Predicting IPO Failures Using Machine Learning Technique *

Transcription

1 Predicting IPO Failures Using Machine Learning Technique * Gonul Colak Hanken School of Economics Helsinki, Finland gonul.colak@hanken.fi Phone: Mengchuan Fu Fordham University New York, USA mfu10@fordham.edu Phone: Iftekhar Hasan Fordham University New York, USA ihasan@fordham.edu Phone: September 27, 2018 * Preliminary Draft. Please do not cite without authors permission. 0

2 Predicting IPO Failures Using Machine Learning Technique Abstract We utilize a machine learning technique to study two important criteria of IPO success: whether an IPO was overpriced at issuance (negative first-day return) and whether the firm delisted soon after issuance. Predicting these IPO outcomes is a challenging task due to involvement of large number of determinants with very different statistical properties. There are various hypotheses that attempt to explain why some IPOs are more successful than others in terms of accurate firstday pricing and long-term survivorship. We put these hypotheses in a horse race and rank each one in terms of its ability to reliably predict an IPO s success. Our machine learning method performs better than the traditional techniques, such as generalized linear models (GLM) and the non-linear models (logit or probit), in sorting out which among the numerous predictors is most reliable. The horse race yields some surprising results regarding the relative importance of free float, proportion of secondary shares sold (insiders participation), and waiting days. Some variables importance is emphasized only through our machine learning algorithm, as the traditional OLS and logit models find these variables impact statistically insignificant. 1

3 1. Introduction While Initial Public Offerings (IPOs) are on average unpriced, the magnitude of the underpricing (or the magnitude of the first-day returns) varies greatly from issue to issue and from period to period. This cross-sectional and time-series variability of IPO underpricing has been emphasized by Lowry and Schwert (2002), Yung, Colak, and Wang (2008), and Lowry, Officer, and Schwert (2010), but understanding the determinants of this variation is still an ongoing investigation. More importantly, a substantial portion of the IPOs (about one third) is in effect overpriced, implying substantial economic losses to any investor who purchased these particular issues at the offer price. Similarly, many IPOs end up getting delisted from the exchange within a few years of issuance (Fama and French, 2004; Demers and Joos, 2007), inflicting major losses to their investors. Predicting which IPOs will be overpriced and which IPOs would fail shortly after issuance, thus becomes an economically valuable undertaking. We contribute to the IPO failure literature by utilizing a new methodology, namely a machine learning algorithm, to determine which IPOs are more likely to be overpriced at the offer and which ones carry a failure (delisting) risk. We present a high-dimensional gradient boosting model that is arguably more suitable for the IPO research than the traditional parametric models, such as non-linear regression models (logit) or the generalized linear models (GLM) like OLS. The gradient boosting is a statistical learning method that has proven to be effective in dealing with a large number of predictors that show non-normal distribution. The model offers significant advantages in several aspects: 1) an adaptability to large numbers of inputs (potentially thousands of variables), 2) it provides a rank of these inputs based on their contribution to the prediction, and 3) it can properly handle predictors that show large skewness and kurtosis (variables that have large outliers and/or are sparsely distributed). By applying this 2

4 model, all the IPO mispricing theories can be tested simultaneously in a horse race setting, and the relative importance of each theory can be estimated. Essentially, the gradient boosting (GB) model provides a rank ordering of the variables representing each theory based on their overall predictive power (Friedman, 2001) without making any major assumptions. Unlike parametric models, it does not rely on the rules of statistical inference, such as normality assumption, significance tests, and no multicollinearity between the determinants. Many existing studies analyze IPO success (underpricing and survivorship) by focusing on a few hypotheses and test these hypotheses using one of the traditional regression models (OLS, logit, etc.). The parametric regression models they use, such as the generalized linear model (or GLM) or the non-linear models like logit/probit, are statistically valid when dealing with a small set of predictors. However, when the number of predictors increases, these models can become unstable, as increasing the number of inputs can lead to overfitting, reducing the overall efficiency. This is why most studies can examine only a few specific theories by using a small number of hypothesis variables, and controlling for all the other factors. This paper tests the predictive power of 25 different determinants of IPO underpricing and 28 different predictors of IPO desilting risk using a version of the above-mentioned machine learning procedure. These predictors (or determinants) are drawn from various theories that have been claimed to explain the first-day IPO returns and the subsequent survivorship rates in newly public firms. The IPO underpricing literature is voluminous and there are a number of different theories and hypotheses in place to explain the reasons for the IPO underpricing, in general. Although many theories have been empirically tested in isolation, there is little literature that systematically compares, in a horse race setting, the explanatory and predictive power of these theories. Similarly, the IPO mortality literature has been able to focus only on a few variables 3

5 when determining the factors that increase IPO delisting risk. The most comprehensive study on the subject is done by Demers and Joos (2007) and they utilize only 13 different predictors. Therefore, the debate still persists on which characteristics can better predict whether an IPO will inflict losses to its investors due to either negative first day return or due to sharp post-issuance underperformance that results in an exchange delisting. Ever since Stoll and Curley (1970) and Ibbotson (1975) laid the foundation for the IPO mispricing (underpricing) studies, many theoretical explanations were provided for this phenomenon. The explanations we focus on are the asymmetric information hypothesis (Rock, 1986; Beatty and Ritter, 1986; Megginson and Weiss, 1991; Michaely and Shaw, 1994), signalling hypothesis (Allen and Faulhaber, 1989; Beneniste and Spindt, 1989; Grinblat and Hwang, 1989; Welch, 1989), partial adjustment phenomenon (Beneniste and Spindt, 1989; Hanley, 1993), money left on the table explanation (Habib and Ljungqvist, 2001; Loughran and Ritter, 2002), investor sentiment or exuberance hypothesis (Krigman, Shaw, and Womack, 1999; Derrien, 2005; Cornelli, Goldreich, Ljungqvist, 2006; Ljungqvist, Nanda, and Singh, 2006), rational market timing explanations (Chemmanur, 1993; Zingales, 1995; Pagano, et al., 1998; Chemmanur and Fulghieri, 1999; Stoughton, et al., 2001; Maksimovic and Pitchler, 2002; Lowry, 2003; Benninga, et al., 2005; Pastor and Veronesi, 2005; Alti, 2006), explanations related to the time-varying adverse selection problem in the IPO markets (Yung, Colak, and Wang, 2008; Khanna, Noe, and Sonti, 2008), hot vs. cold IPO market hypothesis (Ritter, 1984; Helwege and Liang, 2004; Loughran and Ritter, 2004; Yung, et al, 2008; Lowry, et al, 2010), IPO promotion and advertising hypothesis (Cook et al., 2006; Chemmanur and Yan, 2009; Liu et al., 2014; Chahine, Colak, Hasan, and Mazboudi, 2017), high demand from institutional investors explanation (Falkenstein, 1996; Stoughton and Zechner, 1998; Gompers and Metrick, 4

6 2001; Boehmer, Boehmer, and Fishe, 2006; Chemmanur, Hu, and Huang, 2010), and explanations based on certification by prestigious intermediaries such as investment banks (Carter and Manaster, 1990; Carter, Dark, and Singh, 1998) and venture capital (Megginson and Weiss, 1991; Gompers, 1996; Brav and Gompers, 1997). We create one or more variable to represent each of these hypotheses and then conduct our machine learning analysis by focusing on the differences between these theories in accurately predicting which IPO would be profitable (underpriced) to the short-term investors and which one would inflict losses (overpriced). Similar to overpriced IPOs who end up declining in price on the day of offering (overpricing risk), delisting risk is a serious problem for the long-run investors of recently public firms (Fama and French, 2004). Around one third of newly public firms are delisted within five years after the IPO date (Jain and Kini, 2000; Ritter and Welch, 2002; Ritter, 2003), which increases many institutional investors risk from holding onto IPOs shares for the long-run. Therefore, developing new methods that can accurately predict which IPOs are prone to quick failure is a worthwhile exercise. Various firm and offering characteristics are found to be reliable indicators of such failures. For example, studies by Seguin and Smoller (1997) and Fernando, Krishnamurthy, and Spindt (2004) find an association between offering share price and IPO mortality. Presence of venture capitalist (Jain and Kini, 2000) can improve survivorship among recently listed IPOs. Yung, Colak, and Wang (2008) report that the delisting rate from exchanges is higher among hot-market IPOs. Demers and Joos (2007) develop an IPO failure prediction model using a logistic regressions methodology, which shows that the risk of failure is not fully priced into IPOs at the time of the offering. Furthermore, a few previously undocumented determinants of IPO failure risk emerge from their study. Younger and smaller IPOs are more prone to failure, as are the IPOs underwritten by less reputable underwriters. While advertising 5

7 costs increases delisting rates, R&D spending decreases it. Hi-Tech IPOs carry higher delisting risk, as are the leveraged ones. In all of the above studies either OLS or logistic methodology is applied with utilization of a somewhat limited set of variables. The main purpose of this analysis, thus, is to emphasize the efficiency and usefulness of the gradient boosting model in IPO mispricing research. Machine learning has been scarcely used in the accounting and finance literature. Jones (2017) presents a gradient boosting approach to corporate bankruptcy prediction and shows its advantage over the logit regression model. Zhou et al. (2015) proposed a performance-driven gradient boost model that predicts short-run (high-frequency) price movements of the S&P 500 stocks, and they attest that such models have superior predictive power over the traditional pricing models. To the best of our knowledge, our paper is among the first to utilize gradient-boosting models in an IPO setting. Among the 25 determinants we focus on, we find that price revision during the bookbuilding period, equity offer size (the free float), and the waiting days from filing date to issuance date are the most reliable indicators of an IPO s underpricing. While the finding related to price revision is not surprising (Hanley, 1993), the latter two variables importance is emphasized only through our gradient boosting algorithm, as the traditional OLS and logit models find these variables impact statistically insignificant. Among the most reliable predictors of negative first-day returns are the lack of participation by the institutional investors, large equity offer size, and the coldness of the IPO market. Our machine learning technique yields some novel insights into the determinants of IPO delisting literature, as well. The variable with highest relative influence score (RIS) on delisting probability is proportion of the secondary shares within the pool of total offered shares (insiders participation ratio). Put differently, when insiders unload disproportionately larger shares during the offering, that IPO has the highest 6

8 delisting risk. We confirm the findings of prior studies (e.g., Demers and Joos, 2007) that post- IPO stock performance, underwriter reputation, accounting performance (net income and EBITDA), firm age, hi-tech industries, and leverage are reliable indicators of IPO survival. Among the previously unreported determinants of IPO delisting, underpricing and waiting days, are also notable for their predictive abilities. A few prior studies apply new statistical learning methods, such as artificial neural networks (ANNs), and compare their predictive ability with the traditional GLM (Jain and Nag, 1995; Robertson et al. 1998; Reber et al. 2005). These papers emphasize the advantage of using advanced statistical learning methods to predict IPO offer price. However, the financial literature has found that IPO offer prices are sticky and are rarely set outside a certain dollar range (Seguin and Smoller, 1997; Fernando, Krishnamurthy, and Spindt, 2004), which makes predicting the offer price a less useful exercise than predicting the first-day closing price (or underpricing). Thus, our paper adds to this literature, by emphasizing the methodological advantages of the gradient boosting model (a form of machine learning model) in predicting the underpricing of an upcoming IPO and whether it will stay public for a long period of time. The rest of the paper is organized as follows. Section 2 provides a brief literature review of the underpricing theories and the IPO mortality explanations. In Section 3, we explain the estimation methods and the gradient boosting algorithm we use in this study. In Section 4, we discuss our data sources, our sample selection, and the related variables. In section 5, all the empirical results are presented and discussed and in Section 6 we summarize our conclusions. 2. Literature and hypothesis development Initial Public Offerings (IPOs) are underpriced on average. In the past 30 years, at least two major themes have come from IPO underpricing literature. The first is about the role and 7

9 explanatory power of alternative IPO underpricing theories. The second topic relates to the development of statistical models that predict IPO underpricing IPO underpricing theories In general, IPO underpricing studies originated from Stoll and Curley (1970), who pointed out that there is a systematic positive difference between the first day's close and the offer price. Reilly (1977) and Logue (1973) also provide evidence of a positive abnormal firstday return. Ibbotson (1975) provided a possible list of possible underpricing and laid the foundation for IPO underpricing studies. Since then, a flood of different theories and underpricing literature has proliferated. Asymmetric Information Hypothesis for IPO Underpricing Many of the earlier papers attribute the anomalies to the information asymmetry between different related parties to listed companies (underwriters, issuers, and investors). To ensure that unwitting investors receive a fair rate of return and thus participate in the market, they need to underprice the issues on average (Rock, 1986). Many papers, including Beatty and Ritter (1986), Megginson and Weiss (1991), Michaely and Shaw (1994) find evidence to support empirically the asymmetry of information as a determinant of underpricing. The issues characterized by greater uncertainty is underpriced to make up for the higher costs of learning to the real value of these businesses. Much literature relies on firm fundamentals which indicate a firm is inherently too hard-to-value to measure the information asymmetry, such as firm age (Loughran and Ritter, 2001), investment (Eckbo et al., 2007). In addition, some believe that IPOs backed by venture capitalists (VCs may have less information asymmetry (Liu and Ritter 2011), and high-tech firms and firms with higher R&D expenditures may have more information asymmetry. 8

10 Money Left on the Table A different theory explaining the underpricing is that the firm owners and underwriters actually like underpricing. For example, according to Habib and Ljungqvist (2001), some IPOs are more underpriced (money-left-on-the table) than others because their owners have less reason to care about underpricing. These owners sell a small percentage of their shares during the offering. So, the higher percentage of their own holdings they sell, the more they care about underpricing. Participation ratio (the fraction of the total shares offered that is sold by the insiders (founders, existing shareholders, and VCs) is a direct proxy for this problem. Loughran and Ritter (2002) propose a prospect theory answer to this question. Prospect theory assumes that issuers care about the change in their wealth rather than the level of wealth. Thus, in most situations occurring in the IPO market, issuers will sum the wealth loss from leaving money on the table with the larger wealth gain on the retained shares from a price jump, producing a net increase in wealth for pre-issue shareholders. The measure is mainly Equity Offer Size (the total shares offered divided by total shares outstanding after the IPO). Another explanation is the changing issuer objective (Loughran and Ritter 2004) which posit issuers cared less about the money left on the table because they became increasingly focused on analyst coverage. An issuer may be willing to accept higher underpricing as the cost of higher quality analyst coverage. Because the higher quality analysts tend to be concentrated among the banks that represent the highest quality underwriters, this will cause a positive relation between Underwriter s reputation and underpricing. Partial Adjustment Phenomenon Some IPOs adjusts their offer price up or down during and immediately after the bookbuilding. This hypothesis states that if the adjustment is upwards then we can predict that 9

11 underpricing (first-day returns) will be high, indicating that the bookbuilders (underwriters) adjusted the offer price only partially towards its true value (hence the term partial adjustment). Hanley (1993) first documented this pattern based on Benveniste and Spindt (1989) models that attribute this phenomenon to the adjustment of favorable private information revealed during the bookbuilding period. Bradley and Jordan (2002) refined the analysis by examining the file range amendments and showed that the amendment possessed important predictive power. The variable associated with this assumption is Price Revision which is calculated by subtracting middle of the filing range original (i.e., before bookbuilding) from the final middle of the file range. We expect this price correction to be in line with the underpricing. Market Timing Hypothesis The theoretical model of Benninga, Helmanthel, and Sarig (2005) suggests that firms are taken public when the market valuation of the expected cash flows is high. The insiders have private information on their firms prospects, and only propose to float them on the public markets when their profitability is about to decline. As a result, the IPO underpricing should be associated with the timing of stock market or/and the IPO market. Our measures here include Market Heat Degrees, and Market Returns (S&P 500 Last 12 months) Another branch of literature analyzes the issuance order: whether high-quality IPOs such as Facebook will be the first to issue securities or will be waiting for the mediocre IPO to be released first. Colak and Gunay (2011) find evidence that some high-quality companies may strategically postpone initial public offerings until other issuers produce signals and the highquality IPOs have higher waiting times than the low-quality IPO. The paper is going to extend the discussion by looking into the impact of waiting days to the IPO underpricing. 10

12 Signalling Hypothesis Allen and Faulhaber (1989), Grinblatt and Hwang (1989) and Welch (1989) consider highquality companies that underprice their issues to signal their quality to the market. Higher underpricing allows them to raise more capital under more favorable conditions in the future. The same is true for international IPOs, as well (Francis, Hasan, Lothian, and Sun, 2010). Measuring the quality of a business is not an easy task and there is no single means to capture the complex intrinsic quality of the firms. This article will use the company's profitability and earnings measures at the time of the IPO as a representative of firm quality. Specifically, we use Net Income, EBITDA, Leverage Ratio, Profit Margin, ROA (and Volatility), Cash Flow (and Volatility) as proxies for firm quality IPO Underpricing modeling developments Previous studies usually assume that there is a linear relationship between the IPO underpricing and alternative underpricing predictors. Most of the IPO underpricing literature relies on GLM model (Benveniste and Spindt, 1989; Bradley and Jordan, 2002; Loughran and Ritter, 2002; Lowry and Schwert, 2002 & 2004). A few studies applied some new statistical learning methods, such as neural network, and compared the predictive ability with traditional GLM (Jain and Nag, 1995; Robertson et al. 1998; Reber et al. 2005). They show the advantage of using highly sophisticated statistical learning methods to predict IPO underpricing. Few papers have used gradient-boosting models in IPO underpricing studies, but some papers combine the boosting approach to the financial research. Zhou et al. (2015) proposed a performance-driven gradient boost model that predicts short-run price movements and testified the superior predictive power on the S&P 500 high-frequency data. Jones (2017) presents a gradient boosting approach to corporate bankruptcy prediction and shows the advantage over the 11

13 logit regression model. From these studies, it is most obvious that the gradient boosting method provides a potentially more powerful prediction framework for the financial research. Based on the discussion above, we develop the following hypotheses. H1: A gradient boosting model for the IPO underpricing research will have better predictive and explanatory power than a traditional model, ceteris paribus. H2: There is no unique superior theory that can dominate IPO underpricing in a variety of ways over other theories. We tested H1 by evaluating the gradient-boosting model for the full set of predictors described in Appendix 1 using cross-validation method and comparing the performance to the traditional GLM. There is no normalized statistical cut-off rule to determine when H1 should be accepted. However, it is strong enough to say that gradient boosting model has a better predictive power if GB model significantly outperforms the GLM on both training and validation samples. We also test the explanatory power of the gradient boosting model by checking whether the internal consistency of the variables and the direction of impact to IPO underpricing is reasonable. In the gradient boosting analysis, the marginal effect reveals the strength and the non-linear relationship between the predictor and the IPO underpricing. To test H2, we generally compared the relative influence scores (RISs) among all predictors. RIS is a measure of all predictors that can be used to rank the predictors. H2 should be rejected if we do not find the predictors dispersed in the top list according to different theories. We will discuss RIS in detail in the next section. We also conduct a separate GB test to predict which IPOs will have a negative first-day returns (i.e., they will lose their investors some money). 12

14 H3: The determinants of negative first day returns are different from those of underpricing. The dependent variable in this test is not a measure of the underpricing level but whether the IPO has a negative first-day return (0 if the IPO has a positive first-day return, and 1 if the IPO has a negative first-day return). H3 is tested by comparing the RIS output with the previous model. If there is no obvious difference in the highest ranked predictors lists between this model and the previous model, H3 should be rejected IPO delisting risk Delisting risk has not been analysed as intensely as IPO undepricing phenomenon, but as noted by Ritter and Welch (2002), Ritter (2003), and Fama and French (2004), it is a frequently occurring phenomenon whereby more than 30 percent of recent IPOs are forced to delist within five years after the offering due to inability to satisfy the exchange requirements. Such a forceful delisting almost always implies a failing business model, which is associated with rapid and sharp declines in stock returns. Thus, any long-term investor of IPO firms has to be cognizant of this delisting risk and such an investor could benefit from knowing a list of reliable predictors of such failures. Obtaining such a list requires solid prediction models and comprehensive set of candidate predictors. As explained above the gradient boosting method can present a powerful prediction framework for a financial research involving serious hazard of IPO mortality. We set upon ourselves the task to determine whether machine learning can outperform the traditional logit and OLS estimations in picking the determinants of IPO failure risk. Hence, our next hypothesis: H4: A gradient boosting model predicting IPO delisting likelihood will have better predictive and explanatory power than the traditionally applied GLM and logit models. 13

15 Similarly, since the gradient boosting method is able to eliminate some problems with traditional logit and OLS estimations which are often used in predicting IPO delisting rates, new and previously undiscovered variables can emerge as highly reliable predictors of an IPO s delisting probability. We formally state this in our next hypothesis: H5: There are previously undocumented and de-emphasized determinants of IPO delisting risk that are picked by the gradient boosting model as highly reliable predictors of this risk. 3. Methodology 3.1 High dimensional statistics According to statistical theory, the high-dimensional statistical studies data is the one whose dimension is larger than the dimensions considered by classical multivariate analysis. The main difference between the high-dimensional model and the traditional model (low-dimensional model) is that the traditional statistical model is based on the classical asymptotic theory, which assumes that the number of parameters is a few and the number of observations is infinite, while the high-dimensional models usually involves a large set of variables with a fixed sample size. For example, for an IPO underpricing study, the number of successful IPO samples is limited (our sample includes 7312 IPO cases from 1985 to 2016), but the number of parameters (alternative IPO measures and their interactions) is immense. Given the super-complex nature of modern finance, the components involved in various financial activities are massive. From the previous literature, the IPO process is closely related to the firm qualities, market timing, agency issues, asymmetric information, and so on. Moreover, when we consider the complex interaction effects of different aspects, the dimension increases exponentially. Therefore, the IPO underprice problem should be considered in the context of high dimensions. 14

16 3.2 The gradient boosting (GB) model and machine learning algorithm Gradient Boosting is a machine learning algorithm for regression and classification problems that combines the output of many weak predictive models to produce a final robust predictive model. Breiman (1997) first proposed the idea of gradient boosting, in the belief that a weak learner could be modified to become a better learner. Subsequently, Friedman (2001) developed an explicit regression gradient boosting algorithm. The statistical framework describes boosting as a numerical optimization problem whose goal is to minimize the loss of the model by adding weak learners using gradient descent-like process. Boosting refers to the general problem of producing very accurate forecasting rules through a combination of rough and modest inaccurate empirical rules. In the boosting process, samples that can be estimated relatively correctly using previous base learners will be less emphasized in the following learners. Unlike other ensemble methods, such as random forests, the gradient boosting model provides relatively more useful information for the previous continuous model through a strategically re-sampling method to select examples in training data. In simple terms, the weights of selection of the training data set for the latter learners are not equal. Samples with larger error have higher weights. The latter learners in GB are adjusted based on the errors made by the previous learners. Gradient boosting involves three elements: a loss function to be optimized, weak learners to make a prediction, and an additive model to add weak learners to minimize the loss function. The loss of the model measures the amount of deviation between the predicted and the observed values (i.e. the predictive value of underpricing vs. true value of underpricing). Regression trees are used as the weak learner. It should be noted that each regression tree deals with only one input variable. For example, the first tree may regress underpricing on the firm age where all 15

17 observations receive equal weights. The second tree (for example, regress the underpricing on underwriter s reputation) is trained on the same dataset, but observations that have higher squared error in the first tree receive a higher weight. Trees are added one at a time to compensate the shortcomings. In this study, we use the modified version of the GB model. Give a data sample distribution D. M stands for the total number of base models and determines the sample size as N. Define the initial training sample distribution as D 1. From m = 1 to M (1) Train a base model fm( x) from the training sample distribution D m. (2) Compute the error of this model. (3) Adjust the distribution D m to D m + 1 and update the model. (4) Output the adjusted base model fm( x ). More formally, Friedman (2001) illustrate how the gradient boosting algorithm works. The pseudo-codes are as follow: Initialize f ( x ) to be a constant and f 0 0( x ) = arg min L ( y, ) i 1 i. = N For m=1 to M do: For i=1 to N do: Compute the negative gradient : L( yi, f ( xi)) yi = i = 1, N f( x ) i f ( x) = fm 1 ( x) Fit a regression tree gm ( x) to predict the y : i from covariates x i for all training data. Compute a gradient descent step size as m = arg min L( yi, fm 1( xi ) + gm( xi )) Update the model as fm( x) = fm 1( x) + mgm( x) N i= 1 16

18 Output the final model f ( x ) m 3.3 Interpretability Accuracy and interpretability are two basic goals of predictive learning. However, these goals are not always consistent. While most sophisticated statistical learning methods, such as neural networks and support vector machines, provide predictions with very high accuracy, they sacrifice the ability to interpret the results. Compared to artificial neural networks or support vector machines, the gradient-boosting model is designed to generate transparent rules that are easily interpretable by non-statisticians. Although gradient boosting models can be quite complex and involve many potential nonlinearities and the interactions between predictor variables, various standard outputs are available, making it easier to interpret the effects of different predictors. These outputs include (1) the relative influence score (RIS) and (2) the partial dependence (marginal effect) plot. 3.4 The relative influence score (RIS) Relative influence score (RIS) is a measure of how useful a particular variable is to a model by quantifying the importance of the variable marginalizing on other variables. These measures are based on the number of times a variable is selected for improving the model (Friedman & Meulman 2003). Typically, the RIS is expressed as a scale between 0 and 100 where the most important variable always gets 100 and all other variables are readjusted to reflect their effect to the model comparing to the top variable. 3.5 Advantages of GB for IPO underpricing research The gradient enhancement model has some appeal for IPO underpricing studies. It can be seen empirically that the GB has predominance for high-dimensional data (Buhlmann and Yu, 2003), which better reflects the true world context of IPO underpricing. Another advantage is 17

19 that the GB procedures are invariant under all monotonic transformations of a single input variable (e.g. logarithm transform). In other words, while variables in IPO underpricing studies have different scales, there is no need to normalize the input variables. In addition, gradient boosting models are not sensitive to outliers (this algorithm isolates outliers only in separate nodes without affecting the performance of the final model). Gradient boosting is insensitive to multicollinearity and it is more robust due to better handling uncorrelated inputs (Friedman 2001). Also, as a regression tree based model, GB has the ability to select and rank the variables, which provides a feasible way to compare IPO underpricing predictors and sorts related theories and conjectures. 4. Sample data 4.1. The IPO sample We start by retrieving all the initial public offerings (IPOs) between 1985 and 2016 from the U.S. Common Stock Data File of Securities Data Company (SDC). We screen-out the ADRs, closed-end funds, unit offers, and any other non-common stock type of shares. From SDC we obtain various issuance-related features of the IPO firm, including the filing and issuance dates, the offer price, the first-day closing price, the total proceeds it raised, the total shares offered, the number of primary and secondary shares offered, the price revision of the IPO, the name of the lead underwriter, whether the firm is backed by venture capital, and whether or not the firm is from a high-tech industry. The founding year of the IPO firm is from Field-Ritter dataset of company founding dates (downloaded from Jay Ritter s website), as used in Field and Karpoff (2002) and Loughran and Ritter (2004). Underwriter reputation is the lead underwriter s reputation ranking at the time of the IPO, which is based on the updated Carter and Manaster (1990) classification. Our overall IPO market s heat measure (Yung, Colak, and Wang, 2008) 18

20 utilizes the quarterly IPO volume data going back to 1960, which in turn is retrieved from Jay Ritter s website. All the accounting data and the location (state) of the firm s headquarters are from Compustat database. The post-ipo trading information about the stock is from the Center for Research and Security Prices (CRSP). From the daily CRSP data, we obtain the daily closing prices of the stock during the first few days of trading. The stock s monthly trading volume, the monthly stock returns, and the monthly CRSP index returns are obtained from the monthly CRSP data; as is the total shares outstanding of the IPO firm as of the end of the first trading month. The institutional holdings information is from Thomson 13F Institutional Holdings database, which is available between 1980 and The above screening criteria leave us a sample of 7312 IPOs during A more detailed description of all the variables used in this study can be found in the Appendix A and the pairwise correlations among these variables are displayed in Appendix B. The descriptive statistics of all the variables are presented as Table 1. Insert Table 1 and 2 Here 4.2. The sample of delisted IPOs Prior studies often consider an IPO as a failure if the newly listed firm involuntarily delists from its exchange within a few years. For example, Yung, et al. (2008) and Demers and Joos (2007) consider exchange delistings within 3-to-5 years of the offering event as a measure of an IPO failure. We follow their example and consider an IPO as unsuccessful if it gets delisted from an exchange within 5 years 1 of the IPO date (i.e., Delisted IPO=1). Not all delistings can be considered a failure, however. Delisting due to bankruptcy (CRSP delisting codes between Our results are qualitatively the same if we use the delisting within a 3-year window as an alternative cutoff point. 19

21 and 499) and due to inability to meet listing exchange requirements (delisting codes between 500 and 599, or code equal to 700) are a form of failure. However, if firms that stopped trading because they switched to another major exchange (NYSE, Amex, or Nasdaq; delisting codes 501, 502, and 503), voluntarily went private (code 573), or engaged in an M&A (delisting codes between 200 and 399) are not considered failed IPOs. 2 When this procedure is applied to our IPOs between 1985 and 2016, it leaves us with a sample of 869 firms that ended up delisting within five years of issuance. Table 1 s last 4 columns provide various information about the delisting rates of a given cohort of IPOs within the next 5 years and the number of delistings of prior IPOs (issued within the last 5 years) occurred during a given year. As expected, the number of delistings in a given calendar year fluctuates inversely with the IPO market s heat. For example, the highest number of recently-issued IPO delistings (110 such cases) occurred in More interestingly, however, the percent of current cohort of IPOs that will delist within the next 5 years fluctuates in a different pattern, varying from 0.88% for the batch of IPOs issued in 1999 to 35.71% for the cohort of 1990 IPOs. This is likely driven by the fact that many low-quality IPOs issued during the hot-market of the late 1990s were able to raise substantial amount of proceeds that allowed them to survive longer than 5-years. We control for such time-series patterns in delisting rates using variables such as Market Heat Degrees (as developed by Yung, et al, 2008), equallyweighted average undepricing during a given year (EWU), and market return of S&P 500 index during the last 12 months. 2 Zingales (1995) argues that the IPO may be the first step in a gradual sale of the company. According to Brau and Fawcett (2006), facilitating potential takeover transactions is an important motive for going public. Celikyurt, Sevilir, and Shivdasani (2010) report that newly public firms choose to grow predominantly through mergers and acquisitions in the first five post-ipo years. Thus, a recent IPO who engages in an M&A is unlikely to indicate failure. 20

22 5. Empirical results We present the results for undepricing and delisting rates in separate sub-sections Predicting Undepricing with Machine Learning In order to test hypotheses, the paper first runs the gradient boosting model using the entire sample. All predictors are formally defined in Appendix A. The results are reported in Table 3. Insert Table 3 Here The paper use 10-folds cross-validation method to select the best model parameters. Figure 1 shows the performance of the GM model on the training and validation samples with a different number of regression trees (iterations). Insert Figures 1 Here The purpose of the graph shown in Figure 1 is to see the squared error loss for different iterations and to estimate the optimal number of boosting iterations based on the minimum mean square error (MSE) of the validation sample. The figure shows that the gradient boosting model has a very impressive regression performance. The model is optimized on 3,050 trees where it reaches the lowest MSE on the validation sample. The validation error curve in Figure 1 is a measure of the degree of generalization of the model over invisible data. It can be seen that the error on the verification sample decreases with training error until it is minimized in a relatively small number (935), indicating little or no over-fitting on the test sample. This result agrees with the fact that the gradient boosting model is highly resistant to over-fitting, even though the model is estimated on a very large number of trees (Friedman, 2001). To compare with GLM, we run GLM on the same data. The performances of both models are shown in Table 4. Insert Table 4 Here We assign 70% of the observations randomly to the training samples, and another 30% of the observations are assigned to the test samples. This test is based on the performance of 21

23 comparing training and test samples. Mean square error (MSE) is a measure of how close a fitting line is to a data point. Since the MSE shows the level that we can trust the predictions, we expect our model has a lower MSE. It is no surprisingly that GB model significantly outperforms GLM on both training and testing sample since the GB model captured a more subtle non-linear relationship between underpricing and different predictors. Table 4 also provides R 2 (coefficient of determination) for both models. It shows that the GB model better replicated the observed outcomes based on the proportion of the total variation of outcomes explained by the model. One interesting finding here is that the GLM has a negative R 2 over the test sample, which means that the model does not follow the trend of out-of-bag data at all and is worse fitted to data than a horizontal line. This is a clear sign that GLM has overfitted training samples and the model is not very effective. As we mentioned earlier, GLM is not suitable for high-dimensional situations, and over-fitting problems driven by a large number of predictors make GLM a very poor prediction model. However, for the GB model, the larger R 2 is not enough to show that the model is better than the GLM. Since the GB model captures the subtler non-linear relationship between the underpricing and different predictors, this comparison is not appropriate. In order to get a better understand, the paper also tests the symmetric mean absolute percentage error (SMAPE) (Armstrong, 1985), which is an accuracy measure based on percentage (or relative) errors. Both the training sample and the test sample have significant lower SMAPE on the GB model, which indicated that GB model had better prediction accuracy. As shown in Table 3, all of the 25 predictors have non-zero RIS. This implies that 25 input variables in some way contributed to the success of the prediction, although the strength of the different predictors varies widely. The RIS reported in Table 3 is expressed as a scale between 0 and 100 where the most important variable always gets 100 and all other variables are 22

24 readjusted to reflect their effect to the model comparing to the top variable. The RIS is calculated based on the predictive ability of IPO underpricing. The results in Table 3 show that multiple dimensions of the IPO represented by different types of IPO measures have a relatively great impact on the IPO underpricing. The strong predictors in the analysis (RIS > 15) include (1) Price adjustment measure, which represented by price revision (2) Money left on the table variables, particularly equity offer size, and participation ratio; (3) Market Timing variables, including waiting days, market heat degree, and market return; (4) Signalling hypothesis measures including ROA Volatility, EBITDA, Profit Margin, Assets, Leverage Ratio, Cash Flow Volatility, and the Cash Flow; (5) Traditional information asymmetry variables, including firm age, and R&D spending; and (7) Cross-dimensional measure of institutional ownership. Table 3 shows that the strongest predictor is the price revision (RIS=100). The second strongest variable is the equity offer size, with a RIS of 75.45, followed by waiting days variable with a RIS of The next strongest variable is the ROA volatility (RIS = 42.47), followed by EBITDA with a RIS of Some other market timing measures also show quite strong influence in the model of Table 3, but they do not dominate the analysis. For example, the RIS for the market heat degree is and the RIS for the market return variable is Other high-impact factors include firm age (RIS=30.60), profit margin (RIS=27.91), total assets (RIS=22.18), underwriter s reputation (RIS=21.70), R&D spending (RIS=19.81), institutional ownership (RIS=18.24), leverage ratio (RIS=17.27), participation ratio (RIS=15.51), cash flow volatility (RIS=15.45), cash flow (RIS=15.07). To get a better understanding of what theories (dimensions) are driving the result, consider the average RISs across the different predictor categories above. The partial adjustment measure that represented by a single variable of price revision has a RIS of 100, the strongest 23

25 predictors overall. The next are the market timing indicators with an average RIS of The money left on the table indicators follow closely, which have an average RIS of The accounting variables (signalling measures) also have good performances with an average RIS of The next echelon contains advertising predictors with an average RIS of and information asymmetry proxies with an average RIS of To illustrate the explanatory power differences between the GB model and a traditional GLM, we run a separate GLM for the highest ranked variables (i.e., RIS of at least 15) in Table 3. Table 5 displays the summary of a GLM regression based on the highest ranked variables using standardized coefficients. Insert Table 5 Here Nearly half of the GLM parameters are not significant, implying that GLM does not capture their influences to underpricing. Another problem shown in Table 5 is that only a small number of variables in GLM have relatively large coefficients (such as price revision, ROA volatility, cash flow), while the coefficients of most variables are very small, indicating that their contribution to the overall model performance is very small. The problem arises because GLM cannot cure multicollinearity. Some of the variables reported in Table 5 are highly correlated with each other (see the correlation matrix in Appendix B), especially variables such as sales, EBITDA, total assets, net income (Pearson correlations above 50%). Putting so many correlated variables together will reduce the overall validity. Another reason GLM does not work well is that the data is skewed (see Table 2), which violates the GLM's normal distribution assumption, making the result less reliable. Having demonstrated that a gradient boosting model has very superior performance, it is also important to assess whether the explanatory variables are meaningful in terms of their role 24

26 and impact of the IPO underpricing. One of the advantages of the gradient boosting model (as compared to neural networks and support vector machines) as a very sophisticated statistical learning approach is that it provides a way to reveal black boxes and observe internal operations, especially through RIS and partial dependence plots. The partial dependence plot shows the direction and intensity of the relationship between the independent variable and the dependent variable (underpricing). The slope of the graph can be understood as a dynamic coefficient compared to the GLM, which depicts the non-linear relationship between each of the predictor and the underpricing value. The partial dependence plot for each of the top-ranked predictors are reported in Figure 2. Insert Figure 2 Here The first plot in Figure 2 shows the dependence of price revision and IPO underpricing marginalizing over all other predictors. The overall trend seems to be in line with previous literature, arguing that price increases during the filling period are expected to lead to more serious underpricing (Bradley and Jordan, 2002). As can be seen from the figure, in the 0-10 range, the upward price revision substantially aggravated the underpricing. The slope before 0 is fairly flat, with a very small uptrend just before 0, suggesting that the underpricing has little dependence on price cut. The ensuing line after price revision of +10 looks relatively flat, which means that a very high price increase is not necessarily linked to a big first-day return. The second plot in Figure 2 shows the partial dependence of the equity offer size and underpricing. While the proportion of share offered during the IPO is closely linked to the underpricing (RIS of the equity offer size ranked second among all predictors), the relationship itself seems complicated as the curve moves up and down within the sample interval. However, since most of the samples are located on the far left (i.e. shares issued during the IPO period are 25

27 usually less than those offered after the IPO, the equity offer size is mostly between 0 and 1), the equity offer size is basically negatively correlated to the underpricing. It shows that those who reward investors with a higher first-day return issue more shares in the post-ipo market (such as seasoned equity offering). The third plot shows the effect of waiting days on underpricing. In general, it indicates that companies with short waiting days (i.e. days between filing date and issue date) result in higher underpricing. In a 0-40 days range, the longer the waiting time, the lower the underpricing level. After 40 days, the effect of the waiting days on the underpricing began to flatten out, albeit with a change in direction after 120 days or so. It should be noted here that the input data is not normalized to the same scale as the gradient boosting is constant over all monotonic transformations. That is why the curve here looks flatter than the rest of the plots, although the waiting days have a huge impact on underpricing. The fourth plot in Figure 2 shows that higher volatility in ROA is associated with higher underpricing. The 3-year ROA volatility increases by 0.1 standard deviations, resulting in an increase in underpricing rate of 5% (most ROA volatilities are 0.1 or so). The fifth plot shows that a company with a positive income (Ebitda) would have a 10% lower underpricing than a company with a negative income. The magnitude of negative returns also affects the first-day return, as firms with lower negative returns are significantly less underpriced than those with higher negative returns. The directions of influence seem to be consistent with both measures, as they both show that high-quality companies have lower first-day returns. The sixth plot conveys a more interesting story: the impact of market heat degree on underpricing is very complicated. When the heat degree is about 1.1, the first-day return will reach the highest. Whether the market is warming or cooling from 1.1 heat degree, the 26