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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.2016.007  Vol. 16 (2016) 117−131 

Submitted November 30, 2016  ISSN (online) 2450-7067 

Accepted December 20, 2016 ISSN (print) 1234-3862 

Krzysztof Kompa, Dorota Witkowska
*
 

Performance of Pension Funds and Stable Growth 
Open Investment Funds During the Changes in the 

Polish Retirement System 

A b s t r a c t. The conditions of the pension funds (OFE) functioning were essentially 

changed in the years 2011–2014. The aim of the paper is to find out if these modifications 

influence the efficiency of the pension funds and to compare the performance of these funds 

to stable growth open investment funds (FIO). The analysis is provided for selected funds in 

the years 2009–2015. We conclude that in the examined period, OFE performed better than 

FIO, and the modifications of the rules for the pension funds caused the increase of risk and 

decrease of investment efficiency of these funds’ portfolios. 

K e y w o r d s: pension funds, stable growth open investment funds, investment efficiency, 

Sharpe model, CAPM, Sharpe, Treynor and Jensen ratios. 

J E L Classification: G11; C12. 

Introduction 

 The pension system in communist Poland was the defined benefit and 

pay-as-you-go (PAYG) scheme. However, the demographic changes, pen-

sion privileges concerning more and more occupational groups and econom-

ic sectors, together with the so-called early retirement regulations, which 

                                                 
* Correspondence to: Krzysztof Kompa, Warsaw University of Life Sciences – SGGW, 

Department of Econometrics and Statistics, 166 Nowoursynowska Street, 02-787 Warsaw, 

Poland, e-mail: Krzysztof_kompa@sggw.pl; Dorota Witkowska, University of Lodz, De-

partment of Finance and Strategic Management, 22/26 Matejki Street, 90-237 Lodz, Poland, 

Dorota.witkowska@uni.lodz.pl 



Krzysztof Kompa, Dorota Witkowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 117–131 

118 

went into force in late 70-ties
1
, caused the increase of the pension system 

costs. In 1981 the pension contribution was 25% of wages, in the years 

1987–1989 it rose to 38%, and obtained the level of 45% in 1990 (see 

(Wojciechowski 2011, Podstawka 2005, p. 259)).  

 The increasing deficit in the Polish pension system enforced its trans-

formation, which took place in 1999. The new pension system replaced de-

fined benefit scheme by defined contribution one, it enriched the PAYG 

system by the mandatory capital-funded pillar, and introduced voluntary 

plans. New regulations were also to abolish sectoral and occupational privi-

leges and early retirement programs. The reformed retirement system has 

been consisted in three pillars – Social Insurance Institution (ZUS), open 

pension funds (OFE) and voluntary capital-funded system. The pension con-

tribution (i.e. 19.52% of earnings) was divided between both mandatory 

pillars – ZUS 12.22% and OFE 7.3%. 

 The first essential manipulation in the original pension reform was made 

in 2011 when the contribution to pension funds was diminished from 7.3% 

to 2.3%. The second and the most drastic regulation, consisted in shifting 

51.5% of the assets, held by the pension funds, to the Social Insurance Insti-

tution (including all debt securities issued and guaranteed by the State 

Treasury). Overhaul of the pension system also concerned changes in the 

OFEs’ investment portfolio since private pension funds have no longer been 

allowed to invest in government bonds. These new law (from 2013) went 

into effect in February 2014. The third significant modification took place in 

2014 and changed the character of pension funds which have been no longer 

obligatory. According to the new regulations, each employee has had four 

months every four years to decide whether 2.92 percent of their income goes 

to a chosen private fund or to ZUS. It means that after all mentioned above 

regulations the part of the pension contribution transferred to the pension 

funds decreased from 37.4% to 15% or even zero. 

 There have been numerous studies concerning the efficiency of mutual 

and pension funds operating in Poland. Mutual funds’ performance is ana-

lyzed by Karpio and Żebrowska-Suchodolska (2010, 2011, 2012), 

Ostrowska (2003), Perez (2012), Witkowska (2009), Witkowska et al. 

(2009) and Zamojska (2012). Whereas evaluation of pension funds invest-

ment activity is made by Białek (2009), Chybalski (2006, 2009), Dybał 

(2008), Karpio and Żebrowska-Suchodolska (2014, 2016), Kompa and 

                                                 
1 Early retirement regulations decreased the real pension age by several years since em-

ployees who fulfil certain conditions were allowed to obtain pension benefits earlier i.e. be-

fore statutory retirement age.  



Performance of Pension Funds and Stable Growth Open Investment Funds… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 117–131 

119 

Wiśniewski (2015), Kompa and Witkowska (2015, 2016), Marcinkiewicz 

(2009) and Witkowska, Kompa (2012). The mentioned research was provid-

ed for differently defined time spans, length of the samples, various frequen-

cy of measurement, taking into account bear and bull markets, and variety of 

efficiency measures. However, the investigation concerning the influence of 

political decisions to the performance of pension and investment funds mar-

ket is rare. There is also lack of profound comparable research of the effi-

ciency of pension and mutual funds.  

 This paper is to fulfill that gap in literature. The aim of our research is to 

find out if mentioned above changes of the OFEs’ functioning influence the 

efficiency of the pension funds and to compare the performance of these 

funds to stable growth investment funds (FIO). The analysis is provided for 

selected funds applying statistical inference, Sharpe and capital assets pric-

ing (CAPM) models and classical investment efficiency ratios. 

1. Data and Methods 

To answer the question about the consequences of manipulations in the pen-

sion system, the whole period of analysis, denoted by A, is divided into three 

pairs of sub-periods according to the moments when new regulations went 

into effect:  

 B, decreasing of the contribution transferred to OFE,  

 C, shifting of assets from OFE to ZUS and changes in the OFEs’ portfo-

lio composition,  

 D, waving the obligation of pension funds membership. 

Empirical analysis of the investment efficiency is provided on the basis of 

daily observations from the years 2009–2015. The considered time span 

covers seven samples:  

 A from 1.01.2009 to 31.12.2015 (84 months), 

 B1 from 1.01.2009 to 30.04.2011, and B2 from 1.05.2011 to 31.08.2013 

(28 months each sub-period), 

 C1 from 1.04.2012 to 31.01.2014, and C2 from 1.02.2014 to 31.12.2015 

(22 and 23 months respectively), 

 D1 from 1.01.2013 to 30.06.2014, and D2 from 1.07.2014 to 31.12.2015 

(18 months each). 

In our research we use daily logarithmic rate of returns evaluated from: 

 participation units of stable growth open investment funds and account-

ing units of pension funds, which are managed by the same six invest-

ment and pension funds companies, namely: Allianz, Aviva, Nationale 



Krzysztof Kompa, Dorota Witkowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 117–131 

120 

Nederlanden, PEKAO, PKO and PZU Investment and Pension Funds 

Companies
2
, 

 Warsaw Stock Exchange Index – WIG,  

 Poland’s Official Treasury Bonds Index – TBSP.Index, and  

 Warsaw Interbank Offered Rate – WIBOR.  

 WIG, TBSP and WIBOR (being the interest rate of 3 months loans) are 

used as benchmarks
3
 in our analysis since they represent capital, treasury 

bond and money markets, respectively. WIG is treated as the market index 

whereas TBSP and WIBOR – as risk free instruments.  

 Analysis of returns and risk generated by the investment portfolios con-

structed by selected funds is conducted using statistical interference (assum-

ing the significance level 0.05). We will verify
4
 the following null hypothe-

ses concerning:  

rates of return risk Sharpe model / CAPM 

E(ROFE) = 0;  
E(RFIO) = 0;  
E(Rbenchmark) = 0 

 

 = 0;  = 0 

E(ROFE) = E(RFIO) D2(ROFE) = D2(RFIO) OFE = FIO 

E(Rbefore) = E(Rafter) D2(Rbefore) = D2(Rafter) before = after 

where, E(R) – expected returns, D2(R) – variance of returns, ROFE, RFIO – returns from OFE and FIO 

respectively, ,  – parameters of Sharpe model or CAPM, Rbefore, Rafter, before, after – returns from the 

portfolio and beta coefficients before and after the change went into effect, respectively. 

 The comparison of the funds’ efficiency is provided applying Sharpe, 

Treynor and Jensen ratios which are evaluated for all considered pension and 

mutual funds in all analyzed time spans, and for differently defined risk free 

instruments. 

2. Rates of Return 

 In the first step of our analysis we check out if daily rates of return are 

significantly positive or negative. It is visible (Table 1) that expected returns 

from all considered pension funds’ investment are significantly positive in 

                                                 
2 The selection of mentioned above Investment and Pension Funds Companies is connect-

ed with the investigations previously provided by the authors separately for pension funds and 

investment funds. 
3 It is worth mentioning that WIG and WIBOR are used to calculate benchmarks, which 

are used to evaluate pension funds efficiency (Dziennik Ustaw Rzeczypospolitej Polskiej 

2014, poz. 753). 
4 Description of all applied tests is presented in (Tarczyński, Witkowska and Kompa, 

2013, p. 18–19, 25, 72) 



Performance of Pension Funds and Stable Growth Open Investment Funds… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 117–131 

121 

the whole period of consideration (denoted by A), and for the periods B1 and 

C1, describing performance of pension funds before the essential changes of 

their functioning. It is also noticeable that in the periods C2 and D2, i.e. after 

the modifications went into effect, the average rates of return are negative, 

although the null hypothesis cannot be rejected for the significance level 

0.05. 

Table 1. Test statistics verifying the hypothesis about expected returns from pension 

funds in considered periods H0: E(ROFE) = 0 

Period A B1 B2 C1 C2 D1 D2 

Number of observations 1823 604 610 480 499 390 393 
Allianz 1.9306 2.7360 1.3129 2.4911 –0.1800 0.7590 –0.3116 
Aviva 1.7404 2.6509 1.2352 2.2974 –0.2728 0.7827 –0.4601 

Nationale Nederlanden 1.7662 2.6364 1.3028 2.4438 –0.3501 0.8735 –0.5018 
PEKAO 1.5230 2.7997 1.0987 2.2557 –0.4316 0.7572 –0.6005 

PKO 2.0540 2.9102 1.4263 2.6620 –0.1030 0.9630 –0.2776 
PZU 1.7043 2.5413 1.0815 2.2353 –0.1397 0.8623 –0.3361 

Note: Bold letters denote rejection of null hypothesis. 

Table 2. Test statistics verifying the hypothesis about expected returns from stable 

growth investment funds in considered periods H0: E(RFIO) = 0 

Period A B1 B2 C1 C2 D1 D2 

Number of observations 1823 604 610 480 499 390 393 
Allianz 0.0849 0.5640 –0.1806 0.1617 –0.5957 –0.2008 –0.8648 
Aviva 2.0625 1.9847 0.7763 1.8784 0.0660 1.0115 –0.0550 

Nationale Nederlanden 1.7755 1.8450 0.6528 1.6648 0.2879 0.6511 –0.2487 
PEKAO 0.3032 1.6871 –1.0786 0.6526 –0.3112 0.1099 –0.5922 

PKO 2.1753 1.8920 0.8929 1.8669 0.5899 0.9977 0.1458 
PZU 1.1236 1.5555 0.3250 1.3278 –0.6382 0.5266 –0.6100 

Note: Bold letters denote rejection of null hypothesis. 

Stable growth investment funds’ performance (Table 2) seems to be worse 

than the pension funds since only Aviva, Nationale Nederlanden and PKO 

generated significantly positive returns in the periods A, B1 and C1. Howev-

er, the comparison of returns, using Cochran-Cox test (Table 3), shows that 

differences between returns obtained by both types of funds are not signifi-

cant, except PEKAO in B2 when OFE performed better than mutual fund.  

 Analyzing returns from the benchmarks (Table 4) one may notice that 

interest rate WIBOR generated positive returns in all periods, bond market 

performed well with significantly positive returns in all periods but D1 and 

D2, whereas expected returns from WIG do not significantly differ from 

zero, except the period B1. 
  



Krzysztof Kompa, Dorota Witkowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 117–131 

122 

Table 3. Test statistics for comparison of expected returns H0: E(ROFE) = E(RFIO) and 

risk H0: D
2
(ROFE) = D

2
 (RFIO) for pension and investment funds  

Period Hypotheses Allianz Aviva NN  PEKAO PKO PZU 

A Return 1.1902 –0.0116 0.1989 1.0688 0.2125 0.0000 
 Variance 1.0935 1.1017 1.1702 1.0740 1.3329 1.5200 

B1 Return 0.8956 –0.0783 0.1499 0.1975 0.5473 –0.2761 
 Variance 1.6486 1.4068 1.2048 1.4157 1.0283 1.9268 

B2 Return 0.8969 0.3501 0.3934 1.6668 0.3259 0.2907 
 Variance 1.4784 1.0615 1.0968 1.3140 1.0511 2.0000 

C1 Return 1.9833 0.2024 0.6182 0.8171 0.7680 –0.2969 
 Variance 1.1808 1.0581 1.2008 1.1005 1.2324 2.0000 

C2 Return 0.2589 –0.3431 –0.4286 –0.1533 –0.2260 0.4545 
 Variance 2.0667 2.1169 2.1375 2.0351 2.4110 0.9857 

D1 Return 0.8041 0.0796 0.2887 0.5390 0.2098 0.0000 
 Variance 1.6271 1.3958 1.4758 1.3195 1.7198 1.5306 

D2 Return 0.0885 –0.2676 –0.4538 –0.2788 –0.3561 0.2107 
 Variance 2.0134 2.1991 2.1157 2.0944 2.3616 1.0462 

Note: NN is an abbreviation of Nationale Nederlanden. Bold letters denote rejection of null hypothesis. 

Shadowed cells denote situation when D2(ROFE) <D2(RFIO). 

Table 4. Test statistics verifying the hypothesis about expected returns from the 

benchmarks in considered periods H0: E(Rbenchmark) = 0 

Periods A B1 B2 C1 C2 D1 D2 

TBSP 5.4494 2.8694 3.7794 2.3963 2.8731 1.4714 1.6248 
WIG 1.0095 1.7045 –0.0816 1.0326 –0.4643 0.4855 –0.6640 

WIBOR3M 135.2505 299.2855 132.8255 81.5094 109.2820 137.2229 116.3402 
Note: Bold letters denote rejection of null hypothesis.  

Table 5. Cochran-Cox test  statistics  comparing  returns  in  the  pairs  of  periods  

H0: E(Rbefore) = E(Rafter) 

Funds type: OFE FIO 

Periods: B1:B2 C1:C2 D1:D2 B1:B2 C1:C2 D1:D2 
Allianz 1.0242 1.3305 0.7179 0.5409 0.5468 0.4707 
Aviva 1.0356 1.2945 0.8442 1.1207 1.2931 0.8161 
NN 1.0311 1.5763 0.9342 0.9727 1.0382 0.6518 

PEKAO 1.1848 1.3902 0.9399 1.9662 0.6945 0.4579 
PKO 1.0890 1.4153 0.8172 0.7175 1.3803 0.6347 
PZU 1.1246 1.1066 0.7806 0.8989 0.9908 0.7972 

Note: NN is an abbreviation of Nationale Nederlanden. 

 Table 5 contains test statistics comparing expected returns generated by 

both types of funds in two sub-periods: before and after modification of the 

OFE environment i.e. conditions for their functioning. Null hypothesis can-

not be rejected in any case however returns for both pension and stable 

growth investment funds were always bigger before the change than after, 



Performance of Pension Funds and Stable Growth Open Investment Funds… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 117–131 

123 

and this difference was always bigger for the pension than for mutual funds. 

In Table 6 comparison of risk is provided and one may notice that for all 

pension funds risk significantly increased in the periods C2 and D2 i.e. after 

the introduced by the government changes. For mutual funds we do not ob-

serve similar situation since the significant difference of risk between both 

comparing periods is visible only for Aviva and Nationale Nederlanden in 

the sub-periods B together with Aviva and PEKAO – in D but in both sub-

periods the risk before modification of OFE environment is bigger than after. 

Table 6. Fisher-Snedecor test statistics comparing variances in the pairs of periods 

H0: D
2
(Rbefore) = D

2
(Rafter) 

Returns OFE FIO 

Periods B1:B2 C1:C2 D1:D2 B1:B2 C1:C2 D1:D2 
Allianz 1.0153 3.6597 1.5669 1.1152 1.1070 1.0102 
Aviva 1.0448 3.9187 1.6562 1.3252 1.0003 1.2197 
NN 1.1246 2.7625 1.6332 1.1563 1.0788 1.1200 

PEKAO 1.0366 4.2110 1.6346 1.0483 1.1036 1.2319 
PKO 1.0429 3.1506 1.5867 0.7175 1.0869 1.0805 
PZU 1.1452 4.3580 1.8796 1.0395 1.0606 1.1538 

Note: NN is an abbreviation of Nationale Nederlanden. Bold letters denote rejection of null hypothesis. 

Shadowed cells denote situation when D2(Rbefore) < D2(Rafter). 

 Pension funds’ portfolios are characterized by smaller risk than stable 

growth investment  funds only in  the sub-periods B, the  period  C1 for  

PEKAO and PZU, the period D1 for PZU and in the whole period A for 

Allianz and PZU. Although the null hypothesis is rejected only for PZU and 

Allianz in all mentioned periods together with Aviva, Nationale Nederlanden 

and PKO in the period B1. In all sub-periods denoted as C and D risk of 

investments made by OFE is significantly bigger than by FIO Allianz, 

Nationale Nederlanden and PKO, whereas for Aviva and PEKAO this state-

ment is true for C2, D1 and D2 (see Table 3). Comparison of variances in 

pairs of selected sub-periods (Table 6) shows the significant increase of risk 

in all pension funds after the new regulations went into effect in 2014, and 

PEKAO also in 2011 whereas for TBSP and WIBOR only in 2011 (Table 7). 

This conclusion is not true for stable growth investment funds and the rest of 

the benchmarks and sub-periods. It is also visible that significant changes in 

returns took place only in the money market (Table 7). 
  



Krzysztof Kompa, Dorota Witkowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 117–131 

124 

Table 7. Cochran-Cox  and  Fisher-Snedecor  test  statistics  comparing  returns  

H0: E(Rbefore) = E(Rafter) and variances H0: D
2
(Rbefore) = D

2
(Rafter)  

 Expected returns Variance 

Periods B1:B2 C1:C2 D1:D2 B1:B2 C1:C2 D1:D2 
TBSP –0.9878 –0.0836 0.0543 1.3576 1.2631 1.3371 
WIG 1.3593 1.0740 0.8047 1.4129 1.1331 1.2363 

WIBOR3M –5.7610 33.2388 36.1675 5.6374 5.5480 1.6129 

Note: Shadowed cells denote situation when D2(Rbefore) < D2(Rafter). Bold letters denote rejection of H0. 

3. Single Index and Capital Assets Pricing Models 

 The models are estimated for each period of analysis using WIG as the 

market index and two variants of risk free instruments i.e. TBSP and 

WIBOR in the capital assets pricing models (CAPM). Therefore, there are 

21 models for each fund, which parameters will be compared. Beta coeffi-

cients in all models estimated for the pension funds are significantly positive 

(except the models estimated for OFE PZU in the periods: A, B1, C2, D1, 

and D2). Value of parameter estimates increase from 0.2 in B1, by 0.3 in B2 

and C1, 0.4 in D2 to 0.6 in C2 and D2. Parameter estimates of beta and de-

termination coefficients in the single index models and the capital assets 

pricing models with WIBOR as the risk free instrument are almost of the 

same values whereas using TBSP as the risk free instrument gives slightly 

different values of beta for all models estimated for the pension funds (the 

example in Table 8). Similar conclusions may be drawn for the stable growth 

investment funds (see Table 9) however values of the determination coeffi-

cients are different in models describing both types of funds. 

Table 8. Estimates and determination coefficients of different pension funds models 

estimated for in the whole period 

 Allianz Aviva NN PEKAO PKO PZU 

Beta coefficient 

Sharpe 0.2976 0.3003 0.3119 0.3044 0.2897 0.0132 
CAPM WIBOR 0.2976 0.3003 0.3119 0.3044 0.2897 0.0132 
CAPM TBSP 0.2762 0.2785 0.2892 0.2827 0.2682 –0.0027 

Determination coefficient 

Sharpe 0.5567 0.5538 0.5531 0.5189 0.5434 0.0009 
CAPM WIBOR 0.5567 0.5539 0.5531 0.5190 0.5435 0.0009 
CAPM TBSP 0.5182 0.5168 0.5201 0.4802 0.5029 0.0000 

Note: Bold letters denote statistically significant parameters i.e. H0:  = 0; NN as in Table 3. 

  



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DYNAMIC ECONOMETRIC MODELS 16 (2016) 117–131 

125 

Table 9. Parameter estimates and determination coefficients of different models 

estimated for mutual funds in the whole period 

 Allianz Aviva NN PEKAO PKO PZU 

Beta coefficient 
Sharpe 0.3221 0.3379 0.3396 0.3396 0.2638 0.6389 

CAPM WIBOR 0.3221 0.3379 0.3396 0.3396 0.2638 0.6389 
CAPM TBSP 0.2977 0.3155 0.3165 0.3165 0.2409 0.6262 

Determination coefficient 

Sharpe 0.5406 0.8632 0.9029 0.9029 0.8041 0.9406 
CAPM WIBOR 0.5406 0.8632 0.9029 0.9029 0.8041 0.9406 
CAPM TBSP 0.5115 0.8644 0.9435 0.9435 0.8103 0.9400 

Note: Bold letters denote statistically significant parameters i.e. H0:  = 0; NN is an abbreviation of 

Nationale Nederlanden. 

 In the next step we compare betas from the models estimated before and 

after the changes of the pension funds’ situation, introduced by the govern-

ment
5
. It is visible that for all models estimated for the pension funds the risk 

significantly increased in the second considered periods (Table 10). Compar-

ing beta coefficients estimated for the mutual funds the same results are ob-

tained only for FIO Allianz whereas for other stable growth investment 

funds the results of the hypothesis verification are different (Table 11). For 

Aviva, PEKAO and PZU the risk significantly decreased in the period D2 in 

comparison to the period D1, also for the first considered pair of sub-periods 

FIO Aviva are characterized by the smaller risk after the modification of the 

system than before. Compering a pair of sub-periods C1 and C2, we notice 

that there is only one case (PEKAO for the CAPM model with TBSP) when 

risk significantly decreased in the second compared period. 

Table 10. Student test statistics comparing betas estimated for the pension funds in 

the pairs of periods H0: before = after 

 B1:B2 C1:C2 D1:D2 

Models Sharpe CAPM TBSP Sharpe CAPM TBSP Sharpe CAPM TBSP 

Allianz –4.70 –7.51 –33.46 –31.83 –12.89 –12.54 
Aviva –3.80 –6.71 –36.32 –36.51 –14.51 –14.62 
NN –2.95 –5.81 –34.50 –34.90 –14.06 –14.55 

PEKAO –5.35 –8.09 –37.60 –36.23 –14.08 –13.85 
PKO –4.45 –7.44 –35.79 –34.35 –13.31 –13.17 
PZU –0.92 –3.16 2.02 3.22 –1.77 –1.00 

Note: Bold letters denote rejection of null hypothesis.  

                                                 
5 In comparison parameter estimates from the CAPM using WIBOR as risk free instru-

ment were omitted because they were of the same values as in the Sharp models.  



Krzysztof Kompa, Dorota Witkowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 117–131 

126 

Table 11. Student test statistics comparing betas estimated for the mutual funds in 

the pairs of periods H0: before = after 

 B1:B2 C1:C2 D1:D2 

Models Sharpe CAPM TBSP Sharpe CAPM TBSP Sharpe CAPM TBSP 

Allianz –9.9973 –11.5962 –9.8910 –8.7862 –6.1679 –4.8829 
Aviva 13.9977 13.0450 –4.8720 –6.2323 2.0147 3.3168 
NN –0.3876 –0.3003 –2.8112 –1.7663 –0.8466 –0.8954 

PEKAO –8.0196 –8.9997 0.6125 2.2591 4.3964 4.3668 
PKO –11.0755 –11.7400 –14.4898 0.6200 –1.4324 –1.3214 
PZU –18.4045 –20.9368 –89.8678 –85.1736 3.3144 3.9947 

Note: Bold letters denote rejection of null hypothesis.  

We also compare betas from the models estimated for the pension and mutu-

al funds (Table 12), and it is visible that in the periods denoted as A, B1, B2 

and C1, all pension funds except PKO in A and Allianz in C1 are character-

ized by bigger risk than mutual funds since betas are significantly bigger for 

OFE than for FIO in the majority of cases. Whereas in the sub-periods C2, 

D1 and D2 the situation is the opposite except PZU. 

Table 12. Student test statistics comparing betas estimated for the pension and mu-

tual funds in all periods H0: OFE = FIO 

 
A B1 B2 C1 C2 D1 D2 

Sharpe model 

Allianz –3.5144 –3.0930 –16.4158 1.9904 51.7384 16.6141 41.4479 
AVIVA –11.9270 –34.7256 –10.2976 –0.3780 47.4091 9.2631 43.6863 
PKO 8.3548 –5.9057 –12.4800 –0.5507 57.8852 18.6757 47.5616 
NN –10.6034 –28.0973 –17.7427 –5.2973 57.7356 11.6558 47.2607 

PEKAO –21.4350 –31.5047 –23.6178 –13.0494 53.8435 5.1663 47.3234 
PZU –166.4176 –127.2500 –112.5233 –88.3038 –80.0261 –79.1466 –63.7252 

CAPM TBSP 

Allianz –3.1584 –2.8330 –16.8911 3.0855 75.3923 20.0192 64.5078 
AVIVA –13.8325 –37.1812 –12.5294 1.1703 61.7681 15.9266 57.5696 
PKO 10.1111 –6.7755 –17.3235 0.8600 57.1452 25.1786 45.0649 
NN –15.0291 –36.9608 –30.1785 –7.3074 78.8268 23.2502 66.6716 

PEKAO –25.9866 –33.3984 –24.1046 –13.7403 33.1803 0.5113 28.3302 
PZU –169.5121 –134.2389 –115.0464 –90.6541 –81.3673 –80.3593 –64.7672 

Note: Bold letters denote rejection of null hypothesis. NN is an abbreviation of Nationale Nederlanden. 

4. Investment Efficiency Evaluation 

 The last stage of our investigation consists in comparison of classical 

efficiency measures, which are evaluated for different portfolios and sam-

ples. It is worth reminding that applying so called reward-to-variability 

(Sharpe) and reward-to-volatility (Treynor) ratios, it is necessary to define 



Performance of Pension Funds and Stable Growth Open Investment Funds… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 117–131 

127 

the risk free instrument and the market index. Since in our previous analysis 

we use two risk free instruments WIBOR and TBSP together with WIG, 

which represents the capital market, the same instruments are used to evalu-

ate the performance of considered pension and mutual funds. However, to 

evaluate Treynor ratio we use betas from both i.e. single index and capital 

assets pricing models. In other words, for each pension or mutual fund we 

calculate two Sharpe’s and Jensen ratios, together with four Treynor’s 

measures. Tables 13 and 14 contain the average values of these efficiency 

measures.  

Table 13. Average values of the efficiency measures evaluated for pension funds 

Period Measure Allianz Aviva PKO NN PEKAO PZU WIG 

A 

Sharpe 0.0100 0.0060 0.0125 0.0079 0.0025 0.0075 0.0096 

Treynor 0.0002 0.0001 0.0002 0.0001 0.0000 0.0057 0.0001 

Jensen 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000  

B1 

Sharpe 0.0716 0.0681 0.0768 0.0700 0.0731 0.0670 0.0584 

Treynor 0.0013 0.0012 0.0014 0.0010 0.0013 0.0114 0.0008 

Jensen 0.0001 0.0001 0.0001 0.0001 0.0001 0.0003  

B2 

Sharpe –0.0006 –0.0042 0.0007 –0.0004 –0.0095 –0.0087 –0.0212 

Treynor 0.0000 –0.0001 0.0000 0.0000 –0.0002 –0.0013 –0.0002 

Jensen 0.0001 0.0000 0.0001 0.0001 0.0000 0.0000  

C1 

Sharpe 0.0625 0.0535 0.0816 0.0758 0.0540 0.0519 0.0281 

Treynor 0.0007 0.0006 0.0011 0.0010 0.0007 0.0089 0.0003 

Jensen 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002  

C2 

Sharpe –0.0319 –0.0354 –0.0280 –0.0382 –0.0405 –0.0278 –0.0391 

Treynor –0.0003 –0.0004 –0.0003 –0.0004 –0.0004 0.0109 –0.0003 

Jensen 0.0000 0.0000 0.0000 0.0000 –0.0001 –0.0002  

D1 

Sharpe 0.0127 0.0142 0.0232 –0.0024 0.0149 0.0187 0.0075 

Treynor 0.0002 0.0003 0.0003 0.0000 0.0002 0.0052 0.0001 

Jensen 0.0000 0.0000 0.0001 0.0001 0.0000 0.0001  

D2 

Sharpe –0.0334 –0.0291 –0.0313 –0.0418 –0.0461 –0.0326 –0.0449 

Treynor –0.0003 –0.0004 –0.0003 –0.0004 –0.0005 –0.0072 –0.0004 

Jensen 0.0000 0.0000 0.0000 0.0000 0.0000 –0.0002  

Note: Bold letters denote ratios evaluated for pension funds which are bigger than the ones calculated for 
WIG. NN is an abbreviation of Nationale Nederlanden. 

It is visible that in the majority of cases (76%) pension funds performed 

better than capital market if the efficiency is measured by the averages of 

Treynor and Sharpe ratios. Only Nationale Nederlanden OFE did not per-

form better in the periods A, C2 (only Treynor measure), and D2. In fact, in 

C2 and D2 sub-periods also other pension funds show lower efficiency. Ap-

plying Jensen alpha, it is visible that in majority of cases values are nonnega-

tive. Although positive and statistically significant values of the parameter 

alpha in the CAPM (when WIBOR is the risk free instrument) are observed 



Krzysztof Kompa, Dorota Witkowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 117–131 

128 

only for OFE Allianz, Nationale Nederlanden and PKO in the period C1, 

together with OFE PZU in the period B1 (see Table 15). 

It is visible that in the majority of cases mutual funds performed worse than 

capital market. There are only 12 cases among 84 average of Treynor or 

Sharpe measure values (14%) when stable growth investment fund is more 

efficient than capital market represented by WIG. The mutual funds which 

were better managed are FIO Aviva, PKO and PZU. Also Jensen ratio is 

rarely positive for mutual funds and if the constant in the capital assets pric-

ing models, estimated for investment funds, is statistically significant it is 

always negative for FIO Allianz and both risk free instruments in the whole 

period of analysis, FIO Nationale Nederlanden, PEKAO, PKO and PZU for 

TBSP in the whole period of analysis and in the sub-period B1 for Nationale 

Nedrelanden and TBSP, together with PEKAO regardless the risk free in-

strument (see Table 15).  

Table 14. Average values of the efficiency measures evaluated for mutual funds 

Period Measure Allianz Aviva PKO NN PEKAO PZU WIG 

A 

Sharpe –0.0298 0.0097 0.0034 0.0023 –0.0282 –0.0014 0.0096 

Treynor –0.0005 0.0001 0.0000 0.0000 –0.0003 0.0000 0.0001 

Jensen –0.0002 0.0000 0.0000 0.0000 –0.0002 –0.0001  

B1 

Sharpe –0.0021 0.0522 0.0368 0.0442 –0.0743 0.0427 0.0584 

Treynor –0.0001 0.0008 0.0005 0.0005 –0.0010 0.0006 0.0008 

Jensen –0.0002 0.0000 0.0000 0.0000 –0.0001 –0.0001  

B2 

Sharpe –0.0448 –0.0195 –0.0183 –0.0216 –0.0848 –0.0196 –0.0212 

Treynor –0.0006 –0.0003 –0.0002 –0.0003 –0.0010 –0.0099 –0.0002 

Jensen –0.0001 0.0000 0.0000 0.0000 –0.0003 0.0000  

C1 

Sharpe –0.0534 0.0311 0.0271 0.0264 –0.0144 0.0420 0.0281 

Treynor –0.0006 0.0003 0.0003 0.0003 –0.0001 0.0004 0.0003 

Jensen –0.0002 0.0000 0.0001 0.0000 –0.0002 0.0001  

C2 

Sharpe –0.0772 –0.0456 –0.0296 –0.0349 –0.0573 –0.0487 –0.0391 

Treynor –0.0007 –0.0005 –0.0003 –0.0003 –0.0005 –0.0004 –0.0003 

Jensen –0.0001 0.0000 0.0000 0.0000 –0.0001 –0.0001  

D1 

Sharpe –0.0532 0.0143 –0.0187 –0.0033 –0.0256 0.0072 0.0075 

Treynor –0.0006 0.0002 –0.0002 0.0000 –0.0003 0.0001 0.0001 

Jensen –0.0002 0.0000 0.0000 0.0000 –0.0001 0.0000  

D2 

Sharpe –0.0802 –0.0401 –0.0330 –0.0474 –0.0626 –0.0498 –0.0449 

Treynor –0.0008 –0.0004 –0.0003 –0.0004 –0.0006 –0.0004 –0.0004 

Jensen –0.0001 0.0000 0.0000 0.0000 –0.0001 0.0000  

Note: Bold letters denote ratios evaluated for mutual funds which are bigger than the ones calculated for 
WIG. NN is an abbreviation of Nationale Nederlanden. 



Performance of Pension Funds and Stable Growth Open Investment Funds… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 117–131 

129 

Conclusion 

 Investigation is provided for the selected pension funds and stable 

growth open investment funds which have been operating in frame of the six 

Investment and Pension Funds Companies. During the period of analysis, i.e. 

the years 2009–2015, the essential changes of the pension funds functioning 

were introduced therefore, research is conducted for three distinguished pairs 

of sub-periods. These pairs: B (B1 and B2), C (C1 and C2), and D (D1 and 

D2) are characterized by similar numbers of observations to make the com-

parison of the considered pension and mutual funds’ performance possible.  

 Provided analysis let us conclude that changes in the operation of pen-

sion funds influence not only the pension funds market but the whole capital 

market in Poland. The latter seems not to recover after the financial crisis 

2007–2009 (see Table 4) and its performance is worse in all periods after the 

modifications were introduced than before i.e. Sharpe and Treynor ratios are 

positive in the sub-periods B1, C1 and D1 and negative for B2, C2 and D2 

(Tables 13–14). Also pension funds investment efficiency is worse after the 

changes went into effect, especially they cause the significant increase of the 

pension funds’ investment portfolios risk (see Tables 6 and 10). 

Table 15. Parameter estimates of constant in CAPM for which H0:  = 0 is rejected 

Fund 
OFE FIO 

parameter period instrument parameter period instrument 

Allianz 0.0002 C1 WIBOR 
–0.0001 A WIBOR 

–0.0002 A TBSP 

Nationale 
Nederlanden 

0.0002 C1 WIBOR 
–0.0001 A TBSP 

–0.0001 B1 TBSP 

PEKAO 

   –0.0001 A TBSP 

   –0.0003 B1 WIBOR 

   –0.0004 B1 TBSP 

PKO 0.0002 C1 WIBOR –0.0001 A TBSP 

PZU 0.0003 B1 WIBOR –0.0001 A TBSP 

 Comparison of the pension and stable growth investment funds’ perfor-

mance shows that the former were in analyzed periods more effective than 

the latter (compare Tables 13 and 14). Considered changes of the pension 

system have not effected mutual funds’ investment policy directly however 

the general situation of the Polish capital market influences situation of 

FIOs. 



Krzysztof Kompa, Dorota Witkowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 117–131 

130 

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