Share performance and profit efficiency of banks in an oligopolistic market: evidence from Singapore

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1 Journal of Multinational Financial Management 8 (1998) Share performance and profit efficiency of banks in an oligopolistic market: evidence from Singapore Sing Fat Chu, Guan Hua Lim * Graduate School of Business, National University of Singapore, 10 Kent Ridge Crescent, Singapore , Singapore Accepted 28 February 1998 Abstract Using data envelopment analysis techniques, we evaluate the relative cost and profit efficiencies of a panel of six Singapore-listed banks during the period Average profit efficiency (83%) was found to be significantly lower than average cost efficiency (95%). The mean profit efficiency is, however, higher than the averages of banks in the US (64%) and Spain (72%). In a follow-up regression study using the modified efficiency scores of Anderson and Peterson (Management Science, 39 (1993) ), we find that percentage changes in the prices of the bank shares reflect percentage changes in profit rather than cost efficiencies (correlation coefficients of 0.82 versus 0.32). This opens up a new window for understanding share price fluctuations and is to be expected as shareholders desire dividends which are paid out of profits and not income Elsevier Science B.V. All rights reserved. JEL classification: G14; G21; L13 Keywords: Banks; DEA; Profit efficiency 1. Introduction The banking efficiency literature has been dominated to date by cost or X-efficiency studies in the competitive banking markets of Western Europe and North America, e.g.: Ferrier and Lovell (1990); Berg et al. (1993); the review on pp of Berger et al. (1993b); the excellent survey by Berger and Humphrey (1997); Resti (1997); Schaffnit et al. (1997); Drake and Howcroft (1998). Very little has been done on Asian countries (e.g.: Bhattacharyya et al. (1997)) on Indian Commercial Banks; Fukuyama (1993, 1995) on Japanese banks; Yeh (1996) on banks in the Taiwanese market) or on non-competitive banking markets (Berg and Kim, 1994). Profit or P-efficiency is an area that has only recently attracted interest amongst * Corresponding author. Tel.: (+65) ; fax: (+65) ; fbachucl@nus.edu.sg X/98/$ see front matter 1998 Elsevier Science B.V. All rights reserved. PII S X(98)

2 156 S.F. Chu, G.H. Lim / Journal of Multinational Financial Management 8 (1998) researchers ( Berger and Humphrey, 1997, p. 201). The few published studies on this issue (e.g. Berger et al., 1993a; Berger and Mester, 1997; Lozano, 1997) all use parametric methods in contrast to the X-efficiency studies which tend to rely more on non-parametric techniques. Berger and Humphrey (1997), for example, found 69 applications of non-parametric techniques compared with 60 using parametric approaches. Studies on the stock markets, on the other hand, by and large have found that stock prices do incorporate all relevant publicly known information (see for example the collection of articles found in Ball and Kothari (1994)). Efficiency scores are calculated based on published accounting numbers which are public information. Hence, an informationally efficient stock market would have taken such information into consideration in the price discovery process. In this paper, we combine these two literatures by linking bank efficiencies to the market place. Specifically, working within the Singapore domestic banking arena, we investigate the influence of X-efficiencies and P-efficiencies on the share prices of the banks. This exercise contributes an alternative perspective for explaining and understanding fluctuations in the banks share prices and stock market efficiency. At the end of 1996, there were a total of 220 banks operating in Singapore. Most of these banks hold restricted or offshore licenses and deal primarily in the wholesale and offshore markets. Only 34 full-license banks (22 foreign and 12 local ) offer the entire range of commercial banking services and cater to the domestic banking market. The 12 local banks belong to six banking groups which, through their extensive branch network, command some 70% of the markets for deposits and loans. These six local banking groups are Tat Lee Bank (TLB), Keppel Bank ( KB), Overseas Union Bank Group (OUB which also owns the International Bank of Singapore), United Overseas Bank Group ( UOB which includes Chung Khiaw Bank, Far Eastern Bank, and Industrial and Commercial Bank), Overseas-Chinese Banking Corporation (OCBC which has in its stable the Bank of Singapore and Four Seas Bank), and DBS Bank (DBS). All six banking groups are publicly listed on the Singapore stock exchange. In terms of size (as measured by their average total assets in 1996), they ranged from S$9.13 billion to S$52.46 billion1 (see row 1 of Table 1). The domestic banking market can be characterised as an oligopoly. Operationally, the banks offer similar prime rates, savings rates, and fixed deposit rates. UOB was the first mover in 57% of the cases of prime rate increases, whereas OCBC and DBS together initiated about 90% of decreases in prime rates over the period January 1984 to June These changes in prime rates are routinely followed up within days by the other banks. Hence, the competition in the market can be best described by the Stackelberg model. The big three banking groups lead in initiating changes, whereas the other three banks follow closely behind. There are three reasons why we shift the focus of this paper towards the study of profit efficiency and away from cost efficiency. First, as the six banks deploy similar operational technologies, their cost structures may not differ appreciably. Their 1 S$1 is approximately equal to US$0.70.

3 S.F. Chu, G.H. Lim / Journal of Multinational Financial Management 8 (1998) Table 1 Size and average efficiencies of the six Singapore local banks over the period TLB KB OUB UOB OCBC DBS Average Size (S$b) X-efficiency PTXE SXE P-efficiency PTPE SPE Size refers to the simple average of the size of the bank s total assets (excluding contra items) on December 31, 1995 and that on December 31, X-efficiency and P-efficiency refer to cost efficiency and profit efficiency respectively. PTXE=pure technical X-efficiency; PTPT is pure technical P-efficiency. SXE and SPE refer respectively to scale X- and scale P-efficiencies. The six banks are Tat Lee (TLB), Keppel ( KB), Overseas Union Bank (OUB), United Overseas Bank ( UOB), Overseas-Chinese Banking Corporation (OCBC) and DBS Bank (DBS). X-efficiency scores would hence be similar. For instance, in a related study of Taiwanese banks during the pre-deregulation era, Yeh (1996) found that the average X-efficiency ranged between 0.82 and 0.95 for the six banks studied. Since Singapore enforces tight regulatory policies on its banking industry, we posit that the average X-efficiencies of the six local banks would be even higher and possibly less dispersed. Second, Berger et al. (1993a) conclude from their study that profit inefficiency appears to be a bigger problem at US banks than cost inefficiency. They also linked economies of scale to P-efficiency, a result which runs counter to most conclusions on X-efficiency. It is, therefore, of interest to investigate whether we can draw similar conclusions in an oligopolistic banking market like Singapore. This is also a relatively newer area of research and existing studies all use parametric methods rather than the non-parametric techniques favoured by studies on X-efficiency. Third, we are more interested in looking at banking efficiency from the viewpoint of the shareholder rather than from the regulator. We believe that shareholders are more interested in P-efficiency rather than X-efficiency, as profits serve as the source of current and future dividend income. Furthermore, this paper also investigates the existence of a statistical relationship between efficiency scores and how the shares of the banks performed in the marketplace. This does not appear to have been discussed in the literature before. If such a statistical link can be established, it would afford an alternative explanation for share price fluctuations. This would enhance the relevance and value of research in bank efficiencies to investors, stock analysts and banking regulators. The rest of this paper is organised as follows. Section 2 lists our selection of banks inputs and outputs. It also describes the data and justifies the choice of the

4 158 S.F. Chu, G.H. Lim / Journal of Multinational Financial Management 8 (1998) data envelopment analysis (DEA) tool over its econometric competitors for the evaluation of efficiency scores. Section 3 summarises the state-of-the-art for DEA techniques used in this paper. X-efficiency and P-efficiency scores are reported in Section 4. In Section 5 we first modify several X-efficiency and P-efficiency scores to obtain an overall ranking of all the relative bank-year performances. We then regress annual stock returns on annual percentage changes in the bank efficiencies. Section 6 concludes the paper. 2. Research framework We adopt the perspective of Sealey and Lindley (1977) and view banks basically as financial intermediaries whose primary role is to obtain funds from savers in exchange for their own liabilities, and then, in turn, make loans to others for a profit. That is, banks transform inputs such as labour, physical capital, deposits and financial capital into earning assets (see Fig. 1). We define cost or X-efficiency as the relative efficiency of banks at minimising costs in the production of earning assets (Mester, 1996; Resti, 1997). Profit or P-efficiency, on the other hand, is defined as the profit maximising or valued-added efficiency of banks. Notice that X-efficiency does not necessarily equate with P-efficiency, as a bank may not improve its profit margin with a higher production of earning assets. Profit, unlike income, also takes into account expenses, taxes and the degree of financial leverage employed by the bank. Our choice of input and output variables is determined in part by the desire for a parsimonious model and in part by the smallness of our data set. The traditional economic factors of production are land, labour and capital. Labour and land are approximated by non-interest expense which encompasses wages, physical capital expenses as well as provisions for doubtful loans. Capital is provided either by the bank s shareholders or by its depositors. The latter is proxied by interest expenses. Interest expense is more relevant than volume of deposits as not all deposits (savings, fixed or time, and current or checking) carry the same interest expense ( Mester, 1996). Interest and non-interest expenses have been used as inputs in bank efficiency studies by many researchers, including Miller and Noulas ( 1996), Yeh (1996) and Resti (1997). The third input variable we use is the amount of financial capital provided by the bank s shareholders. This includes paid-up capital, capital reserves Fig. 1. The three inputs and two outputs used in the DEA model.

5 S.F. Chu, G.H. Lim / Journal of Multinational Financial Management 8 (1998) (share premium account and asset revaluation account), statutory reserves, and unappropriated earnings. Financial capital has been one of the least used inputs by banking efficiency researchers. Examples of papers that used this input include Hughes and Mester ( 1993), McAllister and McManus (1993), Grabowski et al. (1994) and Mester (1996). Its importance cannot be underestimated. Capital adequacy is a crucial parameter of solvency risks used by all bank regulators, and financial capital can be used as a substitute to deposits and purchased money to fund loans. Two outputs are considered. They are the annual increase in average total assets and either the total income from interest and non-interest activities (for X-efficiency evaluation) or profits (for P-efficiency evaluation). In other words, X-efficiency and P-efficiency differ on the selection of either total income or net profit after taxation as the second output variable. We chose not to disaggregate total income into interest and non-interest categories since an inherent objective of this paper is to compare X-efficiency and P-efficiency scores. For fairness, these two scores should be based as far as possible on the same inputs and outputs. This is also in line with the suggestion made by Berger et al. (1993b, p. 231) for a comparison between a profit and a cost function model estimated using the same data set. The annual increase in average assets does not appear to have been employed before. It may be regarded as a proxy for future income or future profit. Our choice of outputs brings a novelty to the literature as they represent both the present and the future earnings. This is important to shareholders as the bank can always sacrifice long-term profits/income for short-term gains, and the bank s long-term profit potential definitely affects its current share price. The test period selected is from 1992 to is chosen as the starting date as it was only then that the six local banks started to provide a breakdown of their income and expenses into interest and non-interest categories. The latest reporting year for all six banks is All six banks have December 31 as their financial year end. We work with annual data simply because the accounting information required are only available on a yearly basis (not quarterly as in the USA). Thus, our data set consists of 30 bank-year combinations. The small size of the data set forces us to opt for DEA as the tool to evaluate X-efficiency and P-efficiency. Studies on bank efficiency which used DEA techniques include Aly et al. (1990), Berg et al. (1993), Bhattacharyya et al. (1997) and Drake and Howcroft ( 1998). Alternative methods based on the econometric frontier (e.g. Ferrier and Lovell, 1990; Pi and Timme, 1993; Kaparakis et al., 1994; Mester, 1996), thick frontier (e.g. Berger and Humphrey, 1991; Berg and Kim, 1994) or distributionfree (e.g. Berger et al., 1993a; Lang and Welzel, 1996) approaches only achieve stable results with large data sets, a luxury which we do not have. The potential of data error, often mentioned as a shortcoming of DEA (Mester, 1996), is minimised here as we employ only audited figures culled straight from the respective banks annual reports. End-of-the-year stock prices, duly adjusted for capitalisation changes, are obtained from the Dbank financial data base maintained at the National University of Singapore and from the January 1997 issue of the monthly SES Journal for the

6 160 S.F. Chu, G.H. Lim / Journal of Multinational Financial Management 8 (1998) numbers. Section 3 summarises the current state-of-the-art for the technical aspects of DEA that will be required in this paper. 3. DEA technology: the state-of-the-art DEA was developed to measure the relative productive efficiencies of similar multi-input multi-output decision-making units ( DMUs). For each DMU, DEA evaluates an efficiency score defined as the ratio of a weighted sum of its outputs to a weighted sum of its inputs subject to the constraint that the ratio does not exceed one for any DMU. The weights, chosen by DEA, cast each DMU in its best possible portrait. Best-practice DMUs are assigned an efficiency score of one. These bestpractice DMUs define the relative efficiency frontier. Charnes et al. (1978) demonstrate that the output/input ratio or fractional linear programming problem may be transformed into a standard linear programming problem upon either setting the denominator (i.e. weighted sum of inputs) or the numerator (i.e. weighted sum of outputs) to a constant. Thus, DEA may be cast in either an output-maximising (e.g. profit maximisation) or an input-minimising (e.g. cost minimisation) role. The linear program for computing P-efficiencies ( profit maximisation) is given below. s.t. P-efficiency 0 =Max w n wy l Y +S+=0 0 j j j=1 n l X X +S =0 j j 0 j=1 l, S+, S 0 j In the above formulation, subscript 0 refers to the current DMU (or bank-year combination) being evaluated. The variables X j and Y j respectively denote the vectors of inputs and outputs for DMU j ( j=1,, n; n=30). the weights l j indicate the influence of the best-practice DMUs in benchmarking the efficiency of the current DMU. Finally, S and S+ represent the input and output slacks vectors respectively. These provide precise diagnostic feedback on areas of improvement to the managers of the inefficient banks. This paper, as mentioned earlier, focuses on DEA in a profit maximisation role. If constant returns of scale (CRS) is assumed (Charnes et al., 1978), DEA delivers an overall technical efficiency (OTE) or P-efficiency score for each DMU. Banker et al. (1984) assume variable returns to scale (VRS) and show that OTE can be decomposed into a product of two components, viz. pure technical efficiency and scale efficiency. These two components are denoted PTPE and SPE to highlight their link to P-efficiency in this paper. Pure technical efficiency measures how efficiently a DMU utilises its resources. Scale efficiency reflects whether a DMU is operating at the right scale of operation or size. (1)

7 S.F. Chu, G.H. Lim / Journal of Multinational Financial Management 8 (1998) The linear program for computing each DMU s PTPE is provided below (see Miller and Noulas (1996, pp ) for details on the computation of X-efficiency, pure technical X-efficiency or PTXE and scale X-efficiency or SXE). PTPE =Max n 0 s.t. n ny l Y +S+=0 0 j j j=1 n l X X +S =0 j j 0 j=1 n l =1 j j=1 l, S+, S 0 j Notice that the linear programs in Eqs. (1) and (2) differ only in the convexity constraint, Sn j=1 l j =1, implied by VRS that is imposed on Eq. (2). To get an intuitive feel of these linear programs, we now provide a graphical illustration. Fig. 2 illustrates the computation of P-efficiency, PTPE and SPE in the special situation of one input (e.g. shareholders fund) and one output (e.g. increase in total assets). In 1993, Keppel Bank ( KB93) scored the highest ratio of increase in assets to shareholders fund. Thus its P-efficiency is one, whereas the P-efficiencies of the other DMUs are less than one. Under the VRS assumption, however, the (2) Fig. 2. Illustration of CRS and VRS efficiency frontiers.

8 162 S.F. Chu, G.H. Lim / Journal of Multinational Financial Management 8 (1998) relative efficiency frontier is constructed around the convex combination KB92, KB93, and OUB96. These three bank-year combinations are (see Fig. 2) assigned unitary PTPE, whereas the other DMUs attract PTPEs of less than one. Scale efficiency is computed as P-efficiency divided by PTPE. For example, the P-efficiency, PTPE and SPE of OUB94 correspond geometrically to the ratios AB/AD, AC/AD and AB/AC respectively. The nature of the scale inefficiency can be uncovered using the conclusion of Zhu and Shen (1995). They show that a DMU exhibits decreasing (increasing) returns to scale when Sn j=1 l j exceeds (does not exceed) one upon the computation of its OTE. This information may suggest a possible future managerial course of action for the DMU involved, namely whether it should contract or expand its scale of operations in the quest for greater efficiency. A serious shortcoming of DEA is that it may find a disproportionately large number of technically efficient DMUs. This is especially so if the total number of inputs and outputs is high relative to the number of DMUs. To remedy this situation, Andersen and Petersen (1993) propose the ranking of frontier DMUs by comparing them with a reference technology spanned by their frontier peers. This means that in the constraints to the linear program formulations in Eqs. (1) and (2), the summation sign (running from 1 to n) should exclude the current DMU. With this modification, frontier DMUs may attract an efficiency score above one, thereby allowing an overall ranking of all the n DMUs. This enhances the suitability of the modified efficiency scores for follow-up parametric linkages such as regression analyses. 4. X-efficiencies and P-efficiencies of Singapore banks The literature abounds with empirical results on banks X-efficiencies. In their review paper, Berger et al. (1993b) report that authors studying US banks found average X-efficiencies in the 50 to 90+% or 75 to 80% ranges depending on whether they employ DEA or econometric models. In a recent study on 270 Italian banks during the period, Resti (1997) concludes that Italian banks have average X-efficiencies of about 70% under both the DEA and econometric models. Finally, Pastor et al. (1997) report an average efficiency score of 0.86 in their study of banks in the US and seven Western European countries and Lang and Welzel (1996) report average efficiency scores 54% and 61% for German banks. As a bridge to these results, we now report the X-efficiencies of Singapore banks. We find the average X-efficiency of the six Singapore-listed banks for the period to be a remarkable 95.3% (see Table 1). The average 4.7% X-inefficiency of Singapore banks compares favourably with the just over 5 percent reported in the study by Miller and Noulas (1996, p. 507) on 201 large (defined as those with assets in excess of US$1b) US banks between 1984 and It is much higher than that found in the Fukuyama (1993) study on Japanese banks (86%) and the 75 86% averages of Indian commercial banks (Bhattacharyya et al., 1997). A more direct comparison would be with Berg and Kim (1994). In their study on Norwegian banks, which operate in a similar oligopolistic banking environment, they report

9 S.F. Chu, G.H. Lim / Journal of Multinational Financial Management 8 (1998) average inefficiencies of 19%, a number three times higher than what we observe in our current study of Singapore-listed banks. Furthermore, the standard deviation of the X-efficiencies of Singapore banks is only 0.06 compared with 0.09 for Taiwanese banks ( Yeh, 1996). The larger banks appeared to exhibit slightly higher X-efficiencies than the smaller banks. This is similar to earlier empirical findings from the US market (e.g. Berger et al., 1993a; Miller and Noulas, 1996). As a group, UOB, OCBC and DBS had an average X-efficiency score of 0.99 compared with the 0.92 average obtained by the other three banks. Furthermore, the smallest bank, TLB, has the lowest average X-efficiency score of Unlike Miller and Noulas (1996), who found average pure technical inefficiency twice the size of scale inefficiency, the six banks in our sample do not appear to have very different PTXE and SXE scores (see Table 1). The average PTXE is in fact comparable with the average SXE ( versus 0.974). However, if we exclude the two smallest banks (TLB and KB who have average scale inefficiencies some 50% higher than their average pure technical inefficiencies), the other four banks displayed similar results. Though small, their average pure technical inefficiency nonetheless is still about double that of their average scale inefficiency. The average P-efficiency of the six Singapore banks is, however, much lower (significant at the 5% level ) at about 82.6% (see row 3 of Table 1). For comparison, we note that the mean profit efficiency from studies of US depository institutions is 64% (Berger and Humphrey, 1997, p. 201) whereas that for Spanish banks is 72% (Lozano, 1997). On average, scale P-efficiency of Singapore-listed banks is 95%, a number comparable with the 97% for SXE, and pure technical P-efficiency is 87%. Thus, it appears that, P-efficiency arises more from the inefficient production of profits rather than from the wrong scale of the operations. This conclusion concurs with that reached by Berger et al. (1993a). One possible explanation for the lower average P-efficiency compared with average X-efficiency could be the low degree of financial leverage use by Singapore banks. Singapore banks are very conservative by nature and have routinely ranked among the world s strongest banks in terms of Tier 1 capital ratio (as defined by the Bank of International Settlements). Furthermore, the six banks (especially TLB and KB) have been raising additional financial capital over this period to meet new statutory requirements on minimum shareholders equity (S$800 million by 1998 and subsequently amended in 1996 to S$1.5 billion by 2001). Larger banks were once again more P-efficient than the smaller ones. There are several possible explanations for this result. Larger banks attract more deposits and loans transactions and they may actually command larger interest spreads. Larger banks offer more service. In the process, they derive substantial non-interest income from commissions, fees and treasury activities. For example, DBS Bank is the leading manager and underwriter of initial public offerings in Singapore. Furthermore, in an oligopolistic market, the size, and hence economies of scale, also equates to market power and the ability to set rates. It appears, therefore, that this market power has been translated into higher profits for the larger banks. Notice that while UOB obtains perfect X-efficiency scores for all of the 5 years between 1992 and 1996, it ranks a close second to DBS in terms of average P-efficiency over the same period (0.946 versus 0.966). The difference in average

10 164 S.F. Chu, G.H. Lim / Journal of Multinational Financial Management 8 (1998) P-efficiency between the smaller banks (viz. TLB, KB and OUB) and the larger banks is even wider than that for average X-efficiency (0.71 versus 0.94 compared with 0.92 versus 0.99). Furthermore, using the result of Zhu and Shen (1995), we also find that the smaller P-inefficient banks generally exhibited decreasing returns to scale in the generation of current and future profits. This suggests that they may be sacrificing their interest margins in order to maintain or improve their market share. Again, we believe that this is a manifestation of the oligopolistic nature of the Singapore domestic banking market. This result is in contrast to US studies into X-efficiency of banks (e.g. see Hunter et al., 1990; Noulas et al., 1990; Berger and Humphrey, 1991), where the general conclusion was that smaller banks experienced increasing returns. The evidence on larger banks is, at best, CRS (McAllister and McManus, 1993) and at worst, decreasing returns to scale. 5. Efficiencies and stock returns In this section, we investigate the influence of X-efficiencies and P-efficiencies on the share prices of the banks. This exercise appears to be a first in the banking efficiency literature. We first employed the method suggested by Andersen and Petersen (1993) to modify all the ( perfect) X-efficiency and P-efficiencies scores of 1.00 obtained in the original run of DEA. The modified scores were all in excess of one (see Table 2). Their inherent ranking should in theory enhance the statistical fit for this second-stage parametric exercise. Table 2 Modified X-efficiency (first row) and P-efficiency (second row)a Year TLB KB OUB UOB OCBC DBS a These are modified according to Andersen and Petersen (1993). Only original X-efficiency and P-efficiency scores equal to are modified. The six banks are Tat Lee (TLB), Keppel ( KB), Overseas Union Bank (OUB), United Overseas Bank ( UOB), Overseas-Chinese Banking Corporation (OCBC) and DBS Bank (DBS).

11 S.F. Chu, G.H. Lim / Journal of Multinational Financial Management 8 (1998) Fig. 3. Annual changes in share prices and P-efficiencies. Current regulations in Singapore allow foreigners to own collectively at most 40% of a bank s share capital. TLB and KB, the two smallest banks, have yet to reach this threshold foreign shareownership percentage. The other four banking groups have all segregated their shares into local and foreign tranches in order to satisfy this legal requirement. Whereas foreigners are constrained to dealing in foreign shares, Singapore residents or institutions are allowed to invest in both local and foreign shares. Active trading in foreign shares has led them to command premiums as high as 100% over the local shares. For these four banks, we computed their share prices as the weighted averages of 0.6 times their local share prices plus 0.4 times their foreign share prices. We first regressed annual stock returns (adjusted for capitalisation changes) on percentage changes in the annual X-efficiencies. KB92 and KB93 were excluded as KB only got listed on the Singapore bourse in The correlation coefficient was 0.32 (R-square=0.10), statistically significant at the 10% level. Using P-efficiencies in lieu of X-efficiencies improved the correlation to 0.75 (R-square=0.56). However, the scatter plot (see Fig. 3) indicated a significant market overreaction to changes in P-efficiencies. Improvements in P-efficiency created a bull run leading to high prices, whereas falls in P-efficiency scores sent prices tumbling down. We found that the overreaction problem could be attenuated upon using changes in the annual moving averages of both the modified P-efficiencies and the stock returns. Data smoothing mitigates the excessive reactions of investors to year-onyear percentage changes in profit efficiencies. The scatter plot is displayed in Fig. 4. The correlation between the annual changes in the moving averages of P-efficiencies and stock returns improved to 0.82 (R-square=0.67). The slope coefficient was with a standard deviation of Statistically, this implies the slope may not be different from one. This has the interesting implication that percentage changes in smoothed P-efficiencies are associated with equal percentage changes in smoothed stock returns. A similar implication also surfaces in the regression based on using unsmoothed changes in share prices and P-efficiencies.

12 166 S.F. Chu, G.H. Lim / Journal of Multinational Financial Management 8 (1998) Fig. 4. Changes in moving average of share prices and P-efficiencies. If moving averages of X-efficiencies are used instead of moving averages of P-efficiencies, the R-square would have been This leads us to conclude that share prices reflect P-efficiencies to a larger extent than X-efficiencies. This is to be expected, as shareholders desire dividends which are paid out of profits and not income. It also lends support to the hypothesis that the Singapore stock market is indeed price efficient in the semi-strong form sense. 6. Conclusions This paper makes a number of contributions to the literature. It studies cost and profit efficiencies of banks in an Asian (Singapore) market which also happens to be an oligopolistic/stackelberg competition type market. This fills a void in the literature which has to date concentrated on Western European and North American markets where banks operate in a competitive banking environment. Hopefully, our results will be of relevance to other oligopolistic banking markets around the world. Using the DEA technique with three inputs and two outputs, we find that the X-efficiencies of Singapore banks were higher, on average, and less dispersed compared with Taiwanese banks and those in Western Europe and North America. We have further highlighted the relevance and value of the concept of P-efficiency. On average, P-efficiency is lower than X-efficiency at Singapore banks. We attribute this P-inefficiency to the inefficient production of profits rather than to the wrong scale of operations. Furthermore, the larger banks do have better X- and P-efficiency scores than the smaller banks. We also tie the literature on banking efficiency to the vast body of empirical findings on the pricing efficiency of the stock market. We show that percentage changes in share prices reflect percentage changes in profit rather than cost efficiencies. Finally, the market tends to over-react on year-on-year changes in P-efficiency.

13 S.F. Chu, G.H. Lim / Journal of Multinational Financial Management 8 (1998) This leads us to consider data smoothing. This offers an alternative explanation for fluctuations in share prices. Acknowledgements We would like to thank Ike Mathur (the editor), an anonymous referee, and participants at the th Annual Australasian Finance and Banking Conference for their valuable feedback, suggestions and comments. References Aly, H.Y., Grabowski, R., Pasurka, C., Rangan, N., Technical, scale, and allocative efficiencies in US banking: an empirical investigation. Review of Economics and Statistics 72, Andersen, P., Petersen, N.C., A procedure for ranking efficient units in data envelopment analysis. Management Science 39, Ball, R., Kothari, S.P Financial Statement Analysis. McGraw-Hill, New York. Banker, R.D., Charnes, A., Cooper, W.W., Models for the estimation of technical and scale efficiencies in data envelopment analysis. Management Science 30, Berg, S.A., Kim, M., Oligopolistic interdependence and the structure of production in banking: an empirical evaluation. Journal of Money, Credit and Banking 26, Berg, S.A., Forsund, F.R., Hjalmarsson, L., Suominen, M., Banking efficiency in the Nordic countries. Journal of Banking and Finance 17, Berger, A.N., Humphrey, D.B., The dominance of inefficiencies over scale and product mix economies in banking. Journal of Monetary Economics 28, Berger, A.N., Humphrey, D.B., Efficiency of financial institutions: International survey and directions for future research. European Journal of Operational Research 98, Berger, A.N., Mester, L.J., Inside the black box: what explains differences in the efficiencies of financial institutions? Journal of Banking and Finance 21, Berger, A.N., Hancock, D., Humphrey, D.B. 1993a. Bank efficiency derived from the profit function. Journal of Banking and Finance 17, Berger, A.N., Hunter, W.C., Timme, S.G. 1993b. The efficiency of financial institutions: a review and preview of research past, present and future. Journal of Banking and Finance 17, Bhattacharyya, A., Lovell, C.A.K., Sahay, P., The impact of liberalisation on the productive efficiency of Indian commercial banks. European Journal of Operational Research 98, Charnes, A., Cooper, W.W., Rhodes, E., Measuring the efficiency of decision making units. European Journal of Operations Research 2, Drake, L., Howcroft, B A study of the relative efficiency of UK bank branches. Journal of Banking and Finance, in press. Ferrier, G.D., Lovell, C.A.K., Measuring cost efficiency in banking: econometric and linear programming evidence. Journal of Econometrics 46, Fukuyama, H., Technical and scale efficiency of Japanese commercial banks: a non-parametric approach. Applied Economics 25, Fukuyama, H., Measuring efficiency and productivity growth in Japanese banking: a non-parametric frontier approach. Applied Financial Economics 5, Grabowski, R., Rangan, N., Rezvanian, R., The effects of deregulation on the efficiency of U.S. banking firms. Journal of Economics and Business 46, Hughes, J.P., Mester, L.J., A quality and risk-adjusted cost function for banks: evidence on the too-big-to-fail doctrine. Journal of Productivity Analysis 4,

14 168 S.F. Chu, G.H. Lim / Journal of Multinational Financial Management 8 (1998) Hunter, W.C., Timme, S.G., Yang, W.K., An examination of cost subadditivity and multiproduct production in large U.S. banks. Journal of Money, Credit and Banking 22, Kaparakis, E., Miller, S., Noulas, A., Short-run cost inefficiency of commercial banks: a flexible stochastic frontier approach. Journal of Money, Credit and Banking 26, Lang, G., Welzel, P., Efficiency and technical progress in banking: empirical results for a panel of German banks. Journal of Banking and Finance 20, Lozano, A.L., Profit efficiency for Spanish savings banks. European Journal of Operational Research 98, McAllister, P.H., McManus, D., Resolving the scale efficiency puzzle in banking. Journal of Banking and Finance 17, Mester, L.J., A study of bank efficiency taking into account risk-preferences. Journal of Banking and Finance 20, Miller, S.M., Noulas, A.G., The technical efficiency of large bank production. Journal of Banking and Finance 20, Noulas, A.G., Ray, S.C., Miller, S.M., Returns to scale and input substitution for large U.S. banks. Journal of Money, Credit, and Banking 22, Pastor, J., Perez, F., Quesada, J., Efficiency analysis in banking firms: an international comparison. European Journal of Operational Research 98, Pi, L., Timme, S.G., Corporate control and bank efficiency. Journal of Banking and Finance 17, Resti, A., Evaluating the cost-efficiency of the Italian banking system: what can be learned from the joint application of parametric and non-parametric techniques. Journal of Banking and Finance 21, Schaffnit, C., Rosen, D., Paradi, J.C., Best practice analysis of bank branches: an application of DEA in a large Canadian bank. European Journal of Operational Research 98, Sealey, C.W., Lindley, J.T., Inputs, outputs and theory of production cost at depository financial institutions. Journal of Finances 32, Yeh, Q.J., The application of data envelopment analysis in conjunction with financial ratios for bank performance evaluation. Journal of the Operational Research Society 47, Zhu, J., Shen, Z.H., A discussion on testing DMUs returns to scale. European Journal of Operational Research 81,