interesting avenues for future work. I divide these into two major categories: refinements to the methods used in this study, and possibilities for new work expanding on this paper.

Although I view many of the results of this study to be empirically robust, a number of improvements could be made to the methods of this paper. First, as technological limitations prevent me from utilizing daily price data when calculating forward abnormal returns, future work should aim to replicate the work of this paper using daily stock-price data.[22] Second, as CRSP lacks volume or shares outstanding data for a large number of IPO stocks (at least for the first few months post-IPO), future work should aim to complete this dataset, to ensure that there is no sample selection bias occurring in this study as a result of missing data in CRSP. Third, future studies should aim to explore the effects of dropping tech-bubble results from the dataset, as surveys of IPOs tend to be highly sensitive to the time period studied (Ljungqvist 2007). Fourth, future studies should attempt to study the effect of momentum directly, as well as momentum's interaction with disagreement. Finally, future studies should attempt to also aggregate forward abnormal returns and forward volume data by month, as was done in my aggregate dataset, to ensure that there is no frequency or sample selection bias occurring in this paper.[23]

More interestingly, this paper also opens five possible paths for future study. First, given the recent work by Hong and Sraer (2011b), and the fact that aggregate disagreement appears to have an effect on post-IPO price-volume dynamics, future work should consider the relationship between disagreement, beta, post-IPO returns, and post-IPO turnover. Second, future work should explore further the relationship between disagreement and turnover, both from the theoretical and empirical end, to expand on the preliminary analysis performed in this paper. Third, future work should explore the effect of time-of-IPO disagreement on forward abnormal returns in the 3-5 year horizon, given the empirical evidence of long-run reversals (De Bondt and Thaler 1985) and IPO underperformance (Ritter 1991, Loughran and Ritter 1995) for this time-period. Fourth, given the interrelationship amongst price, turnover, and volatility found in Hong et al. (2006), future work should also explore the effect of disagreement on post-IPO volatility. Finally, and perhaps most interestingly, given my failure to find relationships between aggregate disagreement and firm-underwriter IPO decision-making, future work should explore more proxies for firm-level decision-making to see if firms are truly ignoring the effect of disagreement on IPOs.

Although this paper provides a simple explanation to the IPO Puzzle, it may represent only the tip of the iceberg with respect to behavioral factors influencing IPOs. Refining the work of this paper and answering the questions above could therefore help to further explain the anomaly that is post-IPO pricing, and resolve one of corporate finance's most vexing puzzles.

## Footnotes

[1] Note: although Welch (1992) is classically used to explain only short-term underpricing, my usage of this theory in this paper suggests that information cascades theory could potentially explain long-term underperformance of IPOs.

[2] Associated with this theory is the idea that underwriters have reputational incentives to underprice. c.f. Beatty and Ritter (1986) and Hoberg (2003).

[3] See Ritter and Welch (2002) and Ljungqvist (2007) for a survey of institutional incentives models.

[4] See Ritter and Welch (2002), Ritter (2003), Ljungqvist (2007), and Yong (2007) for an extensive survey of asymmetric information models.

[5] Although Kang et al. (1999) provide empirical evidence of the window of opportunity hypothesis, I approach their study with caution, since since Kang et al. use market-to-book ratio---a ratio interpreted very differently in behavioral and conventional finance---as a proxy for over-valuation.

[6] c.f. Shleifer and Vishny (1995). Also related to momentum is post-earnings announcement drift. Most famously, Bernard and Thomas (1989) demonstrated that stock prices tended to drift after earnings announcements.

[7] A number of papers also analyzed related herding behaviors and the effects of career concerns; however, I leave these out of this review for the sake of concision. For further reading, see Scharfstein and Stein (1990), Trueman (1994), Zwiebel (1995), Morris and Northwestern University (1998), Avery and Chevalier (1999), Prendergast and Stole (1999) and Hong et al. (2000) for studies of herding in markets and amongst analysts; and Coughlan and Schmidt (1985), Warner et al. (1988), Weisbach (1988), Grinblatt and Titman (1989), Jensen and Murphy (1990), Gibbons and Murphy (1992), Prendergast and Stole (1996), Khorana (1996), Holmstram (1999) and Chevalier and Ellison (1999) for studies of the effects of career concerns amongst managers and analysts.

[8] On a related note, researchers have also found positive correlations between volume and price variability c.f. Tauchen and Pitts (1983) and Epps and Epps (1976).}

9] Friday earnings announcements triggered 60\% delayed responses as a percentage of total response, compared with 40\% for other weekdays. Interestingly, firms with Friday announcements also are 45\% more likely to have negative earnings responses than their counterparts.

[10] Both of these papers also use these models to explain the strong positive correlation between overpricing and turnover.}

11] A-B models focus on two types of investors, one optimistic and one pessimistic. In the face of short-sales constraints, optimistic ``A'' investors can sometimes force pessimistic ``B'' investors out of the market, causing overpricing.

[12] Note: This represents nature eventually revealing the fundamental value of the asset; I assume here that this revaluation is public knowledge.

[13] Although momentum strategies are not profitable in this model, in a more dynamic, stochastic, continuous-time setting, the profitability of a momentum strategy is more likely to be nonnegative.

[14] To make my model more realistic, I ideally would have \(M\) short-sale constrained at \(t=1\) as well; however, this drastically complicates the analysis in this paper, with almost no effect on the equilibrium solutions. As such, I allow \(M\) to short at \(t=1\). Note also that since prices unequivocally rise between \(t=0\) and 1, short-sales constraints have no effect on momentum traders at \(t=1\).

[15] Compustat price data are fully adjusted for dividends, splits, and other major distribution events.

[16] I choose this terminology as a means for distinguishing *who* controls the magnitude of each measure: for public-side measures, *markets* primarily drive the size of the measure in question (i.e. for price and volume), whereas for private-side measures, *firms* and their *underwriters* determine the size of the measure in question (i.e. whether to undertake an IPO, how to price an IPO, etc). Although markets can certainly affect private-side decisions, and vice versa, I use this distinction extensively for my understanding of the results in this paper.}

[17] Note that all of the data in the firm-level dataset are entirely public-side data.\footnote{Note further that this terminology is styled after distinctions made in many investment banks between public-side information (i.e. information available to both investment banking divisions and trading/research desks) and private-side information (i.e. information available to only investment bankers).

[18] Note here that \(t\) increments on a monthly basis.

[19] Note, however, that I only have significance of 10% for the first and fourth regressions. For the second and third regressions, I have 5% significance.

[20] Note: although SEOs are not directly related to IPOs, I expect in most casts that firm IPO and SEO behavior would be fairly similar to each other for various levels of disagreement.

[21] However, as my methods introduced only left-hand-side error, I don't expect this to yield substantially different results from my current results.

[22] However, as my methods introduced only left-hand-side error, I don't expect this to yield substantially different results from my current results.

[23] c.f. Ritter (2011).