شناسایی اهداف تصاحب انگلستان با استفاده از داده های تاریخی حسابداری هزینه منتشر شده توسط برخی از شواهد تجربی در مقایسه با لاجیت همراه با تجزیه و تحلیل تفکیک خطی و نسبت های مالی خام با نسبت های نسبی صنعت

This study examines whether multivariate models using published financial data have predictive accuracy to successfully identify targets, thereby earning excess stock market returns. Although it was found that in the estimation period the important factors affecting the likelihood of a bid were stockholder profitability combined with poor sales growth, these variables were unable to successfully identify targets in the holdout sample. The empirical study also investigated whether the predictions are affected by the choice of statistical estimating technique and data form. It found that they were and that the choice depended upon the statistical assumptions of the models. The results also showed that raw financial ratios and IRRs based on the same underlying data generated significantly different forecasts using the same statistical technique.

The literature on corporate control presumes that, like financial failure, mergers may be forecast using published financial data. That is, factors increasing the probability of (or vulnerability to) takeover include inefficient management (as represented by declining profitability, for example) and a poor growth resources mismatch. This seems eminently reasonable because although there may be many reasons for mergers, targets are not selected arbitrarily but arise from a desire by a bidding company to reap benefits from merger. The problem for the analyst who attempts to forecast them is simply a matter of identifying the best explanatory/predictive variables. However, Palepu (1986) showed that most of the previous studies that had boasted high predictive accuracy (between 60% and 90%) did so largely because of statistical error. If they had been estimated correctly, their conclusions would have been very different. However, subsequent studies suggest that, while Palepu's methodological points are clearly correct, his conclusions may not be the final word on the subject. For instance, Walter (1994), using Palepu's methodological revisions, showed that current cost accounting (cca) information in the U.S. has quite a high predictive accuracy. Unfortunately, because of the losses sustained on a few of the incorrect forecasts, his model only earned modest excess returns overall.1 Despite his criticism of the statistical methodology of previous studies, Palepu did not address the choice of statistical technique. Most used linear discriminant analysis (lda), whereas Palepu (and subsequent studies) preferred logit, probably because it was generally considered to have “theoretical superiority.” But this may not necessarily be the case. As the statistical literature demonstrates (Ladd 1966, Efron 1975, Press and Wilson 1978, Lo 1986 and Sharma 1996, pp. 263–264), the arguments for and against the two competing methods are more finely balanced in which the statistical nature (or form) of the data plays an important part.2 While lda strictly assumes that the explanatory variables are jointly normal with equal covariance matrices, logit is not restricted by these assumptions; the restriction is merely that the explanatory variables are independent.3 The case for lda, therefore, is that logit estimators are between one half and two thirds as efficient as lda estimators (Efron, 1975).4 On the other hand: • (a) When the two lda assumptions do not hold, the discriminant function estimators of the slope coefficients will not be consistent (Halperin et al., 1971). • (b) lda estimation can give misleading results regarding the significance of the coefficients when the normality condition is violated. That is, under non-normality of the explanatory variables, a slope coefficient that is really zero will tend to be estimated as zero by logistic regression in large samples but not necessarily so by lda. Thus, where normality is violated, meaningless variables may be erroneously included in discriminant functions (Press and Wilson, 1978). • (c) The maximum likelihood method of estimation in logistic regression usually gives under non-normal distribution conditions (and possibly even normal conditions as well) slightly better fits to the model, as evaluated from observed and expected numbers of cases per decile (Halperin et al., 1971). • (d) lda estimators may also mask troublesome data. Press and Wilson (1978) show how, for the same data, lda estimators may provide a perfect fit, while a logistic regression shows the slope and intercept coefficients as non-existent and no relationship between the hypothesised variables. Their concern is that lda “provides no warning signal whatsoever and quite incautiously suggests [in their numerical illustration] a slope coefficient estimate of b = 4.” In a financial context, non-normality is an important consideration as it is their nature to be skewed. Barnes (1982) has shown that if two variables (X, Y) are normally distributed and possess a simple linear relationship with a non-zero intercept (a), the distribution of X/Y will be skewed. If a > 0, it will be negatively skewed, and if a < 0 it will be positively skewed. This prediction has been supported by various empirical studies, for instance Deakin (1976) in the US, Ezzamel et al. (1987) in the U.K., and Buijink and Jergers (1986) in Belgium. Another methodological issue is the dissimilarity of economic relationships across industries. This generates different parameters in industry financial data across industries and the cross-sectional instability of the predictive model because (1) the statistical parameters of cross-sectional distributions of ratios are obviously different across different industries,5 and (2) the prior probability of takeover is not constant across both time and industrial sectors. The motives and reasons for mergers are also diverse, of course, varying across firms, industries, and time. There may also be many different and conflicting motives and reasons present in mergers occurring at the same time and involving firms in similar industries (Jensen & Ruback, 1983). Instability of cross-sectional ratios may be allowed for in various ways. Palepu (1986) used dummy variables. Here a separate model for each industrial sector and industry-relative ratios (IRRs) as suggested by Platt and Platt (1990) are used. A firm's IRR is the ratio between its financial ratio (the numerator) and the relevant industry average (the denominator). It measures the firm's position within the distribution of all firms in that industry relative to its mean.6 The advantage of an IRR is that, because it adjusts for differences between industries, a model based on IRRs may be estimated across all firms. Small sample problems created by having to estimate separate models for each industrial sector are also avoided. Finally, and most conveniently, while cross-sectional IRRs may still not be quite normally (or symmetrically) distributed, they will be much less skewed relative to regular (“raw”) financial ratios. On the other hand, a model based on IRRs will have similarities forced into it because the denominator in that ratio will be the same for all firms in the sector classification. Consequently, error rates will be higher, especially for industries possessing unusual data. One of the purposes of the present study is to examine the relative importance of these pros and cons by comparing the performance of a general model based on IRRs with an industry-specific model. The above discussion suggests that as the objective of estimating the models is to maximize predictions, their relative predictive accuracy (p) should be used to assess their efficacy. Hypotheses may be developed concerning each of these according to points (a–d) in the introductory section and a further point: (e) all other considerations being equal, we would prefer a larger sample population size to a smaller one. The hypotheses, together with the reasons (a–e), are: where p indicates the prediction and the numerical subscripts refer to the 2 × 2 matrix in which rows 1 and 2 relate to the statistical methods logit and lda, respectively, and columns 1 and 2 relate to data form IRR (general model) and raw ratios (specific models), respectively. Additionally, point (d) suggests alternatives to and above. These are Because the logit and lda coefficient estimators are likely to be different, their comparative accuracy is also likely to be different. For instance, in a comparison of the two techniques using credit applicants' variables, Wiggington (1980) found that logit significantly out-performed lda in terms of relative predictive accuracy. Similarly, when looking at predictive ability in a sample of credit unions, Collins and Green (1982) found that, although the two techniques had similar overall accuracy, logit was considerably better at identifying failed firms. On the other hand, in a comparison of the two techniques for corporate bankruptcy prediction, Ohlson (1980) came to the conclusion that they were similar. Also, in a study of whether cash flow data could improve the accuracy of bankruptcy forecasting models, Casey and Bartczak (1985) found that they behaved and predicted similarly. On the other hand, in another bankruptcy study Hamer (1983) found a slight statistical difference in the overall classification accuracy between the two methods, preferring logit because it performed “no worse” than lda.7 In a useful survey of the empirical studies that compare the two methods, including those which have been performed outside finance, Jones (1987) tentatively concluded that logit models tend to be slightly more accurate, and certainly no less accurate, than lda models. Unfortunately, the picture inside finance is unclear because the comparative studies have usually been of classifying accuracy and not of predictive ability. It is the purpose of the empirical study to investigate whether the choice of estimating technique (here between lda and logit). Additionally, whether the choice of data form (IRRs for a general industry-wide model or firm-specific ratios) significantly affects whether takeover targets can be predicted in the U.K. The remainder of the paper is arranged as follows. First, the remaining methodological issues raised by Palepu are addressed. The empirical study is then described and the results discussed.

This study has attempted to investigate whether multivariate models using published financial data have predictive ability to out-perform the market. It also examined whether the selection of statistical technique (logit or lda) significantly affected the outcome. It was shown that this choice depends on how well the assumptions of the estimation model fit the statistical nature of the underlying data. As the assumptions of lda and logit are different, they will perform differently with the same raw data. Here, two versions of the same data were examined: a general model based on IRRs and a set of industry-specific models estimated from raw financial ratios. The empirical study showed that the distributions of the general and specific model forecasts were roughly similar. Although they generally out-performed chance (especially when predicting non-targets), neither technique had any significant success in predicting targets. They were, therefore, unable to earn excess returns. However, the differences between the distributions of forecasts using the general model and the specific model were much greater. This suggests that the choice of data form (IRRs or raw accounting ratios) may be more important than the choice of statistical technique. The latter result is important because it supports the main hypotheses developed in this article concerning the way the models should perform according to their statistical assumptions and the way in which these are violated. That is, hypotheses 2–5 (points b and c) are supported together with the alternatives to hypotheses 1 and 6 (point d). These are that logit should be preferred to lda if the data are not multivariate normal. If they are multivariate normal, lda may be preferred on purely theoretical grounds, but this may produce misleading and uninterpretable results, whereas logit would not be ambiguous. Finally, if the data do conform to the statistical assumptions, the choice of data form should simply be based on the size of the sample population. This finding has an important bearing on the results relating to the factors affecting the likelihood of (or vulnerability to) merger. Logit and lda identified contradictory variables. Because it has now been shown how logit is preferred and lda is unreliable, we may accept the findings of the former: for the estimation period at least, it was a target's profitability relative to sales and to shareholders' equity, together with a poor growth rate (as opposed to say financial factors such as leverage), that raised the likelihood of a bid. The overall conclusions are, therefore, as follows. First, excess returns may not be made in the U.K. using published historical cost accounting data regardless of the choice of estimating technique. Second, the decision to use logit or lda should be based on the statistical nature of the data to be used. If not, as was demonstrated, misinformation may result. The empirical study clearly demonstrated this in two respects. That raw financial ratios and IRRs based on the same underlying data generated significantly different forecasts using the same statistical technique. Finally, it is profitability combined with poor growth that increases a firm's likelihood of a bid.Eisenbeis 1977, McFadden 1974 and McFadden 1976