Factor analysis is a statistical method for reducing the original set of variables into a smaller set of underlying factors in a manner that retains as much as possible of the original information of the data. In statistical terms this means finding factors that explain as much as possible of the variance in the data. (For a more comprehensive description of the factor analysis methodology in categorizing financial ratios see Yli-Olli & Virtanen 1985. For the statistical theory of factor analysis see Johnson & Wichern 1982: 401-420.)
Transformation analysis is a statistical method that is well-suited for testing the temporal stability of the factor patterns of the financial (and market-based) ratios. Applying this approach to testing stability was introduced in financial ratio caterization by Yli-Olli & Virtanen (1985). (See their report, and Ahmavaara 1963, Mustonen 1966, and S„nkiaho 1986 for more on this subject and the methodology).
The stability of financial ratio patterns has traditionally been tested with the correlation or congruence coefficients between the sub-periods of the data. Both these indices measure the degree of similarity between two factor solutions in terms of the pattern of correlations / congruences among factor loadings across all the variables in the reduced factor space. This can also be achieved via transformation analysis. In addition, by applying transformation analysis we obtain a regression type of a model for the shifting of the variables from one factor to another. This also means that the dissimilar part in the factor solutions can be modeled and measured quantitatively. (For a more detailed description about the difference between correlation / congruence analysis, and transformation analysis, see Yli-Olli & Virtanen 1990: 13-15.)
To establish the stable factors the period was subdivided into two subperiods. These are 1974-78 and 1979-84. Again, averages were calculated for both sub-periods. These averages make up our second and third data sets.
In calculating weighted averages for ratios equal-weighted and value-weighted averages can be used. (See e.g. Foster 1988: Section 6.3.) There are two reasons why we used equal-weighted averages. First, the Finnish Compustat equivalent TILPANA computer data base at the University of Vaasa does not readily contain all the information that would have been needed for calculating consistent value-weighted averages. Second, even if using value-weighted averages might increase the explained variance, this is not material for our principal tasks, that is finding stable factor patterns and testing the hypotheses.
The sensitivity of the factor analysis results was also tested in respect to the rotation technique and the data set. First, the analyses were repeated using promax oblique factor analysis rotation. The results are not sensitive to the method of rotation. Second, the three sets of ratios (accrual, cash flow, and market-based) ratios were factorized alone. The results are not sensitive to the set of variables in the data basis.
Transformation analysis was performed between the factor matrices of the 1974-78 and the 1979-84 period. The transformation matrix is given in Appendix E, and the transformations are visualized in Appendix F. The largest coefficients of coincidence (the stable transformations) are indicated by asterisks in Appendix E.
One stable pattern emerged, however, centrally involving a market-based ratio. This is the size / beta factor, which will be discussed at a later stage.
The lack of the expected risk and return factor is an interesting phenomenon. An analysis of the reasons is, however, beyond the scope of this study. Nevertheless, it is interesting very briefly to speculate about the potential explanations. It must be stressed that this is highly tentative.
It has been observed in several empirical studies that the significance of market models involving risk and return is not high. For example the results on the capital asset pricing model have had quite low correlation coefficients. (See Friend & Blume 1970, Blume & Friend 1973, and Levy & Sarnat 1986: 343-346.) Thus our results may be a reflection of the low explanatory power of the market models.
As can be seen from the analysis results, two stable factors emerge, which can be interpreted as a profitability factor and a operational leverage factor. Both these factors are stable, as is depicted by the transformation matrix in Appendix E and F. The strength of the transformation (i.e. the coefficient of coincidence) between the two sub-periods is almost one (0.905) for the profitability factor, and a high 0.874 for the operational leverage factor.
The interpretation of operational leverage factor is much fuzzier than that of the very clear-cut profitability factor. The ratios loaded on the operational leverage factor could not easily be foreseen.
Looking at the individual ratios, return on equity, return on total assets, and the E/P ratio best characterize the performance factor. As was discussed earlier, the E/P (or P/E) ratio can, a priori, be looked at as a profitability kind of a measure. Our results agree with this interpretation of the P/E ratio. Labor intensiveness, times interest earned, dividend payout ratio, and net working assets to total assets characterize this operational leverage factor.
The empirical results of the earlier studies have not been interpreted in this light, but they are not contradictory. If the variation in the classifications of the earlier studies is looked from this point of view, they are more consistent than what is usually stated.
Looking at the individual ratios, cash net income / interest bearing debt, cash net income / cash from sales, and cash to interest / cash margin Ib best characterize the cash flow factor.
This corroborates similar results from earlier studies. The difference is that we had a wider range of variables, and the confirmation of the cash flow factor thus is more general than in the previous studies.
Our result on the standard financial ratio classification fits the earlier research results. No clearly consistent pattern of financial ratios has emerged from the earlier studies beyond the first two or three factors. It is obvious that the patterns beyond are dependent on the particular data set. This raises an interesting question for further research. That is whether the divergence of the financial ratio factor patterns can be explained, or whether it is random behavior.
In addition to the stable profitability, leverage, and cash flow factors three other stable factors were found. These are the size & beta factor, the dynamic liquidity factor, and the growth rate factor.
Admittedly, we did not hypothesize the emergence of the size & beta factor, but with the benefit of hindsight the appearance of this factor is not surprising. Increasing attention has been drawn in finance research to the existence of persistent anomalies from market efficiency. Among these anomalies feature e.g. the monday-effect anomaly, the january-effect anomaly, the price-to-earnings ratio anomaly and the concomitant "size-beta" anomaly. Basu (1983: 142) observed for a Compustat sample covering 1962 - 1978 that the betas (systematic risk) of the common stock of NYSE firms "declines quite dramatically and in a monotonic way as one moves from portfolios consisting of small firms to those consisting of the larger ones". The emergence of our size & beta factor agrees with this result.
The defensive interval measure has traditionally been considered a measure of short-term liquidity. (See e.g. Sorter & Benston 1960, Davidson & Sorter & Kalle 1964, and Fadel & Parkinson 1978.) As discussed in introducing the ratios at the early stages of this report, the defensive interval measure is a balance sheet / income statement ratio. Liquidity ratios which include an income statement element are often called dynamic ratios. We shall consequently call this factor a dynamic liquidity factor.
As observed, the accounts receivable turnover period also loaded on the dynamic liquidity factor. And, as can be seen in Appendices B through D, the factor loadings of the two ratios have opposite signs. This is a natural result. It is to be expected that when the accounts receivable turnover period gets smaller (improves), the defensive interval measure grows (the liquidity improves). In managerial terms it could be said that an efficient control of accounts receivable improve liquidity.
The two ratios of the dynamic liquidity factor also have a definitional dependence, but as stated earlier, all such links cannot be avoided. Receivables feature in both the ratios. (The current assets appearing in the defensive interval measure are made up by cash + marketable securities + accounts receivables.)
The emergence of a growth factor supports including growth measures in conventional financial statement analyses. According to our factor analysis results, growth measures produce information not necessarily present in the conventional X/Y-type financial ratios.
Growth and the generation of revenues (reflected in the operating margin) have a positive relationship. In other words fast growth and better than average revenue generating ability appear to be connected. This seems a sensible result. On the other hand, growth and profitability (measured e.g. by return on equity) did not go on the same factor in our study. At first sight this is somewhat baffling because of the evidence on a relationship between growth and profitability. (See e.g. Miller & Modigliani 1966, Singh & Whittington 1968: Ch. 7., Eatwell 1971: 411, and Ruuhela & Salmi & Luoma & Laakkonen 1982: 340.) A closer look at the results in Appendix B for the entire period of observation shows, however, that the defensive interval measure, times interest earned, and return on equity do have significant factor loadings on the growth factor.
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