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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 ,  
p

S  – 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, 



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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 

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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 



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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   2
0

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.  



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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 



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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-



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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).  



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DYNAMIC ECONOMETRIC MODELS 14 (2014) 105–124 

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 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.  

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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.  


