861 Int. J Latest Trends Fin. Eco. Sc. Vol‐5 No. 1 March, 2015 Efficiency in Stock Markets with DEA: Evidence from PSI20 Nuno Ferreira#1, Adriano Mendonça Souza*2 # Department of Quantitative Methods, IBS-ISCTE Business School, ISCTE Avenida das Forças Armadas, Lisboa, Portugal [email protected] * Department of Statistics, Federal University of Santa Maria Roraima Avenue, 100, Santa Maria, RS state, Brazil [email protected] Abstract - After the US subprime crisis, the first signs of economic efficiency, and technical efficiency. a sovereign debt crisis spread among European Whereas technical efficiency requires only input and financial players. The regulation of the markets by output data, economic efficiency also requires price European Commission and European Central Bank data. The simplest way to differentiate productive and created limitation to obtained great amount of liquidity technical efficiency is to think of productive in commercial banking sector. In this context, the efficiency in terms of cost minimization by adjusting successful survival of some European banks became in a dangerous situation. The present study try to explore the mix of inputs, whereas technical efficiency is the crisis occurred in one of the largest private output maximization from a given mix of inputs. Portuguese banks through the analysis of the efficiency In literature, a large number of papers is based on levels of twenty largest enterprises of the PSI20 since an essentially nonparametric, programming approach 1993. The input variables chosen were market value to analysis of observed outcomes. In fact, the Data and return in a Data Envelopment Analysis model. Envelopment Analysis (DEA) is by far the most used Consistent with earlier studies, the results show methodology to measure efficiency. Traditional DEA substantial revenue inefficiencies among the Portuguese models compare the relative efficiency of each DMU enterprises. (for instances: individual firms or, individual Keywords Stock Markets Indices; Interest Rates; Banking ‐ industries in the sector). Leontief-type input-output sector; EU Sovereign Debt Crisis; Efficiency. models characterize the different sectors dependence, 1. Introduction each sector comprising several industries. In this context, it seems natural to explore the DEA Financial researchers had dedicated a large effort efficiency models in so different economy sectors to discover the factors that explain differences in the such as agriculture, manufacturing, transportation, enterprises financial performance during several and trade. Despite DEA efficiency models mostly years. Around the world stock markets have fallen, emphasize technical efficiency (TE), and allocative large financial institutions have collapsed or been efficiency (AE) concepts, alternative approaches are bought out, and governments in even the wealthiest also covered with this methodology. nations have had to come up with rescue packages to The purpose of DEA is to construct an bail out their financial systems. In this context, all envelopment production frontier. This frontier maps agents focus their attention on productivity and out the greatest output (least input) for a given level efficiency gains since both are central to the growth of input (output) based on observed outputs and of firms in any industry. For this matter, inefficiency inputs of the DMUs. In this context, all observed can be due to structural problems or market points lie on or below this frontier. Thus, the imperfections or even other factors, resulting in firms production frontier or the “best practices frontier” is producing below their maximum attainable output. constructed with the DMUs that lie on it (highest Efforts to measure how efficiently a firm (a efficiency). The efficiencies of the remaining DMUs Decision Maker Unit, known as DMU in literature) that lie below it measured by the distance relative to produces outputs with its inputs have led to the this frontier. development of a number of efficiency concepts, PSI20 (acronym of Portuguese Stock Index) is the including scale efficiency, scope efficiency, main index of Euronext Lisbon. Eligible companies ____________________________________________________________________________________ International Journal of Latest Trends in Finance & Economic Sciences IJLTFES, E‐ISSN: 2047‐0916 Copyright © ExcelingTech, Pub, UK (http://excelingtech.co.uk/) 862 Int. J Latest Trends Fin. Eco. Sc. Vol‐5 No. 1 March, 2015 are required to fulfill the velocity threshold and was based on the evidence that DEA gives analysts minimum free float (corresponding to the value of an opportunity. This opportunity relies in the facility €100 million). The base value of the PSI-20 date back of calculating an overall efficiency score based on to December 31, 1992 and was 3000 points. financial data, to examine different aspects of The Portuguese stock index includes 7 categories financial conditions and financial performance of companies, namely: Banks, Industry, Media, simultaneously rather than sequentially. In this Energy, Food & Allied Products, Construction and context, Chen (2008) by using the size effect through Communications (5, 3, 1, 4, 4, 1 and 2 companies, DEA tried to model for stock selection to form respectively) [see Table 1]. portfolios and compare them against the benchmark market portfolio. Lopes et al. (2008) applying the Table 1. List of the studied Companies from PSI20 Index same DEA model to the Brazilian stock market. But the focus of the analysis relied on into risk measures Group Company Industry Altri SGPS like variance and beta as inputs and quarterly returns Portucel Semapa as the output. Singh et al. (2009), used DEA to form Construction Mota Engil SGPS efficient portfolio in their comparative analysis. Food and Allied Products Jerónimo Martins Sonae Indústria SGPS Wang et al. (2010) formulated a model of stock Sonae.com Sonae SGPS classification to facilitate investors making Media Cofina Comunications Portugal Telecom SGPS investment decisions related to equity stock selection Zon Optimus by two dimensions. These were performance shift Energy EDP Renováveis EDP Energias de Portugal and stock price evaluation (Malmquist productivity GALP Energia SGPS REN index based on DEA and Range adjusted Measure Banks Banco Comercial Português (BCP) (DEA-RAM)). More recently Lim and Zhu (2014) Banco Espírito Santo (BES) Banco Português de Investimento (BPI) proposed a way of using DEA cross-efficiency BANIF Espírito Santo Financial Group evaluation in portfolio selection. They presented an application to Korean stock market. Among the literature focused on the Portuguese In the present study the revenue efficiency levels stock market, we selected the following papers as of twenty largest enterprises of the PSI20 since 1993 relevant research on the topic under study. are analysed in order to better understand how Nascimento (2007) analyzed the Portuguese market efficiency or the lack of it, contribute to the crisis during 1997–2007. In this study the author concluded occurred in one of the largest private Portuguese that 42% of the 26 selected stocks, which had a banks (Banco Espírito Santo). random walk in prices, held a significant part of the (weak) efficiency where the market players did not enjoy supernormal profits. Nevertheless, the author 2. Methodology of DEA hinted at the possibility of the lack of efficiency due The panel data defined to undertake the analysis to the existence of information asymmetries, since considered the individual company’s return as the 58% of the remaining assets of the sample allowed output variable and the market return and the market supernormal profits to be possible. Duque and value as inputs. The DEA output-oriented approach Madeira (2004) presented empirical evidence on the to estimate the revenue efficiency (RE) of each stock existence of abnormal returns of asset prices in the return follows (Färe et al. (1985) : Portuguese Stock Index (PSI) for the period 1996– 2001. The authors evidenced that the Portuguese ∑ | stock market has a weak efficiency. If we extend to international stock markets the , 1,…, proliferation of papers increase substantially. In this context, a large number of papers highlight the DEA importance. The acceptance of this methodology in , financial markets is reaching more popularity in recent years. By using DEA to generate a “financial 1, … , 1 efficiency frontier”, each enterprise achieves an 0, 1, … , overall financial efficiency score comparable to that of its peer enterprises. One great advantage of DEA 0, 1, … , 863 Int. J Latest Trends Fin. Eco. Sc. Vol‐5 No. 1 March, 2015 additional enlighten to the discussion, as the lowest This model considers n DMUs, defined by j score corresponds to the first year of the index (j=1,…,n), which use the inputs xij (x1j,…,xmj), to establishment. obtain the outputs yrj (y1j,…,ysj). In the formulation (1), prj0 is the value of output r for the DMU j0 under Table 3. DEA revenue efficiency scores by year 0 assessment. yr is a variable that, at optimal solution, gives the output r to be produced by DMU j0 to Year Mean Efficiency 1993 0.24 maximize revenue, subject to the technological 1994 0.86 restrictions imposed by the existing production 1995 0.81 1996 0.79 possibility. The RE of each DMU j0 is given by as the 1997 0.89 ratio of current revenue observed at DMU j0 to the 1998 0.93 maximum revenue estimated by the optimal solution 1999 0.89 to model (2): 2000 0.89 2001 0.83 2002 0.81 2003 0.81 2004 0.84 ∑ 2 2005 0.87 ∑ ∗ 2006 0.90 2007 0.92 The DEA model (1) and the revenue efficiency 2008 0.88 2009 0.85 model (2), were estimated using the DEAP software 2010 0.86 (Coelli, 1996). 2011 0.84 2012 0.82 2013 0.76 3. Results Mean 0.82 The Tables 2 to 4 present the DEA scores by economical sector, year and enterprises. The results Nonetheless, from Table 3, three important periods achieved with DEA consider the more efficient, the of economic tension are well identified. The Asian sectors of Media, Communications and Energy. financial crisis in 1996-97; the Iraq and Afghanistan invasion in 2001; the Subprime crisis in the US Table 2.