Microsoft Word - DEM_2014_105to124.docx © 2014 Nicolaus Copernicus University. All rights reserved. http://www.dem.umk.pl/dem D Y N A M I C E C O N O M E T R I C M O D E L S DOI: http://dx.doi.org/10.12775/DEM.2014.006 Vol. 14 (2014) 105−124 Submitted October 20, 2014 ISSN Accepted December 23, 2014 1234-3862 Krzysztof Kompa, Dorota Witkowska* Pension Funds in Poland: Efficiency Analysis for Years 1999–2013 A b s t r a c t. The reform of the pension system in Poland took place in 1999, when the one- pillar Pay-As-You-Go system (PAYG) was replaced by the three-pillars system consisting of two mandatory (PAYG and fully funded) pillars and voluntary (funded) one. However prob- lems concerning budget deficit in Poland caused that the Polish government introduced signif- icant changes in distribution of the pension contribution between both mandatory pillars and in the pension funds’ portfolio composition in 2011 and 2013. The aim of this study is to analyze the performance of the pension funds operating in Poland in the years 1999–2013. Applying Sharpe and Treynor ratios the study provides evidence that well diversified portfo- lio protects pensioners’ interest better than portfolios constructed due to the new rules. K e y w o r d s: pension system, pension funds, Sharpe and Treynor efficiency ratios. J E L Classification: G11, G23, H55, J26, J32. Introduction The main ideas of changes in the retirement system consist in heighten- ing the pension age and introducing funded system instead of Pay-As-You- Go system (PAYG). The most frequent reason given in the public policy debate for a funded system is the apparently superior performance of the capital market (in terms of the rate of return on investment it can offer) in comparison to the returns on PAYG pension contributions (Sinn, 2000; Feld- * Correspondence to: Krzysztof Kompa, WULS in Warsaw, Department of Econometrics and Statistics, 166 Nowoursynowska St., 02-787 Warsaw, e-mail: krzysztof_kom- pa@sggw.pl; Dorota Witkowska, University of Lodz, Department of Finance and Strategic Management, e-mail: dorota.witkowska@uni.lodz.pl. Krzysztof Kompa, Dorota Witkowska DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 106 stein, 1997). However risk of equity instruments must be also taken into account. By now it is widely accepted in most OECD countries that pension systems and rules need to be changed over time, although these changes vary from country to country. Ensuring coverage of employees through one or more pension plans is fundamental to fighting income poverty in old age. All OECD countries have set up mandatory or quasi-mandatory pension plans, either public or private, to achieve quasi-universal coverage. However, mostly in low- income countries, there is still a significant share of population not covered by public or national plans. The age at which workers can retire is the most often discussed compo- nent of a pension system. People now live longer thus it is necessary to in- crease the pension age, and to adjust women’s retirement age upwards in line with men’s age. Many OECD countries have recently done precisely that since it requires an administrative decision thus it is the easiest element of the pension scheme to change. In effect, the majority of OECD countries will have a retirement age of at least 67 years by the middle of this century. The high costs of administering private pension plans that are passed on to members have been a policy concern for many OECD countries in recent years, especially in the states where systems are mandatory or quasi- mandatory. However, administrative efficiency is also a policy priority in voluntary plans. High fees discourage workers from joining voluntary plans and make mandatory ones very costly. In fact, cost inefficiencies are a threat to the sustainability and suitability of plans themselves. Changes in the demographic structure, caused by declining fertility rates and the rise in life expectancy, lead to significant increase of the old-age- dependency ratios1 in Poland, which required a transformation of the pen- sion system. The main reform2 was implemented in 1999, introduced a new system consisted of three pillars: two mandatory ones: Pay-As-You-Go pillar (Social Insurance Institution – ZUS) and fully funded pillar (open pension funds – OFE), and a voluntary, funded pillar. The aim of our research3 is to analyze efficiency of the private pension funds, which were operating in Poland in the years 1999–2013 and compare 1 Old-age-dependency ratio is the population age 65 and over divided by population age 15-64 (Eurostat). 2 Detailed description of the pension reform can be found in Góra and Rutkowski (2000), Hausner (2002) among others. 3 Research is founded by the grant “Analysis of Open Pension Funds Market as Compared to the Open Investment Funds Market Functioning in Poland” 2013/09/B/HS4/00493 financed by National Science Center. Pension Funds in Poland: Efficiency Analysis for Years 1999–2013 DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 107 their performance to the efficiency of constructed benchmarks. We use Sharpe and Treynor ratios evaluated on the basis of monthly returns from the accounting units in the period from August 17, 1999 to October 17, 2013. The analysis is provided for the entire period and separately for the sub- periods when certain market tendency is observed (i.e. bull, bear and neutral market). 1. Changes Concerning Pension Funds Open pension funds started to operate in Poland in 1999 creating the second mandatory pillar of the “new” pension system. Each person could select only one fund and participants were able to change funds with no charge or penalty after a statutory minimum 12 months period of contribu- tion to a fund. Pension funds operate like other open-end mutual funds i.e. they collect retirement savings from employees and their employers, and invest this money in a wide range of assets. At the beginning, there were 21 OFEs but at the end of 2013 only 13 open pension funds were operating on the Polish market, and one more pension fund diapered from the market after last regulations introduced by the Polish government in 2014. In the years 1999–2013 number of participants as well as value of assets were steadily growing, at the end of December, 2013 there were more than 16.3 millions of participants and value of OFEs’ assets exceeded 299 billions PLN4. The summary of evolution of OFEs’ in Poland is presented in Table 1. Retirement savings have been created by a contribution of 12.22% of earnings (or 19.52% for employees born between 1949 and 1968 who did not choose funded tier). The contribution was credited to individuals’ no- tional accounts, while 7.3% of earnings were to be transferred to the pension funds, which created the second mandatory pillar5. There were strict regulations concerning open pension funds investment in risky assets (in order to protect pension plans’ participants). Thus during the worldwide financial crisis the losses of OFE were not as substantial as the ones reported by pension funds in developed countries. However the crisis of 2007–2009 caused some serious problems also in Polish economy. Firstly, open pension funds lost a major part of the profits earned for their members before the crisis. Secondly, slower GDP growth caused the in- crease of the public deficit and the public debenture in relation to GDP. 4 http://www.igte.com.pl/files/notowania/Dane_OFE_12_2013.pdf 5 The ceiling to contributions and pensionable earnings was set at 2.5 times average monthly earnings projected for a given year in the state budget law. Krzysztof Kompa, Dorota Witkowska DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 108 As a result, Poland has been no longer in line with the Maastricht criteria. Therefore, in the years 2011–2013 the Polish government introduced several changes in the pension system. Table 1. Basic characteristics of OFE in years 1999–2014 Year Net assets [billion PLN ] Contributions [billion PLN] Members [million] accounting unit weighting average [PLN] 1999 2.3 2.3 7.0 n.a. 2000 9.9 7.6 10.3 n.a. 2001 19.4 8.7 10.6 n.a. 2002 31.6 9.5 11.0 15.80 2003 44.8 10.3 11.5 17.58 2004 62.6 11.4 12.0 20.08 2005 86.1 14.0 11.7 23.09 2006 116.6 16.2 12.4 26.88 2007 140.0 17.7 13.1 28.55 2008 138.3 20.5 13.8 24.51 2009 178.6 21.0 14.3 27.88 2010 221.3 22.4 14.9 31.10 2011 224.7 15.1 15.5 29.56 2012 269.6 8.0 15.9 34.39 2013 299.3 10.5 16.4 36.88 2014 153.1 7.7 16.6 38.08 Note: all data are registered in December but from 2014 concerns November; http://www.mpips.gov.pl/ ubezpieczenia-spoleczne/ubezpieczenie-emerytalne/skladka-na-ubezpieczenie-emerytalne/, http://www.zus.pl/default.asp?p=2&id=1319&name=of141105.xls. The first manipulation in the original pension system was made in 2011, when the contribution transferred to pension funds was diminished from 7.3% to 2.3%. The remaining 5% was placed in a special individual sub- account. The share of contributions allocated in the sub-accounts within the Social Security Fund and in the funded scheme was to be changing until 2017, when it was to reach 3.8% and 3.5% (for ZUS and OFE accounts, respectively). However, regulation introduced in 2013 affected this scheme transferring 4.38% and 2.92% of earnings to ZUS and OFE accounts, respec- tively (affected from 2014). The new law, which went into affect in February 2014, shifted 51.5% of the assets, held by the OFEs (about 150 billion PLN) to the Social Insurance Institution, including all debt securities issued and guaranteed by the State Treasury. According to the new regulation, pension funds are no longer ob- ligatory and each employee will have four months every four years to decide whether 2.92 percent of their income goes to a chosen private fund or to Pension Funds in Poland: Efficiency Analysis for Years 1999–2013 DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 109 ZUS6. Overhaul of the pension system also concerned changes in the OFEs’ investment portfolio, since private pension funds are no longer allowed to invest in government bonds. That will leave the pension funds with most of their assets held in shares of companies listed on the Warsaw Stock Ex- change or abroad, and give them an increasingly peripheral role in the future retirement benefits of Poles. The government considered the changes (which took place in the years 2011 and 2014) necessary to lower Poland’s budget deficit. Many specialists called these changes “significant step backward”7, “un-privatizing the pen- sion system” (Hagemejer, 2013) or even “the most drastic nationalization of private assets since Soviet times”, although Polish Prime Minister Donald Tusk asserted that “it is no more than a bookkeeping change in the way to handle the public’s retirement money” (Bilefsky and Zurawik, 2013). After new regulations, at the end of November 2014 the private pension funds equaled only 153.1 billion PLN (in September 2014 it was 159 billion PLN8) and it was reported that 2.5 millions of OFE members (only 15.2% of employees) decided to stay in pension funds9. Due to Polish Financial Su- pervision Authority, the value of total contribution transferred to the pension funds in September 2013 was 1050.8 millions PLN compared to 254.3 mil- lions PLN10 in September 2014. The new regulations introduced in 2014 lead11 to a change in the composition of assets’ portfolios managed by OFEs 6 For the first time, employees had to decide till the end of July, 2014 if they stay in the private pension fund by filling and sending to ZUS special form, when the form was not sent the employee was automatically excluded from OFE. 7 David McMillan, chief executive of AVIVA Europe in London, which manages a pri- vate pension fund in Poland with 17.5 billion euros in assets (Bilefsky and Zurawik, 2013). 8 http://www.analizy.pl/fundusze/wiadomosci/17222/aktywa-funduszy-emerytalnych-%28 wrzesien-2014%29.html 9 It is considered as a very good result for OFE since the previous forecasts evaluated that only 5% of employed stay in OFE. 10 http://www.knf.gov.pl/opracowania/rynek_emerytalny/dane_o_rynku/rynek_ofe/Dane_ miesieczne/dane_miesieczne_ofe.html. 11 New regulations also include the following changes: (1) gradual transfer of each per- son’s retirement funds managed by OFE to ZUS, which will start ten years before reaching retirement age; (2) automatic transfer of retirement contributions to ZUS, instead of OFE, unless an individual OFE member files a declaration (first time-slot will be between 1 April and 31 July 2014) requesting his/her contributions be transferred to OFE; (3) decrease of the maximum fee OFE can charge from contributions from 3.5% to 1.75%; (4) value of certain categories of assets in OFEs portfolio (i.e. investment certificates issued by closed-end funds, units of open-ended funds or specialized open-ended funds, or units issued by foreign collec- tive investment undertakings of the closed or open-ended type) will not be included in the Krzysztof Kompa, Dorota Witkowska DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 110 not only due to the forced transfer of assets to ZUS but also due to new rules applicable to OFE investment activities. According to the Polish Financial Supervision Authority, shares of treasury bonds and equity instruments in the OFEs’ portfolios in 2013 were the biggest among all instruments and nearly equal (42% and 43%, respectively). In addition to the management of the fund, the market conditions deter- mine the performance of the investment portfolio. In the analyzed period (i.e. the years 1999–2013) the situation of the Polish economy (and the fi- nancial market) was changing from high rate of the Polish GDP growth and bull market to recession and bear market in Warsaw Stock Exchange (see Figure 1, which contains comparison of rates of return generated by equity market, represented by the Warsaw Stock Exchange index WIG and OFE in investigated years). Figure 1. Cumulative annual returns from OFE and WIG in years 1999–2007 Note: to Figure 1. Own evaluation on the basis of http://www.nbp.pl/publikacje/operacje_or/2012/ raport2012.pdf and http://www.gpw.pl/analizy_i_statystyki_pelna_wersja. Another important aspect of the introduced changes is how the pension fund reform will affect the Polish capital market since the increasing capital- ization of pension funds made them one of the most important institutional investors generated from 16% to 22% of the Warsaw Stock Exchange turno- ver among all institutional investors in the years 2005–2010 (Marcinkiewicz, overall value of total net assets managed by OFE, which means that OFEs may not charge a management fee from these assets. 50 100 150 200 250 300 350 OFE WIG Pension Funds in Poland: Efficiency Analysis for Years 1999–2013 DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 111 2011). Smaller contribution to the pension funds will cause the decrease of the investment level. There is also a danger associated with the changes that the risk of investing in Poland has increased. The private funds hold assets worth about $92 billion, i.e. more than one- fifth of Poland’s gross domestic product, and are among the biggest inves- tors on the Warsaw Stock Exchange (Bilefsky and Zurawik, 2013). Also, due to high market concentration, there is a lack of price and investment competition between Open Pension Funds. In 2011, the OFEs’ commission equaled 553 millions PLN while wages for management totaled 981 millions PLN12. Such situation created broadly critique of pension funds in Poland. As a result of the widespread resentment, Polish government introduced the new pension law. It was estimated that the transfer of 51.5% of OFEs‘ assets would lead to a decrease of public debt in Poland from around 55% GDP to 47% GDP. This is the main short-term purpose of the reform, rather than providing improved financial security for retirees (Mrowiec and Mruk- Zawirski, 2014). 2. Methodology and Data Applied in Research The aim of the research is to analyze performance of the private pension funds. The investigation is provided for the accounting units of eleven pri- vate pension funds that have been operating in Poland from August 17, 1999 to October 17, 2013. These open pension funds contain 85% of all pension funds’ members and 88% net assets (Table 2). Comparison of analyzed funds at the end of July in the years 2013 and 2014 shows that position of particular pension funds on the market did not change however the values of accounting units and 3-year returns increased in 2014 in comparison to the previous year. Values of the accounting units are quite similar and the range is only 5.8 and 6.4 PLN in 2013 and 2014 (i.e. 16.5% and 17.8% of average, respectively). The weighted average of accounting units increased by 2.3% in 2014 in comparison to 2013. Rates of return exhibit more variation since the range is about 32% of the weighted average in both years and they in- creased in average by 23.8% in 2014 in comparison to returns obtained in the previous year. 12 See Forbes (2012). Krzysztof Kompa, Dorota Witkowska DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 112 Table 2. Main characteristics of the analyzed pension funds measured on July, 31, 2013 and 2014 Pension funds names Percentage share of the market Accounting unit [PLN] 3-year rates of return [%] Total returns [%] Members Net assets 2013 2014 2013 2014 2013 2014 2013 2014 2015 AEGON 5.81 5.62 4.24 4.26 33.56 34.56 15.27 18.68 260.1 ALLIANZ 3.43 4.01 3.04 3.08 33.18 33.99 19.13 21.22 254.9 AVIVA 16.49 16.05 22.38 22.29 34.25 35.16 17.23 19.95 266.6 AXA 7.17 6.97 6.27 6.32 34.40 35.32 16.29 19.62 270.1 GENERALI 6.23 6.05 5.03 5.02 35.90 36.39 14.76 19.45 279.9 ING 18.83 18.45 23.99 23.98 37.63 38.31 17.98 21.79 295.1 NORDEA 5.48 5.98 4.52 4.55 36.39 37.32 19.05 24.28 291.1 PEKAO 2.11 2.05 1.50 1.51 32.74 33.47 14.64 18.71 244.6 POCZTYLION 3.67 3.56 1.90 1.88 31.83 31.91 13.77 17.53 234.4 PZU 13.73 13.40 13.42 13.40 34.74 35.68 15.38 19.61 265.6 WARTA 1.92 2.50 1.34 1.35 35.33 36.04 16.82 20.34 292.3 Total 84.87 84.64 87.63 87.64 35.15* 35.95* 16.64** 20.60** Note: Total returns denotes rate of return from the whole period i.e. from the first day of the pension fund operating till Jan. 29, 2015; * denotes weighted averages in considered period, ** weighted averages evaluated for the period 31.03.2010–29.03.2013, and 31.03.2011–31.03.2014, respectively (http://www.igte.com.pl/files/notowania/Dane_OFE_07_2013.pdf). The first stage of the research is statistical analysis of 6-months sub- periods. In the second stage, we consider daily registered monthly logarith- mic rates of return from the accounting units in the entire period of analysis and five sub-periods due to the situation on the Warsaw Stock Exchange i.e. stock index WIG daily quotations: 17.09.1999–20.11.2003 stagnation 1 (1055 observations), 21.11.2003–06.07.2007 bull market 1 (912 observations), 07.07.2007–17.02.2009 bear market (403 observations), 18.02.2009–18.07.2011 bull market 2 (609 observations), 19.07.2011–17.10.2013 stagnation 2 (564 observations). Sharpe and Treynor ratios are evaluated for all pension funds and their per- formance is compared to the efficiency of constructed benchmarks. Treasury Bonds represent the risk free instrument. Portfolios performance usually is measured by comparing their rates of return and risk measures. The former seem to be the most important for the pension funds participants when they select the pension funds. Our study tests several hypotheses in order to find out if the expected value of the ana- lyzed rates of return and their variances significantly differ from the bench- marks. We start from verifying the hypothesis if expected returns differ from zero: Pension Funds in Poland: Efficiency Analysis for Years 1999–2013 DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 113 0)(:0 pREH (1) using well-known test statistics: .T S R u p p (2) To test the significance of differences between expected rates of return generating by pension funds and the benchmarks: Bp RREH )(:0 (3) we employ the following test statistics: ,T S RR u p Bp  (4) where: )( pRE – expected rate of return of the analyzed open pension fund, ,pR BR – average rates of return of the analyzed portfolio and the bench- mark, pS – standard deviation of rates of return generated by the pension fund, T – number of observations, u is normally distributed statistics. In the next step we test equality of the pension fund’s and benchmark’s variances. The null hypothesis is: 22 0 )(: Bp SRDH  (5) and the test statistics is defined as: , 2 2 2 B p S ST   (6) ,1)1(22 2  Tu  (7) where: )(2 pRD – variance of the portfolio, BS – standard deviation of rates of return generated by the benchmark, other symbols are described above. Various researchers who have highlighted numerous factors influencing the portfolio performance have documented investment efficiency. The two Krzysztof Kompa, Dorota Witkowska DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 114 traditional measures of the portfolio performance are the Treynor and the Sharpe indexes13: , p fp p S RR WS   (8) , p fp p RR WT    (9) where: pWS and pWT – Sharpe and Treynor ratios, respectively, ,pR fR – average returns from the analyzed portfolio and the risk free instrument, respectively, p – beta coefficient from the single-index model (also called Sharpe’s model14) estimated separately for each pension fund: ,tBtppt eRR   (10) where: ,ptR BtR – returns from pension funds and benchmark observed in the period t. Significance of beta coefficient, i.e. * 0 :  pH (11) can be tested using the test statistics: , * p S b t p    (12) where: t – t-Student statistics, pb – parameter estimates of , pS – stand- ard error, 0*  or 1. Ratios (8) and (9) are compared to the efficiency measures evaluated for the constructed benchmarks, BWS and .BWT Application of these traditional efficiency measures requires selection of the representative market index and risk-free instrument. We assumed the significance level of 0.05 for all tests. 13 Sharpe and Treynor ratios are composite measure of portfolio performance that also in- cluded risk, for details see: Treynor (1965), Sharpe (1966). Application of Sharpe index to evaluate the private pension funds efficiency is presented in Antolin (2008). 14 Discussion about Sharpe’s model estimated for Polish capital market can be found in Tarczyński et al. (2013) among others. Pension Funds in Poland: Efficiency Analysis for Years 1999–2013 DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 115 3. Empirical analysis In the first stage of research the logarithmic rates of return from of 6- months sub-periods are analyzed. We distinguish 27 such time spans from January 1, 2000 to June 30, 2013 (denoted as P2–P28) and two shorter peri- ods (P1: 17.09.1999–31.12.1999 and P29: 1.07.2013–17.10.2013). P30 de- notes the entire period of investigation. For all analyzed pension funds and for hypothetical portfolios rates of return are evaluated. Table 3a. Rates of returns No. End of the period AEGON ALL AVIVA AXA GEN ING NOREA POC P1 31.12.1999 0.0903 0.0764 0.1058 0.0591 0.0628 0.0777 0.0909 0.0796 P2 30.06.2000 0.0755 0.1026 0.0531 0.0981 0.0796 0.0874 0.0502 0.0888 P3 29.12.2000 0.0337 0.0194 0.0471 0.0281 0.0555 0.0591 0.0438 0.0483 P4 29.06.2001 –0.0452 –0.0350 –0.0170 –0.0187 –0.0433 –0.0336 –0.0177 –0.0476 P5 31.12.2001 0.0809 0.1064 0.1131 0.0951 0.1003 0.1072 0.1126 0.0722 P6 28.06.2002 0.0535 0.0643 0.0562 0.0473 0.0543 0.0786 0.0717 0.0388 P7 31.12.2002 0.0693 0.0662 0.0513 0.0485 0.0617 0.0829 0.0669 0.0539 P8 30.06.2003 0.0504 0.0510 0.0428 0.0456 0.0545 0.0547 0.0495 0.0446 P9 31.12.2003 0.0488 0.0545 0.0561 0.0509 0.0591 0.0552 0.0600 0.0578 P10 30.06.2004 0.0423 0.0452 0.0399 0.0553 0.0506 0.0351 0.0361 0.0455 P11 31.12.2004 0.0848 0.0608 0.0814 0.0865 0.0859 0.0863 0.0779 0.0816 P12 30.06.2005 0.0536 0.0487 0.0655 0.0572 0.0580 0.0702 0.0540 0.0520 P13 31.12.2005 0.0663 0.0525 0.0738 0.0701 0.0763 0.0764 0.0678 0.0789 P14 30.06.2006 0.0374 0.0580 0.0441 0.0410 0.0568 0.0453 0.0454 0.0599 P15 29.12.2006 0.0995 0.0900 0.0971 0.1049 0.1086 0.1066 0.0964 0.0979 P16 29.06.2007 0.1018 0.1102 0.1076 0.1062 0.0918 0.0951 0.1047 0.0967 P17 28.12.2007 –0.0484 –0.0479 –0.0429 –0.0480 –0.0381 –0.0475 –0.0548 –0.0579 P18 30.06.2008 –0.0904 –0.0841 –0.0936 –0.0823 –0.0855 –0.0932 –0.0807 –0.0810 P19 31.12.2008 –0.0449 –0.0363 –0.0642 –0.0445 –0.0510 –0.0565 –0.0498 –0.0468 P20 30.06.2009 0.0294 0.0226 0.0147 0.0283 0.0377 0.0213 0.0252 0.0292 P21 31.12.2009 0.0932 0.0953 0.0990 0.0922 0.0961 0.0994 0.0865 0.0879 P22 30.06.2010 0.0138 0.0174 0.0206 0.0201 0.0173 0.0221 0.0271 0.0210 P23 31.12.2010 0.0779 0.0843 0.0846 0.0750 0.0692 0.0877 0.0842 0.0822 P24 30.06.2011 0.0185 0.0266 0.0212 0.0205 0.0196 0.0261 0.0256 0.0183 P25 30.12.2011 –0.0689 –0.0742 –0.0704 –0.0560 –0.0618 –0.0734 –0.0671 –0.0824 P26 29.06.2012 0.0466 0.0547 0.0533 0.0439 0.0459 0.0550 0.0596 0.0471 P27 28.12.2012 0.1011 0.1059 0.0955 0.0906 0.0901 0.0934 0.1025 0.0912 P28 28.06.2013 –0.0206 –0.0123 –0.0110 –0.0083 –0.0123 –0.0052 0.0008 –0.0039 P29 17.10.2013 0.0760 0.0765 0.0803 0.0737 0.0789 0.0850 0.0796 0.0813 P30 17.10.2013 1.1671 1.2454 1.2501 1.2213 1.2681 1.3210 1.2669 1.1773 Note: description of abbreviations: ALL means ALLIANZ, GEN – GENERALI, POC – POCZTYLION. Considered returns generated by pension funds in analyzed intervals (Tables 3a and 3b) we notice that in general all of them show similar per- Krzysztof Kompa, Dorota Witkowska DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 116 formance. Negative returns are observed only in the following periods: 02.01.2001–29.06.2001, 29.06.2007–31.12.2008, 01.07.2011–30.12.2011, and 02.01.2013–28.06.2013 (except NORDEA in the period P28). Table 3b. Rates of returns No. End of the period PEKAO PZU WARTA Average Bond WIG WIBOR P1 31.12.1999 0.0669 0.0738 0.1101 0.0814 –0.0071 0.0921 0.4291 P2 30.06.2000 0.0611 0.0663 0.0648 0.0751 0.0112 0.0342 –0.1283 P3 29.12.2000 0.0187 0.0300 0.0793 0.0425 –0.0102 –0.0904 0.0793 P4 29.06.2001 –0.0228 –0.0291 –0.0575 –0.0336 –0.0196 –0.2369 –0.1942 P5 31.12.2001 0.1131 0.1223 0.0774 0.0999 –0.0265 0.0072 –0.2891 P6 28.06.2002 0.0312 0.0648 0.0536 0.0561 0.0000 0.0140 –0.2609 P7 31.12.2002 0.0379 0.0752 0.0433 0.0600 0.0324 0.0138 –0.2663 P8 30.06.2003 0.0471 0.0532 0.0524 0.0497 0.0359 0.1061 –0.2586 P9 31.12.2003 0.0538 0.0604 0.0664 0.0567 –0.1041 0.2790 0.0187 P10 30.06.2004 0.0673 0.0486 0.0635 0.0479 –0.0505 0.1173 0.0721 P11 31.12.2004 0.0836 0.0814 0.0788 0.0809 0.1059 0.1086 0.1144 P12 30.06.2005 0.0495 0.0570 0.0548 0.0566 0.0800 0.0590 –0.2648 P13 31.12.2005 0.0604 0.0670 0.0750 0.0697 –0.0267 0.2183 –0.0933 P14 30.06.2006 0.0708 0.0479 0.0598 0.0513 –0.0284 0.1201 –0.1102 P15 29.12.2006 0.1174 0.1092 0.0992 0.1025 0.0276 0.2125 0.0000 P16 29.06.2007 0.1423 0.1097 0.0966 0.1055 –0.0249 0.2550 0.1189 P17 28.12.2007 –0.0759 –0.0457 –0.0630 –0.0517 –0.0188 –0.1651 0.1805 P18 30.06.2008 –0.0963 –0.1033 –0.0904 –0.0893 –0.0267 –0.2996 0.1507 P19 31.12.2008 –0.0553 –0.0403 –0.0560 –0.0497 0.0608 –0.3968 –0.1176 P20 30.06.2009 0.0236 0.0136 0.0211 0.0243 –0.0183 0.0711 –0.3913 P21 31.12.2009 0.0997 0.1038 0.0960 0.0954 0.0061 0.2646 –0.0053 P22 30.06.2010 0.0201 0.0195 0.0253 0.0204 0.0192 –0.0345 –0.0190 P23 31.12.2010 0.0775 0.0854 0.0766 0.0804 0.0010 0.1876 0.0055 P24 30.06.2011 0.0219 0.0185 0.0235 0.0219 0.0000 0.0085 0.2357 P25 30.12.2011 –0.0788 –0.0748 –0.0685 –0.0704 0.0035 –0.2557 0.0320 P26 29.06.2012 0.0488 0.0474 0.0510 0.0503 0.0050 0.0630 0.0289 P27 28.12.2012 0.0953 0.0937 0.0950 0.0958 0.0082 0.1565 –0.1514 P28 28.06.2013 –0.0109 –0.0047 –0.0093 –0.0088 –0.0084 –0.0724 –0.4126 P29 17.10.2013 0.0845 0.0814 0.0824 0.0800 –0.0047 0.1607 –0.0561 P30 17.10.2013 1.1941 1.2483 1.2485 1.2379 0.0244 1.1593 –1.6368 Similar, to some extend, tendencies can be observed in the bond, equity and money market (Table 3b). Negative returns appear in the mentioned above periods (except WIBOR in P17, P18, and P25 and bonds in P19 and P25). However negative rates of return are observed additionally in follow- ing periods: for bond market: P1, P3, P5, P9, P10, P13, P14, P16, P20, P29; for WIBOR: P2, P5–P8, P12–P14, P20–P22, P27, P29 and the entire period of analysis P30. WIG generates negative returns in P22. To summarize, Pension Funds in Poland: Efficiency Analysis for Years 1999–2013 DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 117 among 29 considered sub-periods, pension funds generated negative returns in 6 periods, WIG in 8, bonds in 14 and WIBOR in 16 periods. Table 4. The structure of the hypothetical portfolios Asset representative Structure of the portfolios OFE due to The regulation from Kompa & Wiśniewski (2014) 1997 Dec., 6, 2013 PORTFOLIO 1 PORTFOLIO 2 PORTFOLIO 3 Bond market: Treasury Bonds 42% – 30% Equity market: WIG 46% 79% 70% Monetary market: WIBOR 12% 21% – To analyze efficiency of the pension funds we construct three hypothet- ical portfolios employing aggregate measures of equity, money and bond markets. They are represented by WIG (Warsaw Stock Exchange Index), WIBOR (Warsaw Interbank Offered Rate) and Treasury Bonds, respective- ly. These portfolios, are treated as market benchmarks in evaluation of the pension funds performance. The idea of the portfolio structures (presented in Table 4) is to illustrate changes concerning the structure of the pension fund portfolios due to regulations from 1997 and 2013. The first portfolio is con- structed due to the regulation from 199715, the second one – due to the regu- lation from Dec. 6, 201316 while the third one is the optimal portfolio struc- ture, which was simulated by Kompa, Wiśniewski, (2014), Kompa, (2014) assuming that the portfolio contains only two types of assets. Next we test hypotheses that expected returns obtained in 6 months peri- ods are significantly different from zero (Table 5). The analysis is provided for selected pension funds and three benchmarks. The positive expected rates of return are denoted by “+”, negative by “–“, and blank cells denote the situation when the null hypothesis could not be rejected at the significance level 0.05. As one can notice most funds generated positive returns in the majority of periods. There are only 4 periods when all pension funds and created portfolios generated loses, i.e. from July 1, 2007 to December 31, 2008 and from July 1, to December 31, 2011. In fact, pension funds per- formed better than constructed benchmarks. 15 File:///D:/Katalogi%20robocze/archiwum%20Dorota/Rok%202014/OFE/Ustawa%20o %20OFE.pdf. 16 http://orka.sejm.gov.pl/opinie7.nsf/nazwa/1946_u/$file/1946_u.pdf. Krzysztof Kompa, Dorota Witkowska DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 118 Table 5. Verification hypothesis of expected returns (1)–(2) No. Port.1 Port.2 Port.3 AEG ALL AVI AXA GEN ING NOR PEK POC PZU WAR P1 + + + + + + + + + + + + + P2 + + + + + + + + + + + + + + P3 – – – + – + + P4 – – – + + P5 – – + + + + + + + + + + + P6 + + + + + + + + + + + + P7 – – + + + + + + + + + + + P8 + + + + + + + + + + + + + P9 + + + + + + + + + + + + + + P10 + + + + + + + + + + + + + + P11 + + + + + + + + + + + + + + P12 + + + + + + + + + + + + P13 + + + + + + + + + + + + + + P14 + + + + + + + + + + + + + P15 + + + + + + + + + + + + + + P16 + + + + + + + + + + + + + + P17 – – – – – – – – – – – – – – P18 – – – – – – – – – – – – – – P19 – – – – – – – – – – – – – – P20 + + + + + + + + + + + + P21 + + + + + + + + + + + + + + P22 + + + + + + + + + + + + P23 + + + + + + + + + + + + + + P24 + + + + + + + + + + + + + + P25 – – – – – – – – – – – – – – P26 + + + + + + + + + + + P27 + + + + + + + + + + + + + + P28 – – + + + + + + + + + + + P29 + + + + + + + + + + + + + + Note: description of abbreviations: Port.1 – Portfolio1, Port.2 – Portfolio2, Port.3 – Portfolio3, AEG – AEGON, ALL – ALLIANZ, AVI – AVIVA, GEN – GENERALI, NOR – NORDEA, PEK – PEKAO, POC – POCZTYLION, WAR – WARTA. The conclusion is supported by the tests (3)–(4) and (5)–(7) in the whole analyzed period (i.e. for P30). Table 6 demonstrates that returns from the pension portfolios exceed benchmarks, and variances of all portfolios are smaller than the benchmarks’ ones. Therefore, it can be concluded that the open pension funds investment policy was relatively well established. That type of analysis is also provided for the all sub-periods P1–P29. Results pre- sented in Table 7 indicate “+” if value of expected returns or variance gener- ated by pension funds is higher than the ones obtained from benchmarks; “–“ the opposite situation and “0” – when null hypotheses cannot be rejected. In general, majority of the OFEs’ performance was not worse than constructed portfolios. Expected returns of pension funds are significantly higher than Pension Funds in Poland: Efficiency Analysis for Years 1999–2013 DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 119 returns generated by considered benchmarks in 59% of cases for the portfo- lio 1, in 47% of cases for the portfolio 2, and in 42% of cases in comparison to the last benchmark. For all pension funds, variance of returns (that de- scribe risk) is significantly smaller than the one estimated for the portfolios 2 and 3 while in comparison with variability of returns of the portfolio 1 it is usually smaller. Table 6. Values of the test statistics Hypotheses )()(:0 Bp REREH  2 0 2 0 )(: pRDH Portfolio no. Portfolio no. 1 2 3 1 2 3 AEGON 13.58 10.06 5.87 –29.86 –51.17 –46.86 ALLIANZ 14.96 11.43 7.22 –30.01 –51.27 –46.97 AVIVA 13.73 10.50 6.65 –24.98 –48.21 –43.51 AXA 14.60 11.10 6.87 –29.96 –51.24 –46.93 GENERALI 14.65 11.30 7.30 –27.27 –49.60 –45.08 ING 13.82 10.81 7.22 –20.70 –45.6 –40.57 NORDEA 15.12 11.62 7.46 –29.47 –50.94 –46.59 POCZTYLION 12.78 9.52 5.62 –25.69 –48.65 –44.00 PEKAO 13.28 9.97 6.02 –26.51 –49.14 –44.56 PZU 14.07 10.76 6.81 –26.44 –49.10 –44.51 WARTA 13.57 10.38 6.57 –24.29 –47.79 –43.04 Table 7. Comparison of expected returns and risk in analyzed periods P1–P29 Hypotheses )()(:0 Bp REREH  20 2 0 )(: pRDH Portfolio no. Portfolio no. 1 2 3 1 2 3 + – 0 + – 0 + – 0 + – 0 + – 0 + – 0 AEGON 16 6 7 14 11 4 11 13 5 0 28 1 0 29 0 0 29 0 ALLIANZ 17 7 5 14 10 5 14 13 2 0 26 3 0 29 0 0 29 0 AVIVA 15 5 9 14 11 4 12 13 4 0 25 4 0 29 0 0 29 0 AXA 16 7 6 14 11 4 11 13 5 0 28 1 0 29 0 0 29 0 GENERALI 17 6 6 15 11 3 11 12 6 0 26 3 0 29 0 0 29 0 ING 17 5 7 13 11 5 14 13 2 2 23 4 0 29 0 0 29 0 NORDEA 17 4 8 13 10 6 13 14 2 0 28 1 0 29 0 0 29 0 POCZTYLION 18 6 5 14 11 4 11 12 6 1 26 2 0 29 0 0 29 0 PEKAO 20 7 2 13 11 5 12 13 4 0 26 3 0 29 0 0 29 0 PZU 17 3 9 13 11 5 13 13 3 0 28 1 0 29 0 0 29 0 WARTA 19 5 5 13 11 5 13 12 4 1 25 3 0 29 0 0 29 0 Percentage share 59 19 22 47 37 16 42 44 13 1 91 8 0 100 0 0 100 0 In the second stage of our research we investigate daily registered monthly logarithmic rates of return from the accounting units in the entire period of analysis and five sub-periods. Krzysztof Kompa, Dorota Witkowska DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 120 Table 8. Beta estimates Pension funds AEG ALL AVI AXA GEN ING NOR POC PEK PZU WAR Period Portfolio no. 1 S1 0.483 0.483 0.589 0.507 0.578 0.610 0.456 0.595 0.525 0.463 0.610 Bull1 0.645 0.585 0.641 0.626 0.633 0.698 0.651 0.634 0.631 0.671 0.628 Bear 0.600 0.546 0.660 0.585 0.574 0.674 0.607 0.591 0.585 0.660 0.607 Bull 2 0.542 0.539 0.588 0.546 0.584 0.617 0.544 0.555 0.571 0.636 0.578 S2 0.762 0.773 0.765 0.671 0.742 0.783 0.759 0.778 0.797 0.784 0.748 Period Portfolio no. 2 S1 0.312 0.315 0.380 0.326 0.375 0.402 0.298 0.386 0.339 0.300 0.390 Bull1 0.405 0.379 0.404 0.395 0.400 0.436 0.415 0.401 0.408 0.426 0.403 Bear 0.359 0.326 0.399 0.350 0.346 0.403 0.365 0.353 0.352 0.396 0.365 Bull 2 0.339 0.335 0.365 0.337 0.363 0.382 0.338 0.344 0.354 0.393 0.359 S2 0.441 0.447 0.443 0.389 0.429 0.453 0.440 0.452 0.462 0.454 0.434 Period Portfolio no. 3 S1 0.368 0.371 0.442 0.387 0.438 0.471 0.348 0.454 0.398 0.361 0.456 Bull1 0.465 0.426 0.465 0.450 0.457 0.506 0.472 0.460 0.454 0.484 0.458 Bear 0.435 0.396 0.476 0.424 0.416 0.489 0.439 0.428 0.427 0.476 0.439 Bull 2 0.380 0.372 0.405 0.379 0.405 0.425 0.376 0.387 0.395 0.439 0.400 S2 0.506 0.514 0.507 0.446 0.492 0.523 0.506 0.521 0.532 0.523 0.498 Note: description of abbreviations: S – Stagnation, Bull – bullish market, Bear – bearish market, AEG – AEGON, ALL – ALLIANZ, AVI – AVIVA, GEN – GENERALI, NOR – NORDEA, PEK – PEKAO, POC – POCZTYLION, WAR – WARTA. Table 9. Sharpe and Treynor ratios: hypothetical portfolios Portfolio 1 Ratios Portfolio 2 Ratios Portfolio 3 Ratios Period Sharpe Treynor Sharpe Treynor Sharpe Treynor S 1 0.027 0.001 0.026 0.002 0.085 0.005 Bull 1 0.400 0.011 0.456 0.020 0.472 0.019 Bear –0.565 –0.026 –0.607 –0.045 –0.614 –0.040 Bull 2 0.390 0.012 0.419 0.020 0.413 0.018 S 2 –0.067 –0.002 –0.069 –0.003 0.034 0.001 Note: description of abbreviations: S – Stagnation, Bull – bullish market, Bear – bearish market. Applying tests (3)–(7) for the time series representing logarithmic re- turns in distinguished sub-periods: S1 – stagnation 1, Bull1 – bull market 1, Bear – bear market, Bull2 – bull market 2 and S2 – stagnation 2, we found out that pension funds are characterized by smaller risk in all considered sub-periods. While expected returns are significantly smaller than the ones generated by benchmarks only during two bull market periods, although if the portfolio 1 is taken into account also in these sub-periods some of pen- sion funds generated returns insignificantly smaller than the benchmark (AEGON, AVIVA, AXA, GENERALI, ING, POCZTYLION, PZU, WAR- TA in bull market 1 period, ING and PZU in bull market 2 period), while Pension Funds in Poland: Efficiency Analysis for Years 1999–2013 DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 121 PEKAO’s returns were significantly higher than portfolio 1 in the bull mar- ket 1 period. Table 10. Sharpe ratios: pension funds Period AEG ALL AVI AXA GEN ING NOR POC PEK PZU WAR S 1 0.522 0.531 0.494 0.487 0.476 0.463 0.587 0.413 0.394 0.551 0.434 Bull 1 0.548 0.562 0.569 0.607 0.607 0.529 0.527 0.579 0.676 0.561 0.608 Bear –0.454 –0.460 –0.468 –0.445 –0.457 –0.434 –0.463 –0.461 –0.538 –0.435 –0.497 Bull 2 0.577 0.599 0.565 0.580 0.559 0.561 0.596 0.571 0.579 0.521 0.571 S 2 0.230 0.259 0.249 0.282 0.253 0.260 0.298 0.221 0.236 0.236 0.266 Note: description of abbreviations: S – Stagnation, Bull – bullish market, Bear – bearish market, AEG – AEGON, ALL – ALLIANZ, AVI – AVIVA, GEN – GENERALI, NOR – NORDEA, PEK – PEKAO, POC – POCZTYLION, WAR – WARTA. Table 11. Treynor ratios for pension funds portfolio 1 is the market benchmark in the Sharpe model Period AEG ALL AVI AXA GEN ING NOR POC PEK PZU WAR S 1 0.025 0.027 0.023 0.024 0.022 0.023 0.029 0.020 0.021 0.028 0.021 Bull 1 0.016 0.017 0.017 0.018 0.018 0.016 0.016 0.017 0.020 0.017 0.018 Bear –0.022 –0.023 –0.023 –0.022 –0.022 –0.021 –0.023 –0.023 –0.027 –0.022 –0.025 Bull 2 0.018 0.019 0.018 0.018 0.018 0.018 0.019 0.018 0.018 0.016 0.018 S 2 0.007 0.008 0.007 0.008 0.007 0.008 0.009 0.006 0.007 0.007 0.008 portfolio 2 is the market benchmark in the Sharpe model Period AEG ALL AVI AXA GEN ING NOR POC PEK PZU WAR S 1 0.038 0.042 0.035 0.037 0.034 0.035 0.045 0.030 0.033 0.043 0.032 Bull 1 0.026 0.026 0.027 0.028 0.028 0.025 0.024 0.027 0.031 0.026 0.029 Bear –0.037 –0.038 –0.038 –0.037 –0.037 –0.036 –0.038 –0.038 –0.045 –0.036 –0.041 Bull 2 0.030 0.031 0.029 0.030 0.028 0.029 0.031 0.029 0.029 0.027 0.029 S 2 0.012 0.013 0.012 0.014 0.013 0.013 0.015 0.011 0.012 0.012 0.013 portfolio 3 is market benchmark in the Sharpe model Period AEG ALL AVI AXA GEN ING NOR POC PEK PZU WAR S 1 0.032 0.036 0.030 0.031 0.029 0.030 0.039 0.026 0.028 0.036 0.028 Bull 1 0.022 0.023 0.023 0.025 0.025 0.022 0.021 0.024 0.028 0.023 0.025 Bear –0.031 –0.032 –0.032 –0.030 –0.031 –0.030 –0.032 –0.031 –0.037 –0.030 –0.034 Bull 2 0.026 0.028 0.026 0.027 0.025 0.026 0.028 0.026 0.026 0.024 0.026 S 2 0.010 0.011 0.011 0.012 0.011 0.011 0.013 0.010 0.010 0.010 0.012 Note: description of abbreviations: S – Stagnation, Bull – bullish market, Bear – bearish market, AEG – AEGON, ALL – ALLIANZ, AVI – AVIVA, GEN – GENERALI, NOR – NORDEA, PEK – PEKAO, POC – POCZTYLION, WAR – WARTA. The efficiency of the pension funds is measured using Sharpe and Trey- nor ratios (8) and (9). To evaluate Treynor ratios three versions of single- index models (10) for each pension fund and every considered sub-period are estimated. These models differ by the market indexes, which are repre- Krzysztof Kompa, Dorota Witkowska DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 122 sented by constructed portfolios. In our research we employ OLS method17. The parameter estimates obtained for three hypothetical benchmarks are presented in Table 8, all betas are significantly higher than zero and smaller than one. Tables 9 and 10 present results that all pension funds are more effective than constructed benchmarks in terms of Sharpe ratios. Treynor measures evaluated for pension funds are higher than the ones calculated for the mar- ket benchmarks in all analyzed sub-periods, except bear market for the pen- sion fund PEKAO and portfolios 1 and 2 (Tables 11). In other words, anal- yses of efficiency measures calculated for the hypothetical portfolios shows that portfolio 3 seems to be the most effective especially in terms of Sharpe ratio. Conclusions Demographic structure of the Polish population has been changing that causes the increase of old age dependency ratio from 15.26 in 1989 to 17.75 in 1999, and 19.32 in 2011. Therefore, general reform of the pension system was necessary and it took place in Poland in the year 1999, replacing the Pay-As-You-Go system, by the three-pillars partly funded system. Under the system introduced in Poland in 1999, two pillars were universal and manda- tory, and the third one – voluntary. The first pillar remained to be Pay-As- You-Go financed, whereas the second and third pillars were to be funded. In fact, the “old” PAYG system was downsized and converted to a “notional defined-contribution” system, forming the new first pillar governed by the Social Insurance Institution. In both mandatory pillars, contributions were registered in individual accounts, and the pension benefits depended on con- tributions paid, not contributions that were due. After the subprime crisis, because of the increase of the budget deficit, Polish government introduced the new regulations in the pension system in 2011 and 2013. The most important move was shifting 51.5% of the assets held by the OFEs to the state-run PAYG pension system – ZUS (affected from February 2014). Other changes consisted in changes in:  the retirement age (it has been increasing by a month each quarter begin- ning from the first quarter of year 2013), 17 Discussion of beta estimation has been provided by many researches all around the world however our previous research shows that OLS method is appropriate to this purpose (see: Tarczyński, Witkowska, Kompa, 2013). Pension Funds in Poland: Efficiency Analysis for Years 1999–2013 DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 123  the share of the contribution of earnings that is saved in both mandatory pillars (affected from May 2011),  the role of the mandatory funded pillar that became voluntary (affected from August 2014),  the scheme of investments i.e. the pension funds’ portfolio composition, especially prohibition of investing in debt securities issued and guaran- teed by the State Treasury (beginning from 2014). The research, presented in the paper, shows that the performance of pen- sion funds was better than the constructed benchmarks, regardless the gen- eral situation in the capital market. It proves that diversified (as it was stated in 1999) portfolio better protects pensioner’s interest than portfolios with limited types of financial instruments. It can be noticed also by analyzing accounting units (Table 1), which have been systematically increasing. It proves that new regulations, especially the one concerning structure of the pension funds’ portfolios, does not improve the performance of pension funds. In addition lack of debt securities issued and guaranteed by the State Treasury in OFE’s investments will increase the risk exposure of retirement savings. New regulations significantly limited the role of the funded pillar in the pension system. There is also a danger that declining of the pension funds assets will significantly influence Polish capital market and the whole economy. References Antolin, P. (2008), Pension Fund Performance, OECD Working Papers on Insurance and Private Pensions, 20, DOI: http://dx.doi.org/10.1787/240401404057. Bilefsky, D., Zurawik, M. (2013), Polish Plan on Pensions Arouses Sharp Criticism, The New York Times. October, 9, 2013, http://www.nytimes.com/2013/10/10/business/in ternational/polish-plan-on-pensions-arouses-sharp-criticism.html?_r=0. Feldstein, M. (1997), Transition to a Fully Funded Pension System: Five Economic Issues, NBER Working Paper, 6149, http://www.nber.org/papers/w6149.pdf. Góra, M., Rutkowski, M. (2000), The quest for pension reform: Poland's security through diversity, , William Davidson Institute at the University of Michigan, Working Papers, 286, http://deepblue.lib.umich.edu/bitstream/handle/2027.42/39670/wp286.pdf?seque nce=3. Hagemejer, J., Makarski, K., Tyrowicz, J. (2013), Unprivatizing the Pension System: The Case of Poland, University of Warsaw, Faculty of Economic Sciences, Working Pa- pers, 26 (111). Hausmer, J. (2002), Poland Security through Diversity, in Feldstein M. and Siebert H. (ed.), Social Security Pension Reform in Europe, University of Chicago Press, 349–364, Available at: http://www.nber.org/chapters/c10678.pdf. Kompa, K. (2014), Polish Pension System in Transition: Impact on the Investment Portfolio Construction, Indian Journal of Fundamental and Applied Life Sciences, http:// http://www.cibtech.org/sp.ed/jls/2014/01/jls.htm, 4(S1), 2102–2110. Krzysztof Kompa, Dorota Witkowska DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 124 Kompa, K., Wiśniewski, T. (2014), “Security Through Diversity”: Portfolio Diversification of Private Pension Funds, Quantitative Methods in Economic Research, 15(1), 58–65. Lewicka-Banaszak, E. (2014), Against the grain. Pension systems in the European Union and selected OECD countries, and the direction of changes in the Polish open pension funds (Pod prąd. Systemy emerytalne w Unii Europejskiej i wybranych krajach OECD, a kierunek zmian w polskich OFE), in Biuletyn IGTE, 1(1), 12–20, http://www.igte.com.pl/files/biuletyn/1_biuletyn_14.pdf (in Polish). Marcinkiewicz, E., (2011), Changing the rules for distribution of pension contributions and the importance of pension funds in the financial market (Zmiana zasad dystrybucji składki emerytalnej a znaczenie OFE na rynku finansowym), Polityka Społeczna. Nu- mer Specjalny, Warszawa, 16–19, (in Polish). Pelc, P. (2010), Polish Pension Reform – Lost Decade?, http://www.pawelpelc.pl/index.php? display=5&artykul=167. Pensions at a Glance 2013: OECD and G20 Indicators © OECD 2013. President signs pension reform (2013), Warsaw Bussiness Journal, December, 30, 2013, http://www.wbj.pl/article-64697-president-signs-pension-reform.html Rozłucki, W. (2001), The importance of pension funds for the development of the Warsaw Stock Exchange (Znaczenie funduszy emerytalnych dla rozwoju Warszawskiej Giełdy Papierów Wartościowych), BRE Bank – CASE, 57, 37–41 (in Polish). Security (1997), Security through diversity: Reform of the pension system in Poland. War- saw: Office of the Government Plenipotentiary for Social Insurance Reform. Sharpe, W.F. (1966), Mutual Fund Performance, Journal of Business, 39(1), 119–138. Sinn, H.W. (2000), Why a Funded Pension System Is Useful and Why It Is Not Useful, Na- tional Bureau of Economic Research, Working Paper, 7592, http://www.nber.org/pa pers/w7592 Tarczyński, W., Witkowska D., Kompa K. (2013), The beta ratio theory and practice (Współ- czynnik beta teoria i praktyka), Warszawa: Pielaszek Research, (in Polish). Treynor, J.L. (1965), How to Rate Management of Investment Funds, Harvard Business Review, 43(1), 63–75. Fundusze emerytalne w Polsce: analiza efektywności za lata 1999–2013 Z a r y s t r e ś c i. Reforma systemu emerytalnego została wprowadzona w Polsce w 1999r., kiedy repartycyjny system zdefiniowanego świadczenia zastąpiono systemem zdefiniowanej składki, opartym na 3 filarach. Dwa pierwsze filary – repartycyjny i kapitałowy stały się publiczne i obowiązkowe, a trzeci dobrowolny kapitałowy. Jednakże problemy związane ze wzrostem deficytu budżetowego spowodowały wprowadzenie przez rząd istotnych zmian systemu emerytalnego w latach 2011 i 2013. Regulacje te nie tylko w istotny sposób wpłynę- ły na podział składek przekazywanych do obu obowiązkowych filarów, ale spowodowały zmiany w strukturze portfeli inwestycyjnych otwartych funduszy emerytalnych (OFE). Celem realizowanych badań jest analiza wyników finansowych OFE funkcjonujących w Polsce w latach 1999–2013. Na podstawie mierników efektywności Sharpe’a i Treynora pokazano, że dobrze zdywersyfikowane portfele OFE lepiej chronią interesy emerytów niż portfele hipotetyczne, skonstruowane zgodnie z nowymi zasadami. S ł o w a k l u c z o w e: system emerytalny, fundusze OFE, wskaźniki Sharpe i Treynora.