Ilhan Ege, Int.J.Buss.Mgt.Eco.Res., Vol 2(2),2011,

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1 Post-Crisis Perforance of Turkish Insurance Copanies sing Fuzzy Data Enveloping Analysis Ilhan Ege Faculty of Econoics and Adinistrative ciences, Mersin niversity, Mersin, Turkey Abstract: This study analyzes efficiency of the Turkish insurance copanies in In this study fuzzy data enveloping analysis is used. Data Envelopent Analysis (DEA) is a linear prograing based ethod, used in easuring the efficiencies of organizational units, when any inputs and outputs are involved. In this paper fuzzy DEA (data envelopent analysis) odels are used for evaluating the efficiencies of objects with fuzzy input and output data. The approach transfors fuzzy DEA odels into possibility DEA odels by using possibility easures of fuzzy events or fuzzy constraints. JE Classifications: G22, C14, C67, C81 Key words: Fir Perforance, Insurance Copanies, Fuzzy Data Enveloping Analysis 1. INTRODCTION Econoic crisis are been after These are European Money Crisis in , atin Aerica Crisis in , outh East Asian Crisis in , Russian Crisis in 1998, Brazil Crisis in 1999 and Argentina Crisis in Global capital flows fluctuated between 2 and 6 percent of world GDP during , but since then they have risen to 15 percent of GDP (http://www.if.org/external/about/histglob.ht). These crisis effected Turkish econoy. Over 2001 the GDP contracted by 7.4% in real ters, whole sale price inflation soared to 61.6%, and the currency lost 51% of its value against the ajor foreign onies. The rate of uneployent rose steadily by 2 percentage points in 2001 and then another 3 percentage points in Real wages fall abruptly by 20% upon ipact in 2001 (Yeldan, 2006). In 2006, global capital flows totaled $7.2 trillion ore than a tripling since The ost rapid increase has been experienced by advanced econoies, but eerging arkets and developing countries have also becoe ore financially integrated (http://www.if.org/external/about/histglob.ht). In Turkey year 2007 had best econoic conditions in the period. IMF was applied an exchange-rate based disinflation progra. IMF provided financial assistance of $20.4 billions, net, between 1999 and In the Noveber 2002 elections iportant political revolution was been. Justice and Developent Party (AKP) was cae to absolute power in the parliaent in these elections (Yeldan 2006). But this political revolution did not effect econoical politics. AKP governent was applied the sae post-crisis econoical politics. Consequently, AKP governent reached consensus with the IMF in 2004 according to the new stand-by agreeent. The ai of this study is analyzing Turkish insurance copanies perforances in Data of 2006 were used because this year is post-crisis and before end of crisis, after AKP governent beginning year. In this study fuzzy data enveloping analysis is used. In the literature, there are any studies which deal perforance and efficiency of insurance copanies. In these studies different ethods have been used for easureent of perforance and efficiency. DEA is a widespread ethod for perforance easureent. 2. METHODOOGY Data Enveloping Analysis (DEA) is a new data oriented ethod to easure the perforance and efficiency of firs. It evaluates the perforance of a set of peer entities. These peer entities are called Decision Making nits (DMs) and convert ultiple inputs into ultiple outputs (Cooper, eiford and Zhu, 2004, 1). DEA is a non-paraetric and linear prograing ethod developed by Charnes, Cooper and Rhodes (1978). This odel is called the CCR odel. CCR ratio odel yields an objective evaluation of overall efficiency and identifies the source and estiates the aounts of the thus identified inefficiencies. Other DEA odels are the BCC odel (1984), the ultiplicative odels (1982, 1983) and the additive odel (1985, 1987). These odels ay focus on increasing, decreasing, or constant returns to scale as found in econoies that are here generalized to the case of ultiple outputs (Charnes, Cooper, ewin and eiford, 1994: 24). In DEA, decision aking units and input and output data ust be easured rightly and precisely. Therefore, Fuzzy Data Envelopent Analysis is recoended by using Fuzzy Theory. Thus, better efficiency scores are obtained and iprecise cases can be analyzed. Guo and Tanaka (2001) suggested fuzzy CCR odel for 173

2 easureent efficiency. The efficiencies of decision aking units (DMs) are easured with fuzzy observations. Initially, n basic banking inputs and basic banking outputs were considered for each bank and the Charnes, Cooper and Rhodes (1978) input-oriented odel, CCR were applied. This odel to the Fuzzy DEA x 0 odel is transfored. pper and lower bounds were added to the original CCR odel. Values ij and y rj 0 x ij, x ij y rj, and they were known to be between and bounds (upper and lower bounds). In this case, the atheatical forulation of this Fuzzy DEA odel is (Apaydın and Güneş, 2008): ax j yrk r 1 k xik r 1 1 xij...1), j = 1,., n... (2) r, vi, r, i ax k r 1 u r y v x rk i ik...(3) j r 1 xij r, vi, r, i 1, j = 1,., n...(4) where y is the atrix of the output-vector; x is the atrix of the input-vector. Max for the upper bound and ax k gives best efficiency for the lower bound. k yields best efficiency 3. DATA The priary source of data for the epirical analysis are balance sheets, incoe stateents and other data of each insurance copany in the web page provided by The Association of the Insurance and Reinsurance Copanies of Turkey. The saple of this study includes nineteen insurance copanies operating in Turkey in the 2006 (Given in Table 1). 152 observations are used in the analysis for TABE 1. A AMPE OF TRKIH INRANCE COMPANIE ITED INRANCE COMPANIE AKİGORTA KOÇ AIANZ KOÇ AIANZ H/E AVIVA RMEİ OYAK EMEKİİK AXA OYAK YAPI KREDİ YAPIKREDİ EMEKİİK BİRİK ACIBADEM /H DEMİR HAYAT DEMİR AMERICAN IFE GENE YAŞAM ERGOİVİÇRE BİRİK HAYAT FİNAN HÜR 174

3 Total Equity / Total iabilities and Equity, Total Equity / Technical Reserves, Total Equity / Technical Reserves, iquid Assets / Total Assets ratios, oss Ratio and (Net Insurance Preiu Collections / Gross Insurance Preiu Collections) are inputs and Technical Profit / Insurance Preiu Collections, Gross Profit / Insurance Preiu Collections and Balance heet Profit / Total Technical Profit ratios are outputs in the fuzzy CCR odel. Inputs and outputs of the odel are given as follows: TABE 2. INPT AND OTPT OF THE MODE Inputs Total Equity / Total iabilities and Equity Total Equity / Technical Reserves iquid Assets / Total Assets oss Ratio (Net Insurance Preiu Collections / Gross Insurance Preiu Collections) Technical Profit / Insurance Preiu Collections Gross Profit / Insurance Preiu Collections Balance heet Profit / Total Technical Profit DEA has two liitations for the study of the reliability. If the nuber of inputs is and nuber of outputs p, the nuber of DMs will be at least +p+1. Nuber of DMs is at least twice as high as the total nubers of variables (Boussofiance, 1991). This study has five inputs and three outputs. M+p+1 is equals 9. The nuber of DMs is high than 9 (19>9). In addition the nuber of DMs is higher than the double total variables (19>16). Descriptive statistics of inputs and outputs of odel are given in Table 3. TABE 3. DECRIPTIVE TATITIC OF INPT AND OTPT (2006) Inputs Mean tandard Deviation Min Max Total Equity / Total iabilities and Equity 0, , ,284 1,179 Total Equity / Technical Reserves 0, , ,527 1,104 iquid Assets / Total Assets 0, , ,003 0,258 oss Ratio 0, , ,002 0,18 (Net Insurance Preiu Collections / Gross Insurance 2, , ,528 7,265 Preiu Collections) Technical Profit / Insurance Preiu Collections 0, , ,08 0,845 Gross Profit / Insurance Preiu Collections 1, , ,219 9,289 Balance heet Profit / Total Technical Profit 0, , ,228 0,995 Different norality tests were used in the literature. But ost norality test is hapiro-wilk test for sall to ediu sized saples (saple < 3000) according to hapiro (1968, ) and ost authors (TBB, 127; Tabachnick and Fidel, 2000; Coakes and teed, 1997). Because of this advantage of hapiro-wilk test, it was used in this study. The test statistic was clearly significant at P = 0.05 which rejects the null hypothesis that these data are fro a noral distribution. Norality test results are given in Table 4 for %5 significant degree. TABE 4. HAPIRO-WIK NORMAITY TET RET Inputs hapiro-wilk p Total Equity / Total iabilities and Equity 0,88 0,020 Total Equity / Technical Reserves 0,60 0,0001 iquid Assets / Total Assets 0,73 0,0001 oss Ratio 0,80 0,001 (Net Insurance Preiu Collections / Gross Insurance Preiu Collections) 0,86 0,011 Technical Profit / Insurance Preiu Collections 0,65 0,0001 Gross Profit / Insurance Preiu Collections 0,87 0,0125 Balance heet Profit / Total Technical Profit 0,84 0,

4 4. RET The technical efficiency scores for the upper and lower bounds are given in Table 5. In the upper and lower bounds AKİGORTA, ERGOİVİÇRE, FİNAN, HÜR, AMERİCAN İFE, BİRİK HAYAT, DEMİR HAYAT, GENE YAŞAM and YAPIKREDİ EMEKİİK are fully (relative) efficient because both the upper and lower bound scores are 1. TABE 5. TECHNICA EFFICIENCY CORE (PPER AND OWER BOND) (CCR-I) Insurance Copanies ower Bound (CCR-I) pper Bound (CCR-I) AKİGORTA 1,000 1,000 AVIVA 0,9147 0,9809 AXA OYAK 0,9652 0,9419 BİRİK 0,6939 1,000 DEMİR 0,7306 1,000 ERGOİVİÇRE 1,000 1,000 FİNAN 1,000 1,000 HÜR 1,000 1,000 KOÇ AIANZ 0,4721 0,9408 RMEİ 0,8194 0,9570 YAPI KREDİ 0,5029 1,000 ACIBADEM /H 0,7618 0,9962 AMERICAN IFE 1,000 1,0000 BİRİK HAYAT 1,000 1,0000 DEMİR HAYAT 1,000 1,0000 GENE YAŞAM 1,000 1,0000 KOÇ AIANZ H/E 0,3817 0,9000 OYAK EMEKİİK 1,000 0,8697 YAPIKREDİ EMEKİİK 1,000 1,000 Models for each inefficient DMs are ade using the data in Table 5. Below, inefficient banks for the year 2006 are classified. As can be seen in 2006, DMs of nine insurance copanies are fully efficient. The reaining ten insurance copanies are not efficient. These insurance copanies efficiency scores are easured fuzzy in bound values. EM software was used for these easureents. AVİVA : [0.9147, ] AXA OYAK : [0.9652, ] BİRİK : [0.6939, 1.000] DEMİR : [0.7306, 1.000] KOÇ AIANZ : [0.4721, ] RMEİ : [0.8194, ] YAPI KREDİ : [0.5029, 1.000] ACI BADEM /H : [0.7618, ] KOÇ AIANZ H/E : [0.3817, 0,9000] OYAK EMEKİİK : [0.8697, 1.000] We can classify these insurance copanies according to regret approach. Below is the application of the odel on one insurance copanies using bound values for the year R(AVİVA) = ax [ ax (0.9419, 1.000, 1.000, , , 1.000, , , 1.000) , 0] = R(AXA OYAK) = ax [ ax (0.9809, 1.000, 1.000, , , 1.000, , , 1.000) , 0] = R(BİRİK) = ax [ ax (0.9809, , 1.000, , , 1.000, , , 1.000) , 0] = R(DEMİR) = ax [ ax (0.9809, , 1.000, , , 1.000, , , 1.000) , 0] = R(KOC AİANZ) = ax [ ax (0.9809, , 1.000, 1.000, , 1.000, , , 1.000) , 0] = R(RMEİ) = ax [ ax (0.9809, , 1.000, 1.000, , 1.000, , , 1.000) , 0] = R(YAPI KREDİ) = ax [ ax (0.9809, , 1.000, 1.000, , , , , 1.000) , 0] = R(ACI BADEM /H) = ax [ ax (0.9809, , 1.000, 1.000, , , 1.000, , 1.000) , 0] = R(KOC AİANZ H/E) = ax [ ax (0.9809, , 1.000, 1.000, , , 1.000, , 1.000) , 0] = R(OYAK EMEKİİK) = ax [ ax (0.9809, , 1.000, 1.000, , , 1.000, , ) , 0] = AXA OYAK has the lowest score and thus is accepted as having the high efficiency in the group (ten insurance copanies). Because of this AXA OYAK is excluded fro the list. The sae ethod is applied for the reaining 9 insurance copanies, excluding the insurance copany with the lowest score each tie until two insurance copanies reain. The insurance copanies are classified through CCR-I in 2006 and the following efficiency classification is obtained: AXA OYAK > AVİVA > OYAK EMEKİİK > RMEİ > ACIBADEM /H > DEMİR > BİRİK > YAPI KREDİ > KOC AİANZ > KOÇ AİANZ H/E 176

5 5. CONCION This study easured the efficiency of insurance copanies with using Fuzzy DEA in post-crisis year, In the result ten insurance copanies (Ergoİsvçre, Finans, Hür, Aerican ife, Birlik Hayat, Deir Hayat, Genel Yaşa, Oyak Eeklilik ve Yapı Kredi Eeklilik) are fully efficient. Koç Allianz H/E is the lowest efficient insurance copany in In this paper fuzzy DEA ethod and CCR odel was used for easureent of insurance copany efficiency. Fuzzy DEA odels can play an iportant role for perceptual evaluation probles coprehensively existing in the real world, finance sectors, for exaple insurance sector. Other DEA odels will be applied in other studies. Coparison of national insurance copanies to foreign insurance copanies ay be studied in other papers. In this study one iportant and noral year data used, but this is very short period. Other studies can be used long period data. REFERENCE Apaydın, A., Günes, T., Bulanık veri zarflaa analizi tekniği ile Türkiye de birinci derece kalkına öncelikli yörelerin etkinliklerinin ölçülesi, 5. İstatistik Kongresi. Boussofiane, A., Dyson, R., Rhodes, E., 1991, Applied data envolopent analysis, European Journal of Operational Research, Vol. 2, No.6, Coakes,. J., teel,. G., P analysis without anguish, John Wiley & ons Pub. Cooper, W. W., eiford,. M., Zhu, J., Data envelopent analysis, history, odels and interpretations, in: Cooper, W. W., eiford,. M., Zhu, J. (Eds.), Handbook on Data Envelopent Analysis, Kluwer Acadeic Publishers, A, Guo, P., Tanaka, H., Fuzzy DEA: a perceptual evaluation ethod, Fuzzy and ystes, 119, (2001): Charnes A., Cooper, W. W., Rhodes, E., Measuring the efficiency of decision aking units, European Journal of Operational Research, 2, Charnes, A., Cooper, W. W., ewin, A., eiford,. M., Data Envolopent Analysis: Theory, Methodology, and Application, pringer. hapiro,.., Wilk, M. B., Chan, H. J., A coparative study of various tests for norality, JAA, V. 63, N Tabachnick, B. G., Fidel,.., 2000, sing Multivariate tatistics (4th Edition), Allyn and Bacon, Boston. TBB, Operasyonel risk ileri ölçü odelleri, Bankacılar, ayı 58, Yeldan, E., Turkey acroeconoics of post-crisis adjustents, Global Policy Network, htttp://gpn.org. 177

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