An empirical test of an IPO performance prediction model: are there "blue chips" among IPOs?

Miller, John ; Stretcher, Robert

ABSTRACT

An earlier study of 563 firms which issued IPOs during 1997 identified and estimated a three-stage algorithm in which basic accounting variables and indices available at the time of the IPO were found to predict mean annual wealth appreciation from buy-and-hold stock ownership for the ensuing three years. Firm size predicted membership in the middle sixth and seventh deciles; sales, receivables turnover, and retained earnings per assets predicted the top quintile; current debt and selling costs predicted the lowest quintile. Since February 2001 market trends have been generally negative. The current paper confirms the earlier model despite negative currents.

PURPOSE OF THIS STUDY

An earlier investigation (Miller, 2003) uncovered a non-linear and, indeed, non-metric anomaly in the joint distributions of the wealth appreciation of companies with new initial public offerings and certain accounting data made public at or around the date of the offering. The earlier study was purely exploratory and consisted of specifying the model and estimating the parameters of a three-stage prediction scheme. The model was able to predict approximately three-fourths of the firms correctly into three segments of wealth appreciation. The three segments were the "MID" comprised of the sixth and seventh deciles, "TOP" or the top quintile, and "LOW" or the bottom quintile. It is the objective of this study to evaluate the performance of the model in the face of the generally poor market conditions of the two years immediately posterior to model construction (March, 2001 to July 2003).

INTRODUCTION

It is not rare to find examples of data mining in the literature relating financial data to stock market and general business performance. Even the most influential of the early papers on company failure prediction (e.g., Beaver, 1967, Altman, 1968, and Edminster, 1972) might be accused of tooenthusiastic opportunism by their use of repeated analyses (one suspects) until a statistically significant formulation appeared. And, to make matters worse, sample sizes were very small and drawn as convenience samples rather than probability samples. As is apparent from these cautionary examples, data mining is not always a complementary term. It is also called "data dredging" or the over-working of data, and is a natural result of the statistician's desire to do a thorough job. It may be said that the goal of any statistical analysis is to uncover statistical significances. See Fisher (1986) for a broader discussion of the tensions between the statistician and his client. There is also a careful discussion of the problem in the paper and subsequent comments in Chatfield (1995). Chatfield underscores the potentials for disaster whenever a model is uncovered and fit to a set of data, and then tested on the same set. This is especially true in the cases of step-wise regression and time series analysis. While this is not a novel idea, he goes further to argue that split sample designs are also suspect and that models should preferably be tested on data gathered at another time. Only then can his "model selection biases" be removed. More generally, it can be argued that there are two stages in any kind of scientific enterprise. Tukey (1977) has developed a broad range of powerful "exploratory data" tools to assist the researcher in uncovering explanatory models. But he would agree that there is still a need for "confirmatory" analysis (Tukey, 1980). Good scientific procedure calls for such confirmation not to come from the model source, but from independent investigators operating in other sites on related, but not identical, datasets. The approach of this paper is strictly "exploratory" and the confirmatory phase will be left as a follow-up exercise.

As part of a fundamental reflection on the theoretical underpinnings of the statistical analysis, Hand (1996) has expanded on the opening provided by Velleman and Wilkinson (1993), who were criticizing the psychophysicist Stevens' (1951) data measurement scale hierarchy (nominal, ordinal, interval and ratio) that has become almost routinely accepted in much of scientific work, especially the social sciences and business research. Hand argued that the traditional approach to science used a "representational measurement theory" in which the data are integral parts of mathematical models of empirical theories and are direct attempts to "formulate properties that are observed to be true about certain qualitative attributes" (foreword to the monumental Foundations of Measurement trilogy, Krantz et al., 1971, Suppes et al,. 1989, Luce et al., 1990 quoted in Hand, 1996) This is the dominant assumption used by most scientists in their work and is at least a century old. Later, as physicists became troubled by such difficulties as those caused by the dual nature of light, physicists began to relax the relationship between their data and the real world. The development of "operational measurement theory" is traced by Hand to Bridgman (1927) and is a shift in the focus of the measurement theory from the empirical to the mathematical construct being used to model that reality. In this case, the emphasis is on how that model determines the properties of the data measurement scale. It is exemplified in the elaborate models of latent variables and structural equations used in the social sciences. There the models are less a picture of some external reality and more of a prediction scheme. Now the role of the statistician is merely to insure that the assumptions about the data structure do not violate that model, not some underlying reality. The responsibility for connection between the model and external reality is entirely that of the social scientist, not the data analyst.

There was probably a time when accounting data was (reasonably) thought to be representational. The representational approach is still exemplified in the work of the Banque de France (Bardos, 2000) in which classical Fisher linear discriminant analysis is used to forecast company disasters. But, it is becoming more and more apparent that such reliance upon the external reality of bookkeeping data is not warranted. This relaxed approach is that of Zopoundis (1999), for example. For the purposes of this analysis we will not assume that the SEC-reported numbers are fundamentally precise reflection of a company's situation, but we will assume that the data can be relied on for direction and relative size. That is, for most of the subsequent analysis we assume qualitative rather than quantitative scaling.

The model used to begin this analysis was that of correspondence analysis. It is one of many statistical procedures which have as their raison d'etre the analytic development of a quantitative re-scaling from data which are assumed only to be nominal or ordinal to begin with. One popular model is that of the "tolerance" distribution of Cox and Oakes (1984) and McCullagh (1980). Correspondence analysis has a long history rooted in the work of Fisher (1940) in the middle of the last century; however, it is certainly not the only possible analytic procedure. There are many possible models that are used to rescore the rows and/or columns of a contingency table. These models can have either no conditions on the scores for the rows and/or columns (unrestricted models), or it is possible to require that either the rows or the columns or both must be ordinal in nature (restricted models). On the one hand, Goodman (1981, 1986) has developed his R, C and RC models. The latter is shown (Ritov and Gilula, 1991) to be equivalent to:

[P.sub.ij] = [[alpha].sub.i][[beta].sub.j] exp ([gamma][[mu].sub.i][v.sub.j]) (1)

where Gamma is the coefficient of intrinsic association; the sets of parameters Alpha and Beta are the scores to be "optimized" by maximizing; Mu and Nu are nuisance parameters. The rescorings are centered to zero and scaled to one so that, according to Goodman, they can be compared to the results of correspondence analysis, in which the same standardizing takes place. Gilula, Kreiger, and Ritov (1988) show that this is a model in which entropy in an information theory sense is being maximized

Procedures for estimation of the parameters in the RC model have been developed by Goodman in the unrestricted case. The R and C association models in the restricted case were solved by Agresti, Chuang and Kezouh (1987) and the RC model by Ritov and Gilula (1993).

The correspondence model used in this paper can be expressed as:

[P.sub.ij] = [P.sub.i.][P..sub.J]] (1 + [lambda][[epsilon].sub.i][[delta].sub.j]) (2)

where Lambda is the "coefficient of stochastic extremity" (Gilula, Kreiger, and Ritov, 1988), the sets of parameters Epsilon and Delta and are the scores to be "optimized" by maximizing, and the P's are marginal proportions. "Stochastic extremity" is reference to the cumulative distributions of the rows (columns) which are maximally distanced by this procedure. The coefficient Lambda is a monotonic correlation in the sense of Kimeldorf and Sampson (1978), which they define as the supremum of correlation coefficient over all possible monotonic functions of the two variables. Perhaps the most interesting aspect of monotonic correlation is in its relation to statistical independence. Unlike the case for an ordinary Pearson correlation coefficient, when a monotonic correlation is zero, then the variables are independent. The optimization solution in the unrestricted case of this can be traced at least as far back as Fisher (1940) and even Hotelling (1933, 1936), and can be easily derived through the singular value decomposition of a certain matrix (Hirshfield, later changed to Hartley, 1935). The latter parameter, Lambda, also has the felicitous meaning of a canonical correlation. A further appealing property of the correspondence model (and the RC model, too, for that matter) is that the data are "stochastically ordered" in the sense that if the scores are ordered, then the conditional cumulative probabilities over those scores are similarly ordered (Ritov and Gilula, 1993).

The differences between these two approaches, correspondence analysis and Goodman's RC model, to constructing the restricted ordinal scales will in general result in similar scale values and similarly interpreted measures of association--so long as the association between the pair of variables is "weak." (This is an observation by Goodman, 1981, for unrestricted models extended to restricted models by Ritov and Gilula, 1993.) This is the situation in most social sciences and business applications, and is certainly true for the properties under investigation here. In fact, under the commonly-held "market efficiency" presumption there should be no correlation at all.

For this analysis, the particular algorithm is not that from Ritov and Gilula (1993) in which they reparameterize the scales via a latent variable approach and then use the EM algorithm to optimize the scores. This analysis follows the venerable Benezecri (1973) to Gifi (1990) track which utilizes an "alternating least squares" optimization due to Young, de Leeuw and Takane in the 1970s (see de Leeuw, 1993). The specific implementation of this is found in the routine "Optimal Scoring" developed for the Statistical Package for the Social Sciences (SPSS) by Meulman (1992, but also the technical annotation for the SPSS routine).

However, we actually began this analysis not at the ordinal level, but without any assumptions beyond categorization. Each of the firms' predictor variables was reduced to deciles and submitted to a correspondence analysis. (SPSS "Optimal Scoring") The use of deciles is common in finance literature (e.g., Lakonishok, Shleifer and Vishny, 1994) and it is the basic beginning data structure of this paper's analysis. Later, investigation was made into other "n-tiles" (from quintiles up to "20-tiles") only to find no real difference between the correspondence analysis results. To get a picture of the scale, and unusual nature of this financial data, here are the means of the deciles for the variable measuring the average over several years of the 12-month wealth appreciation (MEANRT). This will be the primary response variable for the subsequent analysis, and a major goal will be to rescale this to a manageable metric. While a nearly linear pattern can be seen over the middle seven deciles, the first and last two deciles break that pattern. The highest decile had an average return four times that of the ninth decile. Note also that half of the deciles had average performances which returned either no gain or, more likely, a loss to those who held the stocks for a year.

This variable is defined by Compustat as: "The Total Return concepts are annualized rates of return reflecting price appreciation plus reinvestment of monthly dividends and the compounding effect of dividends paid on reinvested dividends "(Research Insight, 2001).

The first set of regressions were bivariate analyses of the deciles for each of the 25 financial scales and ratios versus the mean annual wealth aggregate for the period January 1998 (for those companies that went public very early in 1997) to February, 2001. Each of the 25 predictor variables was selected because it had been considered in earlier research and was available at or near the time of issuance of the IPO. (The results of the nominal-scaled analysis showed that the predictor variables could be reasonably approximated as ordinal without much loss of correlation, so the 25 optimal scaling analyses were re-run forcing an ordinal restriction on the predictors but not on the response). The table below and the subsequent graph show an example of the results of those nominal-ordinal analyses. In general, the relationships between the predictors and response were not strong, but for many they were not insignificant.

[FIGURE 1 OMITTED]

One is struck immediately by the respectable performance of such variables as TOTASS (total assets, r = .355), TOTLIAB (total liabilities, r = .344), EBITDA (earnings before taxes, r = .343), OPER.AT (operating income to assets ratio, r = -.328), NETPROFM (net profits, r = -.319), RETE.AT (retained earnings to assets ratio, r = -.310), and SALES (net sales, r = -.306). These correlations are, of course, only potentials. They are the maxima found by a process designed to adjust the response and predictor measures (row and column scores) monotonically until such maxima are achieved. (Recall that ordinary Pearson correlation coefficients are also maxima derived from a process of optimization over all possible linear relations.) But, these are high enough to be encouraging. Note also the valid sample sizes. No attempt was made to eliminate any special classes of businesses (REITs, financial institutions, etc.); if they reported data, they were included. And, for many of these variables, 90% or more of the 563 total firms did report the predictor variable. (See Table 1 below.)

Below are the graphs relating the original "raw" ordinal integer scores to the rescoring values ("quantifications") for an example variable which gave rise to the correlations above. There is a persistent non-linear pattern in the MEANRT (average wealth appreciation) response scorings. It strongly suggests that one end of the predictor variable scale (the right end is indicated by the sign on the correlation coefficient in the table above) is related to middling performance at or above the median ("above average firms") and that the variable is less able to discriminate between those at the extremes. The top decile and the bottom three response deciles receive nearly identical scores.

[FIGURE 2 OMITTED]

This example is only one of the very clear pictures resulting from the pairings of wealth appreciation ("MEANRT") with each of the 25 predictors. The rescoring for total assets (TOTASS chart on right) puts the bottom 70% of the firms' assets at virtually the same score, then distinguishes between the top three deciles. The response curve (MEANRT-chart on left) has the interior sixth and seventh deciles well above the others. It would appear that the larger three-tenths of companies (in terms of assets size) tend to be in the sixth and seventh decile (in terms of wealth appreciation). This pair of deciles will be called the "MID" group.

Almost half (44%) of the middle wealth group were among the largest companies (when they went public), while only about 13% of the remaining companies were in that largest size group. It is apparent that the rescoring found by the procedure and charted above, which has the effect of equating the lowest seven deciles, leads to a linear pattern relating the two variables:

Stage 1

Having discovered the (relative) isolation of the MID Group, recourse was made to a logistic regression to develop a prediction scheme for this middle group. As compared to discriminant function analysis, Press and Wilson (1978) showed that logistic regression is to be preferred, primarily because the latter is better equipped to handle non-normal predictors. All of the variables identified above as having high potential correlations were tried out. The best prediction equation (after a variation of the all possible subsets regression paradigm) turned out to be:

[FIGURE 3 OMITTED]

The detail on the model includes the fact that the model involved all but 38 of the firms (some variables were eliminated because too few firms gave that data (e.g., 345 firms listed no intangible assets); mean annual wealth appreciation was not available for seven firms; 31 had no assets or net profits reported around the time of their IPO.

From this table (Table 2 above) we conclude that above average performance (MID Group membership) is associated with larger total assets and larger net profit margins--and that each (standard deviation) step up the (rescored) asset ladder results in an increase in the odds of being in the above average category (the "Exp(B) column) of 85%, while a corresponding step on the net profit scale results in an increase of the odds of 42%. (Note that the direction of the association must be checked against the Optimal Scoring runs above.) The classification table for this regression shows that when the cut-off is adjusted so that the prediction equation puts 101 firms into the MID Group, it does so accurately in 45 (44%) of the cases. This adjustment of the posterior odds corresponds to placing the costs of misclassification other than at one-to-one. Instead, the cost of misclassifying the smaller quintile--a false negative--were put closer to four-to-one. This assignment of costs is in the spirit of recent papers advocating re-evaluation of previous simplistic cost structures (Provost, Fawcett, and Kohavi, 1998, Adams and Hand, 1999, Drummond and Holte, 2007). Overall, 413 or 79% of the 525 firms for which all of the data were available were correctly classified at this initial stage.

Stage 2

At the second stage, the 101 firms identified by the initial logistic regression were excused from the analysis, and a new search for predictors began. The result of this search for predictors of the TOP group of IPO performers was three variables. Sales, receivable turnover (RECTURN), and the ratio of retained earnings to assets (RETE.AT) all entered the model, all did so with negative coefficients, indicating inverse relationships to the response, wealth appreciation. The details of the table below show the significance of each of the three predictors, and their impact on the probability of inclusion in the TOP quintile of mean annual wealth appreciation firms.

The prediction equation attempts to predict 85 into the TOP group, and it is accurate in 37 (or 44%) of those predictions.

A total of 295, or 74% of the 396 firms available at this stage of the analysis, were accurately predicted at this stage.

Stage 3

The balance of the data, omitting the 101 predicted in Stage I and the 85 predicted in Stage II, were again subjected to logistic regressions with the aim of predicting membership in the lowest quintile. This LOW Group prediction equation involved two variables, current debt (DEBTCURR) and marketing expenses (SELLCOST). Perhaps intuitively, current debt is a positive indicator for the LOW group, while marketing effort is a negative indicator.

The details indicate that 270 firms remained with scores available for the analysis. Every step up of one standard deviation in DEBTCUR doubles the odds of being in the LOW Group while each similar step along the SELLCOST dimension reduces the odds by 37%.

The classification table shows below shows that 43 cases were predicted into the LOW Group, with 17 done so accurately, or 40% correct prediction among them. Overall, 198, or 73% of the 270 used in this analysis were correctly predicted.

DISCUSSION AND SUMMARY

A summary of this multi-stage prediction scheme would include its ability to predict performance at three places along the continuum of mean annual wealth appreciation. At the outset, all the variables are segmented into deciles to preserve the ordinality, but destroy the exact metric of the variables. This is done for two reasons: 1) the distribution of firms along these original variables is distinctly non-normal with astronomical skewness and kurtosis numbers; and 2) it is believed that the accounting practices vary between firms and that their reported numbers bear only a tenuous relationship to the underlying reality they purport to represent. The deciles are then submitted to a re-scoring routine developed by Benezecri, Gifi, and others. This rescoring attempts to maximize a measure of monotone correlation (Kimeldorf & Sampson, 1978). It is these "quantifications," or rescorings, that are used in the balance of the analysis. The model uses different variables at each of three stages. It starts by trying to predict membership in the middle of the distribution (the sixth and seventh deciles). It is entirely possible that this non-linear relationship that is being taken advantage of is the famous "horseshoe" discussed throughout Gifi (1990). It was originally believed that if an accurate prediction could be made off the middle of the distribution, then the middle could be deleted and it would be relatively easier to predict the extremes. While this ease did not eventuate, it was possible to make respectable predictions at each stage.

The summary table for the prediction is as follows. There were at the onset, three sets of firms which were of interest: MID, TOP and LOW. The three accounted for 60% of the firms. The procedure proposed herein actually predicted 253, or 45% of the original 563 firms and was accurate in 99, or 39% of those predictions. However, when the absence of key accounting data is taken into account, the procedure actually was accurate in about three-fourths of its predictions.

CONFIRMATION

The original model was built on data from all IPOs issued during the calendar year 1997. Since the criterion variable of most interest was that of "annual wealth appreciation" (following Gompers and Lerner, 1999 and many others), the earliest data came from January 1998, when only 31 firms were able to show the requisite 13 months of data in order to be able to calculate the annual rate of change. By one year later all 563 firms were showing wealth appreciations. By the end of the model period, January 1998 up to February 2001, virtually all of the 1990s "bubble" had evaporated, and the "interim" period from March 2001 up to July 2003 saw a relatively subdued market with most of the 1997 class of IPO stocks taking money from their investors. (Table below.) As the table demonstrates, only the top quintile was performing at annual rates above zero (returning one dollar in market value plus accumulated and reinvested dividends for one dollar invested at the beginning of the 12 month period). Over 40% had essentially disappeared from the markets, either through failure, merger, purchase, or any of the other exit routes from the markets. This exodus posed a difficult challenge for the model to perform well.

[FIGURE 7 OMITTED]

The present confirmation study involved inspection of data from Standard & Poor's Research Insight, and included all but 24 of the original IPOs, which showed stock price and other company information up through July, 2003. It might be expected that the missing companies would be from the lower performing groups. In fact, though, seven were from the TOP group, three from the MID group, and nine were from the LOW group.

The additional data provided nearly 1.5 years (17 months, the so-called "interim" period) more data than the earlier analysis, which had a cut-off date of February, 2001.

A more serious concern was that many of the companies were missing one or more months of wealth appreciation data. In fact, 164 or 30.4% were missing at least 20 of the months (the maximum missing was 29 months). Again, however, there was no indication that the absence of data was related to the performance of the company's stock. The percentages of those missing 20 data points or more was 28%, 35%, and 26% in the TOP, MID and LOW groups, respectively (these groups are those established in terms of their mean performance over the original three years). And, the same missing class represented 25%, 31%, and 27% of those firms predicted to be in the TOP, MID and LOW groups, respectively.

The missing data, then, was not seen as a differentially distorting factor. All missing data (from 1999 on) were replaced by the value "-100," representing the depressing fact that for most of these firms their investors would have lost all of their investment had they held onto their stock for the full 12 months. Discriminating between the various shades of disappearances will be the subject of a future analysis. For the purposes of this confirmation analysis, however, any distortions due to this oversimplification will simply be absorbed into the error estimation for the model.

The Model Tested. Two tests formed the basis of the confirmation of the model: 1) study of the mean shifts of the predicted groups since they were formed in mid-2001; and 2) study of the composition churn in the predicted groups since mid-2001.

Questions to be answered are 1) are the predicted groups performing at their (relative) predicted levels over the full five-year period? 2) does the model still predict full five-year performance better than chance?

As might be expected from the overall patterns, the predicted groups performed much differently in the "interim" period than they had during the original three years. In the original period the TOP group demonstrated a mean annual growth of about 50%, while the MID group (actually the sixth and seventh percentiles) was nearly even and the LOW group depreciated at about a third per year. All three groups declined during the interim period, and they did not all decline at the same rate (p-value = .03 for a simple ANOVA including only the data from the three groups). The TOP group actually declined the most, losing more than 50 percentage points from its mean Wealth Appreciation level during the original period. The MID group dropped the least, but still performed at a level about 30 percentage points below its pre-2001 level. The LOW group lost performance at a rate mid-way between TOP and MID.

However, despite the distortions caused by the differential interim performances, the fiveyear means retained their original relative standings. The TOP group lost all investor advantage they had had in the earlier period to return essentially what was invested, while the MID group slid to a mean loss level of about a sixth of what was invested 12 months earlier. The LOW group maintained both its relative position at the bottom, and its absolute level of draining about one-third of its investors' money each year. The statistical test of these five-year performances was very significant (p-value under .0001).

Finally, note that the range between the means of the TOP and LOW predictions groups dropped from about 85 percentage points to about 41.5 percentage points. This is a very striking reduction and is no doubt at least partially due to some sort of "regression to the mean" effect. However, the entire market for IPOs went through a compression relative to the earlier period. For example if one looks at the "interdecile range" (difference between the tenth and ninetieth percentiles), its value for the original period was about 148 percentage points. The value for the interim period was about 135 points while the overall five-year interdecile range was only 118 percentage points (not shown).

Further, a comparison of the performance groups' composition based on all five years of wealth appreciation shows the same pattern as the means above. While the original model correctly predicted 43.2% of the training set (99 out of 229 predicted into one of the groups) into the three quintiles, the quintiles based on the full five years' data were correctly predicted 29.6% of the time (64 of the 216 firms in the TOP, MID and LOW quintiles were accurately predicted).

Under the random model, in which only 20% of the quintile predictions should be accurate, a chi square goodness-of-fit test of the original model had a test statistic value of 88.6 with a p-value starting with 20 zeros, indicating a very high significance. The test of the updated model had a chi square of 12.5 with a p-value of 0.0004.

DISCUSSION

The purpose of this empirical analysis was to evaluate a model created in mid-2001 which has as its objective the prediction of annual wealth appreciation performances over a three-year period (January 1998 to February 2001) of 563 IPOS issued in 1997. Since creation of the model, the markets have suffered through a prolonged period of poor returns to its investors. In fact, the data do suggest that forecasting during the pre-2001 period may have been more likely to be successful than the "interim" period since. The great bulge in the performance of the TOP group (top quintile) had disappeared in early 2001. However, the strength of the stocks during 1998-2001 was enough that the five-year (actually January 1998 to July 2003) means still reflected that earlier performance. Perhaps it is a further mark of the potency of the model that it was able to weather these extremes.

Like all models there are more questions than answers. While this empirical test may have contributed to the question about whether any modeling might be effective, we still are concerned about generalizing it. There are structural issues about using the techniques in other times and for other types of equities. There are substantive questions about the cause and effect-the process by which the variables utilized in the prediction scheme materialize and lead to the results in the markets.

Future research is very much needed in several areas. To start with, it would be of great interest to see if the non-metric, "deconstructive" methods used to develop this model will be similarly successful using the full five-years' data. And, if successful, is the five-year model similar to the earlier one? Does the new model "find" the same groups? Does it employ the same, or related, variables? (These variables are, to put it mildly, inter-correlated. Each of the 26 predictors considered relates to one of only a handful of underlying factors. While an untangling of the variable intercorrelations might shed light on which of the variables is most or least effective, the overall model strength should not be affected.

Use of alternative classification algorithms to the logistic regression techniques is also worth considering. Some recent research has found the new boosting procedures useful in predicting corporate failures (Cortes et al., 2007). On the other hand, it should be noted that the inherent strengths of older techniques like logistic regression have been shown both in a study of successful companies very similar to this one (Johnson and Soenen, 2003), and in more basic research coming out of the statistical and machine learning communities (Holte, 1993, Lim et al., 2000).

More work needs to be done on the "missing" firms. Not all of the missing firms suffered catastrophic declines. Perhaps more artful estimates of the transformed entities derived from the original 563 IPOs will provide more insight into the model's accuracy.

Not only the missing group, now accounting for nearly half of the 1997 IPOs, are of interest. It would be instructive to follow-up on the TOP group. How many of those in the TOP group are still up there? How does the turmoil in TOP membership relate to the prediction model? What characterizes the TOP firms which maintained versus those that slid?

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John Miller, Sam Houston State University

Robert Stretcher, Sam Houston State University

Table 1: Optimal Scoring Correlations

Predictor Valid Data Correlation [R.sup.2]

EBITDA 515 -0.343 0.118
SALES 532 -0.306 0.094
COSTSALE 532 -0.254 0.064
SELLCOST 442 0.290 0.082
INTEXP 504 -0.299 0.090
CURASTOT 469 0.238 0.045
INTANG 556 -0.179 0.032
TOTASS 540 0.355 0.125
DEBTCURR 507 -0.225 0.051
TOTCLIAB 476 0.241 0.058
TOTLTDBT 540 0.276 0.076
TOTLIAB 540 0.344 0.118
DEBTEBIT 515 -0.262 0.068
LIABNETW 540 -0.201 0.041
EBITASS 515 -0.279 0.078
CURRENTR 468 0.208 0.043
QUICKRAT 474 0.206 0.043
RECTURN 489 -0.209 0.044
TOTASST 507 -0.176 0.031
CASHTURN 505 -0.269 0.073
NETPROFM 525 -0.319 0.101
WCAP.AT 467 0.186 0.034
RETE.AT 534 -0.310 0.096
OPER.AT 439 -0.328 0.108
SALES.AT 509 -0.181 0.033

Source: Compustat estimates of mean wealth appreciation for 563 IPOs
in 1997. Input data were decile memberships and were not forced to
be ordinal.

Table 2: Prediction of the MID Group

Variable Coefficient Standard Error Significance Exp(B)

TOTASS 0.6157 0.1058 0.0000 1.8510
NETPROFM 0.3506 0.1434 0.0145 1.4199
Constant -1.6119 0.1277 0.0000 0.1995

Source: Compustat; logistic regression

Table 3: Stage I--Classification Table

Predicted Actual Others Mid Group Total

Others 368 56 424
MID Group 56 45 101
Total 424 101 525

Table 4: Stage II--Prediction of the TOP Group

Variable Coefficient Standard Error Significance Exp(B)

SALES -0.4169 0.1714 0.0150 0.6591
RECTURN -0.3527 0.1544 0.0224 0.7028
RETE.AT -0.5055 0.1313 0.0001 0.6032
Constant -1.4973 0.1463 0.0000 0.2237

Source: Compustat, logistic regression

Table 5: Stage II--Classification Table

 Actual Others TOP Group Total
Predicted Others 258 53 311
 MID Group 48 37 85
Total 306 90 396

Table 6: Stage III--Prediction of the LOW Group

Variable Coefficient Standard Error Significance Exp(B)

DEBTCUR 0.676 0.2389 0.0047 1.9660
SELLCOST -0.461 0.1705 0.0069 0.6307
Constant -1.158 0.1573 0.0000 0.3141

Source: Compustat; logistic regression

Table 7: Stage III--Classification Table

 Actual Others LOW Group Total

Predicted Others 181 46 227
 LOW Group 26 17 43
Total 207 63 270

Table 8: Classification Results Summary

 STAGE I STAGE II STAGE III
GROUP PREDICTED MID TOP LOW
Prediction Variables TOTASS SALES DEBTCURR
 NETPROFM RECTURN SELLCOST
 RETE.AT
Odds Effects 1.85 1.42 1.97
 1.42 0.70 0.63
 0.60
Firms Available for Prediction 525 396 270
Firms in Target Group 101 90 63
Predicted Total 101 85 43
Predicted Accurately 45 37 17
Conditional Prediction
 Accuracy Rate 79% 74% 73%

Table 9: Mean Shifts in Wealth Appreciation

 1997 to Feb Interim to 1997 to July Number of
 2001 2003 2003 Firms

Predicted
 Group
TOP 51.20 -51.44 2.73 75
MID -5.26 -31.61 -17.96 98
LOW -33.87 -44.77 -38.82 43
Other -5.35 -31.44 -17.57 324
Total 0.25 -35.31 -16.52 540

ANOVA tests of the means from the three prediction groups alone have
F ratios and p-values of 14.114, 0.00000175; 3.542, 0.0306;
7.814, 0.000531, respectively.

Table 10: Prediction Accuracy--Wealth Appreciation Quintiles

 1997 to Feb 2001 1997 to July 2003
 Correct TotalCorrectTotal

TOP 37 852375
MID 45 1012798
LOW 17 431443
Total 43.2% 100%29.6%100%