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Main DEA ResultsThe SBM model was optimized for the sample of 292 stocks, and the rankings of every company are shown in Figure 6.1. There are 13 companies in total which have an efficiency score equal to unit value, and 124 which are inefficient with the score equal to zero. The empirical histogram is shown in Figure 6.2. Some of the most efficient companies are shown in Figure 6.3 (i.e., their efficiency scores, equal to unit value), while some of the inefficient ones (with efficiencies greater than zero value) in Figure 6.4. Now, a company can compare itself to others, where it stands in terms of relative (in)efficiency and can make a better focus on those companies which are most interesting to it. The interest could be based on similar production and business focus to see the position of the competitors; or simply by observing the most efficient ones and what the characteristics of those companies are. The focus can be shifted solely on several most important or interesting companies and their financial ratios and other relevant aspects of the business itself. A company does not need to observe the entire sample, i.e., all of the companies within the branch. This is one of the advantages of having such an approach in comparing the performances. Those companies which were shown in Figure 4 as inefficient were examined in more detail in Table 6.2. This table depicts the optimal slack values from optimizing the problem (6.2). The first five columns show output slacks, i.e., how much does each DMU (i.e., firm) needs to increase output values, whereas the last four columns indicate how much does each firm needs to decrease its input values. This is helpful in depicting the sources of inefficiencies of each firm which can be in focus of the researcher, manager, investor, or other interested parties. As an example, the DMU number 38 does not need to affect business regarding the P/E ratio, return on investment (ROI), EPS, dividend yield, and pricetotangible book ratios. However, it needs to reevaluate part of the business which affects the asset turnover, price to sales, pricetocash flow, and cash per share ratios. Thus, it could be said that this company may be having problems with stock pricing as the majority of needed changes are related to the ratios which involve the prices of its stocks. Similar interpretations can be made for other companies. Thus, the usefulness of the SBM model can be seen in observing in detail which aspects of the business itself need to be taken into greater consideration when thinking about what needs to be improved upon. From the point of view of the investor, he can obtain insights into which company FIGURE 6.1 SBM rankings of all 292 companies. (Source: author’s calculation.) FIGURE 6.2 Empirical histogram of efficiency scores from Figure 6.1. (Source: author’s calculation.) FIGURE 6.3 Most efficient companies (efficiency scores). (Source: author’s calculation.) FIGURE 6.4 Sample of inefficient companies (efficiency scores). (Source: author’s calculation.) is under or overpriced on the stock market based on many different measures used in the analysis. Thus, he can adjust his portfolio structure with respect to the results and his preferences. Finally, Table 6.3 is showing optimal weights of the efficient DMUs in the optimization process for every inefficient DMU from Table 6.2. These weights are interpreted as how much percentage of the efficient DMUs’ outputs and inputs has been used in order to project an inefficient DMU to the efficient frontier. In essence, this tells the researcher or the manager on which specific efficient DMUs and their characteristics he needs to focus so that he can enhance the business in a way which would provide the arrival on the efficient frontier in the best way possible. If one observes DMU number 38, it is seen that 87.5% in total weighting scheme is given to DMU 183. Thus, DMU 38 should aim to observe the business of DMU 183 in greater detail compared to other efficient DMUs, and especially, the whole sample. Thus, such analysis provides even such detailed information, which reduces the number of DMUs which need to be taken into consideration when making important decisions on the future business itself. Discussion on the Best and Worst Ranked CompaniesThe bestperforming companies have high P/E ratios, which suggest that investors can expect higher earnings growth in the future. This is one of the most important TABLE 6.2 Slacks for Inefficient DMUs from Figure 6.4
Source: author’s calculation. TABLE 6.3 Weights of Efficient DMUs (First Row) Which were Used in Optimization for the Inefficient DMUs (First Column) DMU/
Source: author’s calculation criteria in the financial analysis for potential investors. As the bestranked companies have high P/E ratios, it is expected that by investing in them, the earning will grow over time and the expectations on achieving good returns could be justified. The opposite is true for the lowranked companies. Furthermore, the ROI can gauge the investment’s profitability, and this was also recognized as an important variable in the analysis. The worstperforming companies often had negative ROI values. Thus, this should be improved over time so that they become more efficient and attractive to investors. As EPS was found to be an important variable for the most efficient companies, the inefficient ones have problems with profitability. As profitability is today one of the most relevant indicators on a company’s health, it is not surprising that the most inefficient ones were ranked based on this indicator. The asset turnover was also used in the analysis. This indicator is best to use within the same type of companies, which makes it excellent for the analysis provided here. The bestperforming companies had good usage of the given assets in order to generate sales. This is a good indicator of an efficient company. The dividend yield indicated that it is obvious that dividends are important for assessing the efficiency of a company. Although not all companies can payout dividends or they do not want to do that, investors care about the dividends and their relations to the company’s value. The dividend yield indicates if a company is more mature than others. Thus, greater values of this indicator have shown that the company is a better performer if it is not in its infant state. As the P/S ratio should be lowest possible, those companies which had the highest values of this ratio had problems in terms of low sales and revenues. This immediately indicates that the inefficient companies have problems in either attracting customers to generate revenues, or is struggling with the products and new releases so that the revenues could increase. Another variable used was the pricetocash flow ratio, which is better to use than the P/E ratio as cash flows cannot be manipulated as much as the earnings. Greater cashgenerating companies were found to be more efficient in the analysis. The final two indicators used were the pricetotangible book ratio and the cash per share. The first indicator was the smallest for the efficient companies, as they obtained smaller share price losses, whereas the latter indicator is considered more reliable compared to EPS. As the most efficient companies were found to have the lowest values of the cash per share, this was due to their greater liquidity compared to others. As can be seen from the discussion so far, there exists a great complexity in such an analysis. This is due to different knowledge being needed to understand both financial theory and quantitative methods used to assess the efficiency of a company. Robustness Checking – MCDMFinally, the robustness of the results has been checked via the MCDM model. The main idea in the MCDM approach was made that all of the previously mentioned output variables were examined as objectives that need to be the greatest possible. On the other hand, the input variables from the DEA approach were observed in MCDM as objectives that need to be the smallest possible. Thus, it is obvious that the objectives are conflicted, as it is a usual case in business decisionmaking. As 9 inputs and outputs variables are used in the MCDM, and the decisionmaker can FIGURE 6.5 Comparison of rankings based on SBM (v axis) and MCDM (x axis). (Source: author’s calculation.) give weights to the objectives based on previous knowledge and experience, it was opted that all of the objectives have equal weights. In that way, the analysis is as objective as possible. The rankings from the MCDM results have been contrasted to the rankings of the SBM model from the previous subsection. These comparisons are shown in Figure 6.5. It can be seen that the correlation between the two ranking systems is more than 80%, which gives confidence that the results are reliable and can be used in future research as well. The analysis in practice should not stop here. Now, with all information obtained as in previous subsections, the management, alongside financial experts and quantitative modellers, would need to focus on the specific aspect of the business, which is indicated in the poorperforming financial ratio results. Further Possible Integrations of DEA and MCDMSomething which can be considered for future theoretical and empirical work is as follows. A researcher or the investor can opt for a multistep optimization process in which in the first step, the MCDM approach could be used on the initial data set. The obtained rankings could be used to divide companies into several groups: bestranked ones, middle ones, and lowestranked ones. Each subgroup can be then evaluated via DEA models so that detailed insights can be obtained into the business characteristics of the best, middle, and worstranked companies. Something similar could be done in obtaining the DEA results first as was done in this research. Then, in the second step, the input excess and output slacks could be used in MCDM rankings so that the researcher can obtain one number (rank) regarding the company of interest concerning the excess and slacks of that company. Of course, these individual values are important for a company to make the best decisions possible on which inputs should be reduced and which outputs should be increased. However, to obtain fast results in terms of where the company is standing compared to others, such an approach could be useful. Other considerations for future work are examined in the conclusion section. 
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