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IPO Pricing with Accounting Information
Randolph Beatty
Susan Riffe
Rex Thompson
Southern Methodist University
April 2000
Abstract
In this paper, we examine the relation between IPO stock values and available financial statement accounting information. Contrary to the conclusions of Kim and Ritter (1999), we find that accounting book value, earnings and revenue, in conjunction with several other firm and market characteristics, explain a large portion of IPO offer prices (R2 near 80%). Explanatory power is very sensitive to model form, however, and can appear diminutive (R2 less than 10%) in raw, per share regressions. We also find that earnings and book enter significantly in risk estimation regressions where the dependent variable is aftermarket return variability. Finally, while investment bankers set the offer price in light of most of the explanatory power of earnings and book, the first day stock return from offer price to closing market price is also significantly positively correlated with these firm characteristics.
1. Introduction
The valuation of initial public offerings (IPOs) and the setting of IPO offer prices represent a challenging crossroads between valuation theory and practice. Theory dictates the use of discounted cash flow as the conceptual foundation of valuation (see Brealey and Myers (2000)). Unfortunately, as emphasized by Kim and Ritter (1999), estimates of future cash flows and discount rates for IPOs are imprecise. Stereotypical industry practice emphasizes the use of accounting numbers as cash flow surrogates and comparable firm multiples such as P/E ratios as proxies for discount factors (see Palepu, Bernard and Healy (1997)).
Of course, even casual inspection of the data reveals that offer prices and initial market prices do not conform rigidly to simple multiples of accounting numbers, implying that underwriters and market participants incorporate additional information into the valuation equation. An important question raised within the IPO literature, therefore, is just how much variation in IPO prices remains to be explained by factors other than accounting numbers and comparable firm multiples. Kim and Ritter (1999) paint a rather bleak picture of the explanatory power of accounting comparables, suggesting that IPO pricing is largely unrelated to historical accounting information. One interpretation of their results is that underwriters and investors build their cash flow and discount rate estimates with vastly different information.
The view that historical accounting information is relatively unimportant in explaining the variation in stock prices contradicts much of the evidence compiled in marketbased accounting research. Accordingly, in this paper, we revisit the use of accounting comparables as a pricing mechanism for IPOs. Our principal research goal is to put the investigation of IPO pricing on a balanced footing and clarify what information may be important in explaining the IPO offer price (the price paid by purchasers of the initial offering). To this end, our focus is on the explanatory power of revenue, accounting earnings, and book value as cash flow surrogates. Our models also include the pricing relations for recent IPO firms in comparable industries as estimates of discount factors. We find that the explanatory power of our models depends critically on model form. Rather innocuous changes in design can improve the explanatory power of the model from an R2 of approximately 2% to one exceeding 70%. One of our best models uses a log transformation consistent with recent evidence suggesting a nonlinear relationship between accounting fundamentals and stock value (see Riffe and Thompson (1998), Hand (2000) and Finn and Ye (1999)). Moreover, adding economic considerations such as the percentage of ownership retained, market conditions, and time factors leads to explanatory power around 79%.
Although our primary focus is explaining offer price, we also investigate the relevance of accounting information for the average filing price put forth in the preliminary prospectus typically filed several months before the stock offering date. We find our accountingbased model has slightly higher explanatory power for filing price then it does for offer price. Interestingly, after controlling for filing price, accounting information is not significantly related to offer price. Both results suggest that underwriters do not use any additional accounting information in setting offer price not previously considered in setting the filing price range.
A vast literature has struggled to understand why the average first day return for IPOs (i.e., change between offer price and first day closing market price) is between 1015%. Numerous theories to explain this phenomenon have been tested using various risk proxies (see Ibbotson et al. 1994). Improvements in modeling the IPO offer price interplay with empirical investigations into these theories because the IPO offer price forms the basis for the initial return. Investor perceptions of an IPO not incorporated into the offer price end up in the initial return. Since we find accounting information is related to filing and offer prices, we also investigate its relationship to first day return. We start by showing that earnings, book value and revenue are strongly negatively correlated with our proxy for risk, the standard deviation of IPO firm returns in the first year of trading. We then find that earnings and book value help explain first day returns after controlling for expected risk, market conditions, and residuals from the offer price model. This result indicates that from an investors perspective, accounting information is not fully incorporated in the offer price. We link our results to a partial adjustment process described by Benveniste and Spindt (1989) and Hanley (1993) to explain why underwriters may choose to strategically ignore some accounting information in setting offer price that is relevant to investors in setting the first day market price.
We review the previous literature in Section 2, and Section 3 discusses our data. Section 4 focuses on predicting IPO offer price and processes the data through a series of model specifications so that the impact of altering model form can be shown within our data set. In Section 5, we examine the filing price and market price after the first day of trading. Section 6 investigates the importance of accounting information in the prediction of return risk during the first year of public trading and the prediction of first day return. We summarize our conclusions in Section 7.
Literature Review
The process of going public is governed by The Securities Act of 1933. Firms that decide to issue equity securities in public markets for the first time hire an underwriter who performs an initial due diligence investigation of the firm and files an S1 registration form with the SEC. SEC Regulations SK and SX govern the required disclosures. Part 1 of the S1 includes a preliminary prospectus that contains audited financial statements and information about the proposed offering, company background, risk factors, and auditors and underwriters involved in the issuance. The prospectus generally provides a high and low filing price estimated before the underwriters market the stock. We refer to the geometric mean (square root of the product) of these two prices as the filing price.
After the preliminary prospectus is filed, the underwriters market the stock to investors over a road show period of several months to assess market demand. Usually, the day before the stock begins trading, the final IPO offer price is set. The offer price incorporates both available financial information and what the underwriters learn about investor demand during the marketing phase. After final SEC approval, the shares are then sold at the offer price. The shares sold include both primary shares, where the net proceeds (after underwriter discount) go to the firm, and secondary shares, where the net proceeds go to existing stockholders. The final price we consider is the market price, which is defined as the stock price at the end of the first day of trading. The market price is determined by the confluence of all market participants, including investors not taking part in the IPO itself. Figure 1 summarizes the definitions of filing price, offer price and market price.
While there have been numerous papers investigating the relevance of accounting information for pricing stocks in general, there are very few papers addressing the pricing of IPOs in particular. Three notable exceptions are Klein (1996), Kim and Ritter (1999), and Hand (2000). Klein (1996) investigates the explanatory power of accounting variables and other items contained in the prospectus. She concludes that accounting information is important in the pricing of IPOs. However, her measurement of book value is problematic because it uses ex post information affected by the offer price to explain the offer price itself. By contrast, we only use accounting information available prior to the offering to estimate prices.
Kim and Ritter (1999) focus on the usefulness of accounting information in the context of the method of comparables for a sample of 190 IPOs from 1992 and 1993. They project the P/E multiple of IPOs on the median P/E multiple from recent IPOs in the same industry. Their initial regression has an R2 of about 5%, and they improve the results only slightly by using other accounting ratios. They conclude that historical accounting information is relatively unimportant in pricing IPOs. Although we confirm their empirical findings, we argue in Section 4 that their model is capturing time and industry variation in pricing relations rather than the explanatory power of accounting information itself. We also control for time and industry factors in our models.
Hand (2000) demonstrates that a loglinear model of accounting data is useful in explaining 7080% of the offer price of Internet stock IPOs as well as the market prices over the subsequent two years. While the log model we use to explain the level of IPO prices is complementary to Hands approach, we focus on the usefulness of accounting information across all industries after controlling for recent comparable pricing relations.
For our sample, the average first day return is about 12%, which is consistent with previous studies (see Ibbotson, Sindelar, and Ritter (1994)). The underpricing of IPOs by underwriters reduces the amount of cash received by the issuing firm and is often referred to as leaving money on the table. This result is anomalous because it is difficult to understand why issuers would tolerate receiving lower proceeds than the market will bear, on average. We now briefly describe several proposed theories of underpricing.
Rock (1986) suggests a winners curse in the pricing of IPOs. His model contains informed and uninformed investors who bid for a fixed number of shares at the offer price. The informed investors only bid on underpriced shares. To compensate uninformed investors for a potential adverse selection problem where they only receive a full allocation of overpriced shares, offerings are underpriced on average. Beatty and Ritter (1986) find evidence consistent with an implication of Rocks model that riskier issues with greater ex ante uncertainty have greater underpricing. This result motivates our interest in how accounting information relates to ex ante uncertainty.
Benveniste and Spindt (1989) develop a dynamic information acquisition model where underpricing is used to encourage investors to reveal positive private information in the marketing phase. Investors have no incentive to reveal positive information that increases offer price unless the amount of underpricing is greater for firms where good news is revealed. Their model predicts that the upward adjustment from filing price to offer price is a partial adjustment relative to the favorable private information available; this partial adjustment then leads to underpricing.
Hanley (1993) finds empirical results consistent with Benveniste and Spindt (1989). She documents that the percent change from filing price to offer price is positively related to first day returns. In her return regression with a 17.8% R2, other significant factors are size of the offering, market returns, and underwriter market share. We incorporate these same control variables, but extend her regression model to consider accounting information and the possibility that underpricing is different for downward versus upward revisions from filing price to offer price.
Loughran and Ritter (1999) offer a prospect theory to explain why underwriters can underprice issues on average without reproach. They suggest that underpricing by underwriters is intentional because it provides them with an indirect form of compensation. Issuers tolerate underpricing because it is associated with positive adjustments from filing price to offer price. Since issuers are receiving a higher offer price than expected given the filing price, they tolerate leaving money on the table by receiving an offer price thats lower than the first day market price. Loughran and Ritter (1999) find evidence consistent with an implication of their model that the first day return is related to publicly available information about preoffer market returns. However, while they do not control for other potential risk factors identified in the literature, we control for both preoffer market returns and estimated risk in our analysis.
3. Data Description
We use the Securities Data Corporation (SDC) database to build our initial sample of IPOs during the 19861998 period. We identify 6,132 U.S. common stock IPOs after excluding unit and best efforts offerings. Panel A of Table 1 shows that our sample is reduced to 2,577 after requiring the IPOs to have an offer price, filing price, market price, positive book value and earnings, revenue, percent shares retained, and SIC code. Panel B reveals substantial variation in the number of IPOs from each year, ranging from a low of 78 in 1988 to a high of 325 in 1993. This is consistent with the finding that the volume of IPOs increases during hot markets (Ibbotson, Sindelar and Ritter 1994) and suggests the need to control for market and time factors in our regressions.
Table 2 presents descriptive statistics for the sample. Fully diluted earnings per share, book value of equity per share and revenue are measured in the year prior to the offering. To be consistent, shares outstanding before the offering are used to convert per share amounts to total values. The table shows statistics for the accounting variables and offer price expressed in different forms relating to the various models we consider in Section 4. We report statistics for per share amounts, total value amounts multiplying per share amounts by number of shares, amounts deflated by book value or revenue, and the log of total value amounts. In addition, we show statistics for the log of total filing value and log of total market value along with several other variables discussed in Section 4.
4. Role of Accounting Information in Explaining Offer Price
Sufficient conditions for using accounting earnings as a cash flow surrogate along with industry multiples as estimates of the discount factor are easily stated and we wish not to get bogged down in this exercise. The question receiving our focus is how to specify an empirical model that reveals the explanatory power of accounting information.
First, consider a simple model that projects IPO offer price per share on earnings per share absent any other considerations about time period or industry. For consistency with other studies that use financial ratios, only firms with positive earnings and book value are used in the regressions. As shown in row (1) of Table 3, earnings per share has little explanatory power with an R2 around 2%. Including book value per share as an additional explanatory variable in row (2) contributes nothing to the model as the coefficient on book is not significant.
Based on these two models, it would appear that nuances in cash flow estimation along with crosssectional and timeseries variation in discount factors have a lot of work to do if we are to explain IPO offer prices by traditional valuation principles. Indeed, from the perspective of hard core critics of accounting practice, the results are almost too good to be true. One has to ask before proceeding, if there isnt something fundamental being ignored in the first two regressions. The answer lies in the convention of basing regressions on per share amounts.
The IPO process involves the determination of offer price in conjunction with number of shares because the true economic variable being priced is total value of equity. Underwriters partition total equity value into an arbitrary number of shares, which itself is correlated with value. Indeed, bankers could, if they chose, offer every IPO at the same price of, say, $10 per share, forcing all of the explanatory power in earnings to come through the correlation between earnings and the number of shares. They could equally well offer all stock at $0.10 in earnings per share with the same implication.
To remove the arbitrary effect of number of shares issued, we estimate regressions of total offer value projected on total earnings and total book value. Rows (3) and (4) show the explanatory power has increased considerably to 13% for earnings alone and 13.56% for earnings and book. Book value is now significant with a tratio approaching 4. An obvious question at this juncture, however, is whether the models shown in Table 3 arent merely regressions of size on size. In some sense, however, that is the point; that accounting information reveals the size of a firms equity market value. On the other hand, an important issue is whether other surrogates for size might do just as well as earnings and book in approximating firm value. Row (5) shows the model with revenue included as a third explanatory variable. The model R2 and the tratio for revenue reveal that revenue contributes as much to the model as book value, but it does not eliminate the relevance of either earnings or book. The adjusted R2 increases slightly to 14.3% with the inclusion of revenue.
While an improvement, the R2s for the models based on total value are still not very satisfying. If accounting information represents a first approximation to cash flow, one would like to come quickly to a model that explains more than 50% of value variation. An additional place to look for a big increase in explanatory power is through a transformation of the data that controls for outliers and heteroscedasticity. One approach is to trim or winsorize the data to neutralize the impact of outliers on the regression coefficients. Of course, by doing so, the models explanatory power relates only to the data not discarded. As an alternative, a transformation of the data might lead to a betterbehaved model. Clearly, if we are interested in explaining value, we are interested in explaining any transformation of value. The transformation really gets at the question of model form. If the true model is linear and homoscedastic, a transformation of the data will not improve explanatory power.
In their discussions of levels regressions relating price to earnings and book information, Brown et al. (1999) and Easton (1999) advocate deflating by an estimate of scale such as book value or revenue to remove what they call spurious size effects. Row (6) reports the row (4) variables (including the intercept) transformed through division by book value. While we are now technically explaining the ratio of market to book, the pickup in explanatory power is dramatic, with the model R2 attaining 89.61%. Deflating model (5) by revenue is reported in row (7) and results in a model R2 of 60.01%. One could conclude from these regressions that accounting information represents a first approximation to cash flow that goes beyond mere scale effects. It is interesting that the thrust of Easton (1999) and Brown et al. (1999) is that deflating by a scale variable reduces spurious correlation of size in levels regressions. The IPO data reveal that deflating can increase the models explanatory power.
In row (8), we report the explanatory power of a log transformation of the total value regression in row (5). There are theoretical reasons to posit a nonlinear relation between accounting information and value as suggested by a log transformation (see Burgstahler and Dichev (1997), Fischer and Verrecchia (1997), Riffe and Thompson (1998), and Finn and Ye (1999)). Econometric issues also support the use of log scale for estimation because it can reduce the influence of potential outliers and correct the problem of heteroscedastic errors. Finn and Ye (1999) and Hand (2000) document a superior fit for log models compared to linear models. In finance, Kaplan and Rubak (1995) used a log scale to examine the valuation of highly levered transactions. For our sample, the log transformation improves the model fit from 14.3% to 71.45%. From the significant tratios, we again conclude that accounting is probably not merely a proxy for size. Earnings has by far the most explanatory power (t>30) and revenue the least (t<7). Book value has a t of 16.75.
Now that a baseline has been established, it is interesting to examine how time and crosssectional variation influences the results. As mentioned in Section 2, Kim and Ritter (1999) project P/E multiples of IPOs on the median P/E multiples of recent IPOs in the same industry and are disappointed with a low R2 of about 5%. To put the regressions of Kim and Ritter in perspective, one would only expect their regressions to have explanatory power if P/E ratios vary systematically by time and industry. The model is silent on the explanatory power of earnings itself. Moreover, even if P/E ratios vary by time and industry the regressions might have very low explanatory power in an absolute sense. This is because the model measures only the incremental explanatory power of time and industry variation in multiples. Clearly, relative to the raw data, 5% isnt explaining very much. On the other hand, if it were possible for time and industry variation to explain an additional 5% on top of a baseline of 70%, the incremental improvement would be highly significant. For our sample, an unreported regression including our measures of recent comparables and time dummies as defined below has an R2 of 4.5%, remarkably close to the explanatory power of P/E multiples documented by Kim and Ritter (1999). By contrast, in Table 3 we show that the explanatory power of accounting information alone is around 70%.
To clarify how time and industry variation contributes to the incremental explanatory power of the models reported in Table 3, Table 4 works with the log transformation, time dummies and a variable that captures the pricing multiples of recent IPOs in the same industry. This latter variable, called recent comparables, is defined as the average pricing residual from the five or fewer most recent IPOs in the same threedigit SIC code within the last 2 years. The estimated residuals are from the regression of the log of total value of the IPO on the log of the total value of earnings, book value and revenue. If a threedigit match is not available, an average based on a twodigit match is used. IPOs without a twodigit match have their residual set to zero. While this measure is crude, it captures an influence from both industry clustering and time variation. Column 1 in Table 4 reveals that recent comparables is highly significant with a t exceeding 15.
Perhaps a comment on the use of accounting ratios is in order at this stage because we use a regression format rather than a ratio format to estimate multiples. Several studies starting with Lev and Sunder (1979) question the rigid use of ratios as a modeling tool. Where measurement error in earnings and book value are incorporated into the pricing model, Riffe and Thompson (1998) show that regression with an intercept has a firmer theoretical footing than the assumption of proportionality that underlies the use of ratios. The argument ultimately comes down to whether or not an intercept is included in the pricing model. We include the intercept in the analysis here although it is unlikely that much of importance would be changed if the intercept were not included.
Column 2 of Table 4 includes 12 yearly time dummies for 19871998. Seven of the time dummies are significant and recent comparables remains highly significant (t>12), reinforcing the notion that industry is playing a role beyond time variation.
The next column includes an explanatory variable implied by the signaling literature to exert an influence in IPO pricing: the percentage of shares retained by management. Percent retained is calculated as shares outstanding after the offering minus primary and secondary shares issued all divided by shares outstanding after the offering. Leland and Pyle (1977) suggest that greater share retention is a positive signal because insiders should have superior information about expected future cash flows. This variable has a t exceeding 22, confirming earlier findings in studies such as Klein (1996) about the importance of share retention.
At this point, it is clear that accounting information and recent comparables explain a significant portion of IPO values. We show that modest attention to model form can generate the perception of a fortyfold improvement in explanatory power. Supposing that no additional improvements in model specification are forthcoming, we are left with approximately 20% of IPO offer price variation driven by that part of the investment banking process not explained by the variables considered above.
5. Role of Accounting Information in Explaining Filing Price and Market Price
We have focused, so far, on explaining the IPO offer price. This is because offer price receives the most attention in the literature and is the price Kim and Ritter (1999) emphasize. We now highlight two additional price points described in Figure 1, the filing price and the first day market price. In Table 5, we report results from applying the log model to each of these prices multiplied by the number of shares outstanding prior to the offering. Recall that the filing price is set by the underwriter based on available information before the offer is fully marketed. The offer price is set in light of both available financial information and everything that the underwriter learns about specific investor demand during the marketing phase. The market price after the first day of trading is determined by the force of all market participants, including investors not taking part in the IPO itself.
The first column in Table 5 shows results including the same independent variables described in Table 4, but the dependent variable is now the log of the total filing value based on the (geometric) average of high and low filing prices. All of the important coefficients retain significance and, indeed, the model has higher explanatory power for the filing value (R2 = 80.40%) than for the IPO offer value (R2 = 78.89%). This is consistent with the notion that underwriters adjust the offer price for information learned during marketing, while the accounting information is knowable and incorporated by the underwriters before the marketing phase begins.
The second column in Table 5 shows results for the log total market value based on market price. While all of the important variables are still highly significant, the explanatory power of the model falls to an R2 of 76.82%. This drop in explanatory power reinforces the logic that public information is impounded early in the IPO price process, with additional variation in the later stage prices caused by the incorporation of private information about value.
Results in Table 6 add further clarification. The first column shows an offer value regression similar to the last column of Table 4, except we add the cumulative market return prior to the IPO. Following Loughran and Ritter (1999), we measure preoffer market return as the continuously compounded, valuedweighted NYSE, AMEX, and NASDAQ return for the 15 days prior to the offering. The logic for including this variable is that changes in the overall market should cause revisions in the offer price of IPOs. While the logic is sound, the coefficient is insignificant, primarily because our levels model has too much residual variation to pick up the impact of overall market returns within a few week period.
The second column of Table 6 includes a final variable in the log total offer value regression that reveals a lot about the offer price process. This final variable is the log of total filing value. The model now includes information about what the underwriters thought the offer price would be before the offer was marketed. Not surprisingly, the model explanatory power jumps to over 98%. What is interesting is that earnings and book value lose significance while all three accounting variables, including revenue (tratio of 3.38), have negative coefficients. The preoffer market return is now significant both because the residual variation of the model is lower and the coefficient on market return is higher.
Insignificant coefficients on earnings and book value in column two have the pleasing interpretation that underwriters use available accounting information before the marketing begins. In other words, underwriters have a good model of how the offer price relates to accounting information at the time the filing price range is set. Underwriters depend on accounting data to set filing price, but the adjustments from filing to offer price are not based on accounting information known when the filing price range is set. Kim and Ritter (1999, p. 111) question whether this adjustment is related to superior analysis versus canvassing market demand. Our results suggest that market demand is a more important determinant of the adjustment.
Role of Accounting Information in Explaining Risk and First Day Return
Numerous papers attempt to explain IPO underpricing, the large average first day market return that ranges from 1015%. Most of the prior literature uses variables that serve as risk surrogates; the working hypothesis is that only risk considerations should affect the rate of return. However, according to the models described by Benveniste and Spindt (1989), Hanley (1993) and Loughran and Ritter (1999), there may be another force at work in the data. These papers suggest that only part of the information available about IPOs is impounded into offer price; the rest is incorporated into the first day return by investors. Hanley (1993) and Loughran and Ritter (1999) provide two pieces of empirical evidence that a partial adjustment phenomenon is present in IPO returns. First, an offer price that is higher than the filing price range leads to higher initial returns. Second, preoffer market return is correlated with both the appreciation from filing price range to offer price and the first day return.
Table 5 shows that accounting information is significantly related to the first day market value of IPOs. In this section, we investigate whether accounting information is related to first day returns because it captures elements of risk and/or because it reflects information that is only partially reflected in the offer price. Table 7 reports descriptive statistics for the variables we introduce in this section.
Since risk is such a crucial element in the underpricing literature, we begin by modeling what Beatty and Ritter (1986) identify as ex ante uncertainty about the IPO market price. Several studies employ as a risk proxy the standard deviation of daily returns for the year or so after the IPO (see, among others, Carter, Dark, and Singh (1998)). Although this proxy has intuitive appeal, it includes ex post information that is not known at the time of the IPO; thus, it measures ex ante uncertainty with error. We propose a forecast model that correlates information variables available at the time of the offering with standard deviation of returns for the first year after the IPO begins trading. Our purpose is twofold. First, we use this model to estimate a cleaner proxy for ex ante expected risk in our return regressions. Second, our model allows us to explore the usefulness of accounting measures in predicting risk.
In Table 8, our model of risk relates size, offering choices, industry, and accounting measures to standard deviation of aftermarket returns. We expect larger offerings (log total proceeds) to exhibit lower aftermarket standard deviation since size of offering captures the inflow of new equity to the corporation. This inflow reduces financial leverage and the risk of insolvency. Table 8 reveals the expected negative coefficient.
Next, the structure of the IPO arrangement is likely to reveal information concerning owner and underwriter beliefs about the risk of future cashflows. However, the exact association of the resulting IPO choice variables and risk is unclear. For example, high share retention may indicate that the firm is less risky. However, an insider for an especially risky IPO may also be forced to retain an unusually high amount of ownership to reveal positive information to the market. Since these relations are likely to be complex and are not central to our inquiry, in Table 8 we include a set of IPO choice variables suggested by the literature to control for the relation between IPO structure and risk. Our reported risk regression in Table 8 includes percentage of shares retained by insiders, underwriter market share as a proxy for underwriter reputation, a dummy variable for venture capital involvement, and size of offer price prior to the The Penny Stock Reform Act of 1990. Table 7 provides more extensive descriptions of how we measure these variables. From these variables, percent retained, pre1990 offer price, and underwriter market share are significantly associated with standard deviation of aftermarket returns at conventional levels. Because we also expect risk to vary by industry, we create a hightech dummy variable for the 14 hightech industries identified by Francis and Schipper (1999). Not surprisingly, we find higher risk for this segment of the market.
Our regression also documents the relation between accounting measures and standard deviation of aftermarket returns. We expect the debt ratio and earnings variability to be positively related to risk. Earnings variability is defined as the absolute value of the percentage change in earnings per share in the three years prior to the IPO. The debt ratio measures total debt to total assets. Interestingly, neither the debt ratio nor earnings variability is significant in our regression. We also include log of total earnings, book value and revenue as defined in Section 3. These three variables measure different aspects of profitability for the IPO firm; since higher profitability should lead to less risk, we expect them to all have negative coefficients. Table 8 documents the expected relation and provides strong evidence that accounting measures play an important role in IPO risk evaluation. We view this as an important finding given that the usefulness of accounting measures for IPO risk assessment is largely unexplored.
To investigate partial adjustments in our model of first day returns, we use the residuals defined as actual offer value minus predicted offer value from the last model presented in Table 6. These residuals capture variation in offer value that is unexplained by filing value and the other fundamental value drivers in the model. Positive correlation between the residuals and first day return indicates that underwriters use a partial adjustment process to alter the offer value away from fundamentals in response to specific investor demand. For example, assume underwriters believe the expected market value is higher than the predicted offer value because of positive investor perceptions. Remember that the predicted offer value from Table 6 does not incorporate information about investor demand assessed during the marketing phase. For such hot IPOs, underwriters increase the offer value partially, but not completely, to the expected market value; this leads to a positive relation between the residuals and the first day return. As suggested by Hanley (1993) and Loughran and Ritter (1999), we also include the preoffer market return as another indicator of the partial adjustment process. If first day return is related to knowable market returns, it suggests that underwriters are knowingly not fully reflecting this information in their offer price.
Our first day return regressions in Table 9 are designed to clarify the role of risk, partial adjustment and accounting information in the pricing process. The first column includes (1) residuals from the offer value model in the last column of Table 6 (offer value residuals), (2) the size of the offering (log of total proceeds) as an initial risk proxy, and (3) the preoffer market return. The highly significant positive coefficients on offer value residuals and preoffer market return are consistent with a partial adjustment process. The negative and significant coefficient on log of total proceeds is consistent with larger IPOs having less risk.
The second column investigates the difference in return relations for negative and positive offer value residuals. The intercept captures underpricing; the regression includes a dummy for negative residuals to estimate the change in the intercept for negative versus positive residuals. The estimated slope coefficient on the residual variable captures the partial adjustment phenomenon; the regression also includes the negative residual dummy interacted with the residual amount to estimate the change in slope for negative versus positive residuals. The negative and significant coefficients on the negative residual variables indicate that firms with offer prices below the predicted prices have both a lower intercept (.24 .05=.19) and virtually no slope (.59.58=.01). Thus, there appears to be a discontinuity and kink in the offer pricing function, suggesting partial adjustment and underpricing for IPOs with positive residuals and no partial adjustment with less underpricing for negative residual IPOs. This result is consistent with Hanley (1993) and Loughran and Ritter (1999), but they did not use a multivariate regression context to explore these relationships.
The third column includes earnings, book value and revenue in the model. Earnings is not significant, while book value and revenue have negative and significant coefficients. We would argue, however, that these coefficients are difficult to interpret because they include two forces. The first is a potential partial adjustment aspect, while the second is an opposing relation between accounting fundamentals and a firms risk. To purge the accounting variables of their risk component, we use our predicted risk surrogate from Table 8 that includes whatever information is contained in the accounting variables about the standard deviation of return during the first year of trading.
The final column of Table 9 includes the predicted risk variable, which is created by multiplying the estimated coefficients in Table 8 by firmspecific variables. Risk enters positively and is highly significant. Moreover, earnings and book value are now significantly positive at the 10% level. The coefficient on revenue is negative. The positive sign on earnings and book value may be given a partial adjustment interpretation. Underwriters choose to ignore a portion of accounting information that is relevant to investors given their incentives to underprice IPOs on average. Because investors impound this information into the first day market price, accounting information is positively related to first day return. It is noteworthy that the final return regression of Table 9 has a respectable R2 exceeding 28%.
Conclusions
This paper set out to investigate whether historical accounting information is relevant for the offer price of IPOs. We begin by demonstrating that after paying modest attention to model form, historical accounting information does provide information that helps explain between 75% and 80% of the variability of offer value. Our preferred model captures the loglinear relationship between value and accounting information and considers recent comparable pricing relationships. We conclude, contrary to Kim and Ritter (1999), that accounting information is important for IPO pricing.
We also provide some insight as to when and how accounting information is impounded by examining three price points: filing price, offer price, and first day market price. We show that accounting information is impounded by underwriters when setting the filing price, but adjustments from the filing price to the offer price are not based on accounting information. However, apparently underwriters do not integrate into offer prices some of the accounting information that is important to investors because we find that accounting information is significantly related to the first day return. In our return regressions, we consider two important elements of the IPO underpricing puzzle: risk estimation and a partial adjustment process. We demonstrate that accounting data are important in predicting risk, measured as the standard deviation in aftermarket stock returns. Previous papers supporting a partial adjustment process show that preoffer market returns and the difference between filing price and offer price are related to aftermarket returns; we show that underwriters also partially adjust the filing and offer prices for accounting information. The literature awaits better modeling before the various forces underlying partial adjustment can be separated convincingly.
References
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Beatty, R., S. Riffe, and R. Thompson. 1999. The Method of Comparables and Tax Court Valuations of Private Firms: An Empirical Investigation. Accounting Horizons, 13, 177199.
Beatty, R., and J. Ritter. 1986. Investment Banking, Reputation, and the Underpricing of Initial Public Offerings. Journal of Financial Economics 15, 213232.
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Brealey, R., and S. Myers. 2000. Principles of Corporate Finance. 6th edition. New York: IrwinMcGraw Hill.
Brown, S., K. Lo, and T. Lys. 1999. Use of R2 in Accounting Research: Measuring Changes in Value Relevance Over the Last Four Decades. Journal of Accounting and Economics 28, 83115.
Burgstahler, D., and I. Dichev. 1997. Earnings, Adaptation, and Equity Value. The Accounting Review 72, 187215.
Carter, R., F. Dark, and A. Singh. 1998. "Underwriter Reputation, Initial Returns, and the LongRun Performance of IPO Stocks." Journal of Finance 53, 285311.
Dechow, P., A. Hutton, and R. Sloan. 1999. An Empirical Assessment of the Residual Income Valuation Model. Journal of Accounting and Economics 26, 134.
Easton, P. 1999. Discussion of Revalued Financial, Tangible and Intangible Assets: Association with Share Prices and NonMarketBased Value Estimates. Journal of Accounting Research, 36 Supplement, 235247.
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Francis, J., and K. Schipper. 1999. Have Financial Statements Lost Their Relevance? Journal of Accounting Research 37, 319352.
Frankel, R., and C. Lee. 1998. Accounting Valuation, Market Expectation, and CrossSectional Stock Returns. Journal of Accounting and Economics 25, 283319.
Hand, J. M. January 2000. Profits, Losses and the NonLinear Pricing of Internet Stocks. Working paper, UNCChapel Hill.
Hanley, K. W. 1993. The Underpricing of Initial Public Offerings and the Partial Adjustment Phenomenon. Journal of Financial Economics 34, 231250.
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Kim, M., and J. Ritter. 1999. "Valuing IPOs." Journal of Financials Economics 53, 409437.
Klein, A. 1996. Can Investors Use the Prospectus to Price Initial Public Offerings. The Journal of Financial Statement Analysis, 2339.
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Loughran, T., and J. Ritter. December 1999. Why Dont Issuers Get Upset About Leaving Money on the Table in IPOs? Working paper, University of Florida.
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Figure 1
Timeline of IPO Prices
Accounting Data Marketing Phase First Day of Trading
Filing Price ( Geometric Mean (i.e., Square Root of the Product) of Low and High Filing Price Listed in the Preliminary ProspectusOffer Price (Price Paid by Purchasers on IPO Date Market Price ( Stock Price at the Close of the First Day of Trading
Table 1
Sample
We used the Securities Data Corporation (SDC) Database to identify IPOs during the 19861998 period. The following criteria resulted in a sample of 2,577 IPOs with complete data available and positive earnings and book value.
Panel A: CriteriaNSDC data available 198619986,132Filing price, offer price and market price available5,230Book value, earnings, and revenue information available3,909Percent shares retained and SIC code available3,897Positive earnings and book value
2,577Panel B: Year FrequencyN1986283198722019887819898619908019911971992250199332519942591995232199626319971951998109Total2,577
Table 2
Descriptive Statistics
2,577 observations are used in the analysis. Offer price is the price paid by purchasers on the day the stock goes public. Earnings per share is fully diluted and measured over the 12 months prior to the offering. Book value per share is the stockholders equity per share before the offering. Total Value indicates that the per share amounts are multiplied by the number of shares outstanding before the offering. Offer price and earnings are shown deflated by book value along with the inverse of book value per share. Offer price, earnings, and book value are shown deflated by revenue along with the inverse of total revenue. Log indicates that the natural log was taken of the total value undeflated numbers. Total and log numbers are reported in millions. Some small numbers deflated by total revenue are reported in scientific E notation. The number before the E is scaled to the power of 10 listed after the E. Recent comparables are based on residuals from the log total value regression including earnings, book value and revenue. The comparables are calculated using the five or fewer most recent IPOs in the same 3digit SIC code within the last 2 years. An average based on 2digit matches is used if a 3digit average is not available. Missing values for 132 observations are set to zero. Percent retained is the percentage of shares retained by management and is calculated as outstanding shares after the offering minus total primary and secondary shares offered all divided by shares outstanding after the offering. Log total filing value is the log of the geometric mean of the high and low filing price multiplied by number of shares outstanding before the offering. Log total market value is the log of the first day closing price multiplied by the number of shares outstanding before the offering. Preoffer market return is continuously compounded, valueweighted return from NYSE, AMEX and NASDAQ for the 15 days prior to the offering. The mean, minimum, maximum, standard deviation and 25, 50 and 75 percentiles are reported for each variable.
VariableMean
Min.25th50th75thMax.Std. Dev.Offer Price Per Share12.2318.751215645.14Earnings Per Share.70.01.28.51.82861.90Book Value Per Share9.85.01.821.773.866540162.91Total Offer Value311.26.0126.6057.25134.43750002082Total Earnings Value12.19.00011.072.345.8687351.4Total Book Value173.87.0013.348.6725.502423004795Total Revenue219.08.120.2045.9012726180 956.29Offer/Book21.96.0023.115.9212.201950100.88Inverse Book 1.93.0002.26.561.221007.43Earnings/Book.90.00002.14.27.491274.50Offer/Revenue2.66.0001.601.212.5653113.10Inverse Revenue 5.8E83.8E117.9E92.2E85.0E81E52.6E7Earnings/Revenue.103.3E6.03.05.1025.56Book/Revenue.583.9E6.10.21.404088.16Log Total Offer Value17.979.2117.1017.8618.7225.041.44Log Total Earnings Value14.754.8713.8814.6715.5820.591.56Log Total Book Value16.096.9115.0215.9817.0526.211.81Log Total Revenue17.7711.5116.8217.6418.6623.991.49Recent Comparables.0011.76.330.284.25.54Percent Retained.670.60.69.76.99.16Log Total Filing Value17.999.3017.1517.9018.6925.261.42Log Total Market Value 18.089.2417.1717.9618.8725.041.46PreOffer Market Return.02.34.001.02.03.19.03
Table 3
Offer Price and Accounting Data Regressions
2,577 IPOs are used in the regressions. The dependent variable is based on the offer price. Earnings per share is fully diluted and measured over the 12 months prior to the offering. Book value per share is the stockholders equity per share before the offering. Total value regressions use the per share amounts multiplied by the number of outstanding shares prior to the offering for both the dependent and independent variables. Deflated regressions deflate the independent and dependent variables from the total value regressions, including the intercept, by either revenue or book value. The log total value regression uses the natural log of all of the undeflated total value amounts. Coefficient estimates are reported along with tvalues in parentheses. An adjusted R2 is reported for each regression.
Dependent Variable Based on Offer Price
Intercept
EarningsBook ValueRevenue1/
DeflatorAdj. R2Per Share
11.96
(111.98).39
(7.43)2.06%Per Share
11.96
(111.79).39
(7.42).0002
(.38)2.03%Total Value
132880872
(3.38)14.63
(19.65)13.00%Total Value
133509754
(3.41)14.10
(18.72).03
(4.18)13.56%Total Value
112360101
(2.86)11.67
(12.94).03
(3.88).23
(4.83)14.30%Book Value Deflator
2.00
(3.02)8.36
(37.25)8.53
(62.71)89.61%Revenue Deflator
.87
(5.16)18.29
(60.40).02
(.98)816065
(1.28)60.01%Log Total Offer Value5.20
(28.57).50
(32.24).21
(16.75).11
(6.81)71.45%
Table 4
Log Total Offer Value Regressions Including Recent Comparables,
Time Dummies and Percent Retained
2,577 IPOs are used in the regressions. Log total offer value is the log of offer price times number of shares outstanding prior to the offering. All the accountingbased independent variables are the log of the per share amount times the number of shares outstanding prior to the offering. Recent comparables are the residuals from the log total value regression including earnings, book value and revenue. Average residuals are calculated using the 5 or fewer most recent IPOs in the same 3digit SIC code within the last 730 calendar days. An average based on 2digit matches is used if a 3digit average is not available. Missing values are set to zero. Time dummies are created for each of the years except 1986. Percent retained is the percentage of shares retained by management and is calculated as outstanding shares after the offering minus primary and secondary shares issued all divided by shares outstanding after the offering. Coefficient estimates are reported along with tvalues in parentheses. An adjusted R2 is reported for each regression.
Dependent VariableLog Total Offer ValueLog Total Offer ValueLog Total Offer ValueAdjusted R273.97%74.75%78.89%Intercept5.03 (28.88)4.98 (28.69)4.30 (26.62)Log Total Earnings.50 (33.84).50 (34.15).41 (29.15)Log Total Book Value.21 (17.35).21 (17.40).21 (18.75)Log Total Revenue.12 (7.82).12 (7.62).15 (10.98)Recent Comparables.43 (15.81).36 (12.87).29 (11.43)Time87.02 (.24).01 (.12)Time88.05 (.59).11 (1.26)Time89.02 (.26).02 (.28)Time90.20 (2.21).23 (2.68)Time91.06 (.88).16 (2.62)Time92.10 (1.52).20 (3.43)Time93.22 (3.67).30 (5.51)Time94.16 (2.58).24 (4.13)Time95.32 (4.90).38 (6.43)Time96.44 (6.92).46 (7.87)Time97.21 (3.00).34 (5.36)Time98.24 (2.94).35 (4.62)Percent Retained2.02 (22.42)
Table 5
Log Total Filing Value and Log Total Market Value Regressions
Log total filing value is the log of the geometric mean of the high and low filing price multiplied by number of shares outstanding before the offering. Log total market value is the log of the first day closing price multiplied by the number of shares outstanding before the offering. All other variables are as defined in Tables 2 and 4. Coefficient estimates are reported along with tvalues in parentheses. An adjusted R2 is reported for each regression.
Dependent VariableLog Total Filing ValueLog Total Market ValueAdjusted R280.40%76.82%Intercept4.34 (28.31)4.57 (26.69)Log Total Earnings.40 (30.26).41 (27.37)Log Total Book Value.20 (19.48).20 (17.36)Log Total Revenue.16 (12.24).14 (9.73)Recent Comparables.27 (10.42).31 (12.20)Time87.003 (.05).08 (.12)Time88.08 (1.01).08 (.94)Time89.02 (.27).07 (.85)Time90.19 (2.40).27 (3.07)Time91.12 (2.11).22 (3.41)Time92.20 (3.70).24 (3.94)Time93.25 (4.76).36 (6.27)Time94.26 (4.72).27 (4.42)Time95.34 (5.95).48 (7.59)Time96.44 (7.88).53 (8.58)Time97.35 (5.72).40 (5.92)Time98.35 (4.84).39 (4.91)Percent Retained1.99 (23.22)2.13 (22.28)
Table 6
Log Total Offer Value Regressions with PreOffer Market Return
and Log Total Filing Value
Preoffer market return is continuously compounded, valueweighted return from NYSE, AMEX and NASDAQ for the 15 days prior to the offering. Log total filing value is the log of the geometric mean of the high and low filing price multiplied by number of shares outstanding before the offering. All other variables are as defined in Tables 2 and 4. Coefficient estimates are reported along with tvalues in parentheses. An adjusted R2 is reported for each regression.
Dependent VariableLog Total Offer ValueLog Total Offer ValueAdjusted R278.88%98.71%Intercept4.30 (26.58).13 (2.75)Log Total Earnings.41 (29.09).00 (1.24)Log Total Book Value.21 (18.76).00 (.66)Log Total Revenue.15 (10.99).01 (3.38)Recent Comparables.29 (11.40).02 (3.75)Time87.01 (.21).02 (1.52)Time88.11 (1.31).04 (1.97)Time89.02 (.27).03 (1.73)Time90.23 (2.71).04 (1.97)Time91.16 (2.49).03 (1.73)Time92.19 (3.20 ).04 (2.41)Time93.29 (5.28).03 (2.41)Time94.24 (4.12).03 (1.83)Time95.38 (6.24).03 (2.09)Time96.45 (7.73).01 (.47)Time97.34 (5.26).03 (1.89)Time98.35 (4.60).01 (.51)Percent Retained2.03 (22.44).00 (.04)PreOffer Market Return.41 (.92).88 (7.90)Log Total Filing Value1.02 (198.60)
Table 7
Descriptive Statistics for Risk and First Day Return Regressions
2,577 observations are included in the analysis. Standard deviation of aftermarket returns is the standard deviation of returns for the 255 days beginning 7 days after the offer. For the 7% of the sample that does not have returns for the full 255 day period, we use the length of the return series available. Log total proceeds is the log of the aggregate amount of cash raised by the offering calculated as offer price times number of shares issued all divided by CPI index relative to 1986. Underwriter market share is the cumulative offer proceeds underwritten by the lead underwriter during the sample period divided by the aggregate offer proceeds for the whole sample. Pre1990 offer price equals the offer price prior to 1990 and is 0 otherwise; it is intended to capture the risk of small stock prices prior to The Penny Stock Reform Act of 1990. Debt ratio is total debt divided by total assets. Missing values for 623 observations are set to the mean of the distribution. Earnings variability is the absolute value of the percentage change in earnings per share over the 3years prior to the IPO. Missing values for 1,205 observations are set to the mean of the distribution. Risk is the predicted standard deviation of aftermarket return using the regression coefficients reported in Table 8. First day return is the log of the ratio of first day market price divided by offer price. Offer value residuals are the regression residuals from the last model listed in Table 6 including the log of total filing value. Filing price range is the high filing price minus the low filing price all divided by the low filing price. The mean, minimum, maximum, standard deviation and 25, 50 and 75 percentiles are reported for each variable.
VariableMean
Min.25th50th75thMax.Std. Dev.Std. Dev. After Market Returns.04.01.03.04.05.27.02Log Total Proceeds16.8714.1016.1716.8217.4521.811.11Underwriter Market Share.03.00001.001.01.03.19.05Pre1990 Offer Price 2.940004.556.55.68Debt Ratio.25.001.09.24.291.21Earnings Variability3.9701.273.973.971226.82Risk (Predicted Standard Deviation After Market Returns).04.003.03.04.04.06.01First Day Return.10.780.06.171.96.15Offer Value Residuals 01.12.08.02.091.34.16Filing Price Range.160.13.17.21.6.09
Table 8
Risk Regression
2,222 observations are used that have CRSP data to measure standard deviation of aftermarket returns. The continuous variables are as defined in Tables 2 and 7. Hightech Dummy equals 1 if firms are in the following SIC codes: 283, 357, 360368, 481, 737, and 873. 678 observations or 26.3% of the sample are in these SIC codes. Venture capital dummy equals 1 if the prospectus indicates venture capital backing for the offering. 788 firms or 30.6% of the sample have venture capital financing. Coefficient estimates are reported along with tvalues in parentheses. An adjusted R2 is reported.
Dependent VariableStandard Deviation After Market ReturnsAdjusted R223.47%Intercept.11 (19.97)Log Total Proceeds.002 (3.54)Percent Retained.01 (3.00)Underwriter Market Share.01 (1.71)Venture Capital Dummy.0001 (.15)Pre1990 Offer Price.0002 (4.39)Hightech Dummy.01 (7.98)Debt Ratio.001 (.55)Earnings Variability.00005 (1.07)Filing Price Range.004 (1.17)Log Total Earnings.001 (3.44)Log Total Book Value.001 (5.43)Log Total Revenue.001 (1.97)
Table 9
Initial Return Regressions
2,577 observations are used in the analysis. The dependent variable is the log of the ratio of stock price at the end of first day of trading divided by the offering price. Offer value residuals are the regression residuals (offer value minus predicted offer value) from the last model listed in Table 6 including the log of total filing value. The dummy for negative offer value residuals equals 1 if the offer value residuals are negative. The slope for negative offer price residuals equals 0 for positive residuals and equals the actual residual amount for negative residuals. The risk variable uses the coefficients from the regression reported in Table 8 to estimate predicted standard deviation of aftermarket returns for each sample firm. The other variables are as defined in Tables 2 or 7. Coefficient estimates are reported along with tvalues in parentheses. An adjusted R2 is reported for each regression.
Dependent VariableFirst Day ReturnFirst Day ReturnFirst Day ReturnFirst Day ReturnAdjusted R218.41%24.00%25.56%28.30%Intercept.25 (5.97).24 (5.89).23 (5.67).80 (7.19)Offer Value Residuals.37 (21.89).59 (16.06).56 (15.40).50 (13.87)Dummy Negative Offer Value Residuals.05 (6.22).05 (6.36).05 (6.86)Slope Negative Offer Value Residuals .58 (12.09).57 (12.10).50 (10.54)Log Total Proceeds.01 (3.84).01 (4.02).01 (3.09).03 (6.96)PreOffer Market Return.93 (10.38).93 (10.73).90 (10.48).86 (10.26)Log Total Earnings.0005 (.20).01 (2.83)Log Total Book Value.006 (2.72).004 (1.70)Log Total Revenue.01 (5.13).005 (1.78)Risk (Predicted Standard Deviation of After Market Returns)7.90 (9.96)
For example, see Beatty, Riffe and Thompson (1999), Ohlson (1995), Feltham and Ohlson (1995), Frankel and Lee (1998), Dechow, Hutton, and Sloan (1999), and Francis and Schipper (1999).
Throughout the paper, we use the term R2 to refer to adjusted R2.
In rare instances, IPO firms offer securities without an underwriter.
For our sample, the mean (median) number of days between the filing and the offering is 69 (53) days.
For our sample, the mean amount left on the table is $7MM.
To be consistent with Kim and Ritter (1999), we also estimated all of our models for a sample that excludes IPOs with an offer price less than $5 or total proceeds of less than $5 MM. This reduced our sample size to 2,423. The empirical results were very similar to those reported.
Notice that total offer value is the offer price*number of shares outstanding before the offering. It does NOT equal the gross proceeds from the offering, which is defined as offer price*number of shares issued in the offering.
For the variables presented in Table 2, the noteworthy correlations among variables are as follows. There is positive correlation greater than .70 between the pairwise groupings of log total earnings value, log total book value and total revenue. The correlation between percent retained and log total earnings value is .32.
For example, accounting earnings provides a first order approximation of cash flow if accounting accruals capture the permanent component of cash flow. Timeseries variation in cash flow is a second order effect except for the permanent growth component. This growth component is accounted for through the discount factor. Book value provides a first order approximation of cash flow (up to a scalar multiple) for firms in long run competitive equilibrium, earning a fair return on invested capital (Ohlson 1995). As a result, one could easily expect accounting numbers to provide a reasonable approximation to cash flow. Assume the discount factor is expressed as (1b)/(rg), where b is the retention rate, r is the cost of capital and g is growth. Then timeseries variation in the factor components are second order effects and the issue of central importance is the degree to which comparables are easily identified that have similar average components.
Brown et al. (1999) and Easton (1999) make similar observations about the problems of using number of shares as a deflator in levels regressions.
Revenue is also of interest given that some analysts argue that total revenue is a more important value driver than earnings in hightech industries (Hand 2000).
What should be considered a spurious size effect depends on the question at hand. See Barth and Clinch (1999) for a critique of this concept.
Kim and Ritter (1999) examine book value and revenue as well with similar results.
The average lag between offer date and match date for 3digit (2digit) matches is 229 (216) days. 132 missing observations were set to 0. We found similar results using the residual from only the most recent IPO in the same threedigit or twodigit SIC code within the last two years.
Beatty, Riffe, and Thompson (1999) show that regression coefficients are weighted averages of accounting ratios when the regression model does not include an intercept.
Of course, since we are using log transformations, the untransformed model actually has no intercept. The intercept in our model represents a slope coefficient for the untransformed data.
We provide preliminary evidence on the usefulness of accounting information for IPOs with negative earnings by estimating our model for a sample of 3,277 firms that includes IPOs with both negative and positive earnings. Given Hand (2000), we add one to all of the accounting variables. We include an additional variable that equals (1) the negative log of the absolute value of (total earnings value plus one) if earnings are negative and (2) 0 if earnings are positive. This variable essentially allows the earnings slope coefficient to differ for negative and positive earnings firms. An estimated R2 of 77.95% suggests that accounting still does a good job of pricing IPOs on average even when considering firms with negative earnings. The negative earnings variable has a negative coefficient suggesting that the more negative the earnings, the higher the future growth potential and the higher the value. A negative slope on negative earnings has also been documented by, among others, Hand (2000), Burgstahler and Dichev (1997), and Riffe and Thompson (1998).
We use the geometric mean of the filing price, which equals the square root of the product of low price and high price, rather than the arithmetic mean. The geometric mean is more appropriate when using logged data because the log of the geometric mean is equal to the average of the logs.
Negative coefficients on accounting information implies that the filing price range overweighted the accounting numbers relative to the ultimate offer price. Judging from the small coefficients on the accounting variables in the last regression, however, the difference is very small in magnitude (less than .01).
For the variables used in the risk regression reported in Table 8, all the pairwise combinations for the following variables have positive correlation coefficients of at least .30: log total proceeds, log total earnings, log total book value, log total revenue, and underwriter market share. The hightech dummy and venture capital dummies have a correlation coefficient of .31. Percent retained and log total earnings have a coefficient of .32. All of the other coefficients are much smaller. For the variables used in the return regression reported in Table 9, the correlation coefficients between predicted risk and log total proceeds, log total earnings, log total book value, and log total revenue range from .78 to .81.
See Beatty and Kadiyala (1999) for a discussion of why smaller stocks prior to the The Penny Stock Reform Act of 1990 may have greater risk.
The ts on earnings and book increase to 3.5 and 2.2, respectively, when log of total proceeds, which is highly correlated with accounting information, is excluded from the model.
When we use percent return, (market priceoffer price)/market price, as the dependent variable, our R2 is 19.9%. Subject to the caveat that you cannot directly compare R2s across different samples, our results are slightly better than the 17.8% R2 for a percent return regression reported by Hanley (1993).
PAGE 12
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