9. Discussion and Conclusion
9.1 Future Research Questions
In this thesis, we test the performance of several funds, managed by different fund contributors.
A study on differences within one fund contributor or even between each fund manager might give some answers to whether it does matter where an investor invests money or if, for example, DNB Norge I, DNB Norge IV, DNB Norge Selektiv I, and DNB Norge Selektiv III all provide the same active return.
We are questioning survivorship bias in our thesis, but its effects are not assessed. A different approach towards this would possibly result in a different conclusion.
The limitation of empirical data by passively managed funds leads to a comparison issue. To run regressions with a data sample of only, in our case, four and a half year would lead to a fair comparison but with few observations. Therefore, this will be more relevant in the future where the observations of passively managed funds have increased.
84
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88
Appendices
Appendix 1
Overview over the funds’ ranking based on the various performance measures, including their overall rank.
Fund name SR Rank TM Rank TE Rank IR Rank M2 Rank Average Rank Overall Rank
Active funds:
Alfred Berg Aktiv 0.2393 4 0.0114 3 0.0126 12 0.1174 4 0.0015 4 5.40 3
Alfred Berg Gambak 0.2683 2 0.0134 2 0.0188 3 0.1251 3 0.0028 2 2.40 1
Alfred Berg Humanfond 0.1937 18 0.0091 18 0.0104 13 -0.0883 21 -0.0006 21 18.20 19
Alfred Berg Norge Classic 0.2424 3 0.0113 4 0.0081 21 0.1515 1 0.0016 3 6.40 4
C WorldWide Norge 0.2009 14 0.0094 15 0.0088 18 -0.0300 16 -0.0003 17 16.00 15
Danske Invest Norge I 0.2165 10 0.0101 10 0.0187 4 0.0148 11 0.0004 10 9.00 8.5
Delphi Norge A 0.1995 16 0.0099 12 0.0186 5 0.0028 12 -0.0003 19 12.80 12
DNB Norge (IV) 0.1906 19 0.0089 19 0.0086 19 -0.1182 23 -0.0008 22 20.40 23
Eika Norge 0.1561 23 0.0075 22 0.0074 22 -0.2742 26 -0.0023 24 23.40 26
Fondsfinans Norge 0.2139 11 0.0106 8 0.0093 16 0.1116 5 0.0003 11 10.20 11
Handelsbanken Norge 0.2248 6 0.0110 5 0.0096 15 0.1272 2 0.0008 6 6.80 5
Holberg Norge 0.1478 25 0.0073 23 0.0148 11 -0.1875 25 -0.0027 26 22.00 25
KLP AksjeNorge 0.1957 17 0.0091 17 0.0165 9 -0.0076 15 -0.0005 20 15.60 13.5
Nordea Avkastning 0.2167 9 0.0101 11 0.0181 8 0.0308 10 0.0004 9 9.40 10
Nordea Kapital 0.2257 5 0.0105 9 0.0082 20 0.1024 6 0.0009 5 9.00 8.5
Nordea Norge Verdi 0.2710 1 0.0135 1 0.0184 6 0.0733 8 0.0029 1 3.40 2
ODIN Norge C 0.1521 24 0.0077 21 0.0196 2 -0.1521 24 -0.0025 25 19.20 21
Pareto Aksje Norge B 0.1721 20 0.0089 20 0.0213 1 -0.0945 22 -0.0016 23 17.20 18
Pareto Investment Fund A 0.2210 8 0.0109 6 0.0182 7 0.0795 7 0.0006 8 7.20 6
Storebrand Norge 0.2240 7 0.0108 7 0.0150 10 0.0376 9 0.0008 7 8.00 7
Index funds:
Alfred Berg Index Classic 0.2114 12 0.0098 13 0.0071 23 -0.0606 18 0.0002 12 15.60 13.5
DNB Norge Indeks* 0.1721 21 0.0069 24 0.0062 25 -0.0369 17 0.0001 14 20.20 22
KLP AksjeNorge Indeks II 0.2093 13 0.0097 14 0.0069 24 -0.0655 19 0.0001 13 16.60 16.5
Nordnet Superfondet Norge* 0.1166 26 0.0038 26 0.0053 26 -0.0033 14 -0.0002 16 21.60 24
PLUSS Indeks (Fondsforvaltning) 0.1998 15 0.0094 16 0.0097 14 -0.0685 20 -0.0003 18 16.60 16.5
Storebrand Indeks - Norge A* 0.1595 22 0.0051 25 0.0088 17 0.0026 13 -0.0001 15 18.40 20
89 Appendix 2
Overview over the funds’ factor values and their associated p-values based on Carhart’s 4-factor model.
Fund name βMkt p-valueMkt βSMB p-valueSMB βHML p-valueHML βUMD p-valueUMD Active funds:
Alfred Berg Aktiv 1.0494 0.1020 0.1399 0.0002 -0.0035 0.9133 0.0772 0.0031
Alfred Berg Gambak 1.0145 0.7310 0.2074 0.0001 -0.0054 0.9053 0.1354 0.0003
Alfred Berg Humanfond 0.9816 0.4662 0.0479 0.1232 0.0097 0.7216 0.0666 0.0024
Alfred Berg Norge Classic 0.9932 0.7256 0.0640 0.0076 0.0015 0.9435 0.0478 0.0043
C WorldWide Norge 0.9966 0.8745 -0.0019 0.9431 -0.0371 0.1160 0.0441 0.0189
Danske Invest Norge I 0.9895 0.6387 0.0434 0.1160 -0.0187 0.4389 0.0128 0.5010
Delphi Norge A 1.0785 0.0858 0.2179 0.0001 0.0015 0.9762 0.0607 0.1183
DNB Norge (IV) 0.9428 0.0158 0.0010 0.9734 -0.0214 0.3961 -0.0233 0.2443
Eika Norge 1.0912 0.0108 0.2129 0.0000 0.0482 0.2064 0.0105 0.7261
Fondsfinans Norge 1.0863 0.0618 0.2277 0.0001 0.0477 0.3349 -0.0315 0.4203
Handelsbanken Norge 1.0666 0.1061 0.1547 0.0025 -0.0143 0.7459 0.0728 0.0389
Holberg Norge 1.0337 0.4240 0.2561 0.0000 0.0422 0.3521 0.0123 0.7308
KLP AksjeNorge 1.0578 0.0166 0.0905 0.0024 0.0024 0.9256 -0.0207 0.3085
Nordea Avkastning 1.0321 0.1238 0.0677 0.0087 -0.0057 0.7983 0.0184 0.2987
Nordea Kapital 1.0130 0.4902 0.0528 0.0237 -0.0179 0.3800 0.0145 0.3687
Nordea Norge Verdi 0.8718 0.0015 0.1588 0.0013 0.1023 0.0174 -0.0031 0.9262
ODIN Norge C 0.9477 0.2477 0.2113 0.0002 0.0491 0.3135 0.0197 0.6077
Pareto Aksje Norge B 0.9326 0.1702 0.2342 0.0002 0.0413 0.4337 -0.0508 0.2243
Pareto Investment Fund A 1.0471 0.3145 0.0544 0.3431 -0.0767 0.1296 0.0640 0.1096
Storebrand Norge 0.9511 0.1978 0.0150 0.7460 -0.0150 0.7136 0.0626 0.0541
Index funds:
Alfred Berg Index Classic 0.9033 0.0000 -0.0412 0.0367 0.0232 0.1784 -0.0097 0.4748
DNB Norge Indeks* 0.9356 0.0005 -0.0288 0.2020 0.0492 0.0081 -0.0142 0.3192
KLP AksjeNorge Indeks II 0.9095 0.0000 -0.0418 0.0321 0.0243 0.1551 -0.0126 0.3502
Nordnet Superfondet Norge* 1.0350 0.4460 0.0053 0.9098 0.0986 0.0134 -0.0153 0.5748
PLUSS Indeks (Fondsforvaltning) 0.8914 0.0000 -0.0833 0.0042 0.0106 0.6744 -0.0427 0.0331
Storebrand Indeks - Norge A* 1.0237 0.3735 0.0179 0.5149 0.0713 0.0020 -0.0037 0.8160
p-valueMkt is under the null hypothesis of βMkt ≠ 1
90 Appendix 3
Estimates of the test statistics, t-values and p-values in the Spearman Rank correlation test for Heteroscedasticity in the Single Index model.
Active funds:
-0.0643 0.0208 -0.1150 -0.0036
-0.6973 0.2245 -1.2518 -0.0392
0.4870 0.8227 0.2131 0.9688
-0.1303 -0.0476 -0.0399 -0.1169
-1.4212 -0.5157 -0.4319 -1.2734
0.1579 0.6070 0.6666 0.2053
0.1130 -0.0494 -0.1839 0.1413
1.2297 -0.5345 -2.0237 1.5443
0.2212 0.5940 0.0452 0.1252
-0.0220 0.0131 -0.0100 -0.0825
-0.2385 0.1412 -0.1079 -0.8958
0.8119 0.8879 0.9142 0.3722
0.1042 -0.0386 -0.0133 0.0199
1.1327 -0.4183 -0.1439 0.2153
0.2596 0.6765 0.8858 0.8299
Index funds:
-0.0135 -0.0221 -0.0096
-0.1463 -0.2389 -0.1038
0.8839 0.8116 0.9175
-0.0693 -0.0137 -0.0529
-0.6878 -0.1014 -0.3818
0.4932 0.9196 0.7041
T-stat T-stat T-stat
P-value P-value P-value
DNB Norge Indeks Storebrand Indeks Norge Nordnet Superfondet Norge
rx,e rx,e rx,e
T-stat T-stat T-stat
P-value P-value P-value
Alfred B. Indeks Classic KLP AksjeNorge Indeks Pluss Indeks
rx,e rx,e rx,e
T-stat T-stat T-stat T-stat
P-value P-value P-value P-value
Danske Invest Norge I DNB Norge IV Nordea Avkastning Storebrand Norge
rx,e rx,e rx,e rx,e
T-stat T-stat T-stat T-stat
P-value P-value P-value P-value
Alfred B. Norge Classic Nordea Kapital Holberg Norge Pareto Investment Fund
rx,e rx,e rx,e rx,e
T-stat T-stat T-stat T-stat
P-value P-value P-value P-value
Alfred B. Humanfond C WorldWide Handelsbanken Norge Pareto Aksje Norge B
rx,e rx,e rx,e rx,e
T-stat T-stat T-stat T-stat
P-value P-value P-value P-value
Alfred B. Gambak Delphi Norge Eika Norge Odin Norge C
rx,e rx,e rx,e rx,e
T-stat T-stat T-stat T-stat
P-value P-value P-value P-value
Alfred B. Aktiv Fondsfinans Norge KLP AksjeNorge Norge Norge Verdi
rx,e rx,e rx,e rx,e
91 Appendix 4
Calculations of the Durbin-Watson statistic to test for autocorrelation in the Single Index model.
92 Appendix 5
Estimated test statistic and p-value in the skewness/kurtosis test for normality in the Single Index model generated by Stata.
Active funds:
2.9300 1.0400 7.0000 0.4800
0.2315 0.5960 0.0301 0.7865
No No No No Yes No No No
9.1400 7.3000 7.4600 3.6100
0.0104 0.0260 0.0240 0.1647
Yes No Yes No Yes No No No
4.9600 4.2400 2.6400 0.7600
0.0839 0.1198 0.2671 0.6828
No No No No No No No No
1.8600 6.4700 3.3000 5.4800
0.3951 0.0394 0.1919 0.0647
No No Yes No No No No No
1.9100 9.9600 2.0900 50.8900
0.3855 0.0069 0.3510 0.0000
No No Yes Yes No No Yes Yes
Index funds:
Reject H0 on % level:
12.2000 11.5100 14.3800 95% 99%
0.0022 0.0032 0.0008
Yes Yes Yes Yes Yes Yes
9.8500 6.0300 1.8300
0.0073 0.0490 0.4012
Yes Yes Yes No No No
Reject H0 Reject H0 5%/1% Reject H0
adj chi2 adj chi2 adj chi2
Prob>chi2 Prob>chi2 Prob>chi2
Reject H0 Reject H0 Reject H0
DNB Norge Indeks Storebrand Indeks Norge Nordnet Superfondet Norge
adj chi2 adj chi2 adj chi2
Prob>chi2 Prob>chi2 Prob>chi2
Reject H0 Reject H0 Reject H0 Reject H0
Alfred B. Indeks Classic KLP AksjeNorge Indeks Pluss Indeks
adj chi2 adj chi2 adj chi2 adj chi2
Prob>chi2 Prob>chi2 Prob>chi2 Prob>chi2
Reject H0 Reject H0 Reject H0 Reject H0
Danske Invest Norge I DNB Norge IV Nordea Avkastning Storebrand Norge
adj chi2 adj chi2 adj chi2 adj chi2
Prob>chi2 Prob>chi2 Prob>chi2 Prob>chi2
Reject H0 Reject H0 Reject H0 Reject H0
Alfred B. Norge Classic Nordea Kapital Holberg Norge Pareto Investment Fund
adj chi2 adj chi2 adj chi2 adj chi2
Prob>chi2 Prob>chi2 Prob>chi2 Prob>chi2
Reject H0 Reject H0 Reject H0 Reject H0
Alfred B. Humanfond C WorldWide Handelsbanken Norge Pareto Aksje Norge B
adj chi2 adj chi2 adj chi2 adj chi2
Prob>chi2 Prob>chi2 Prob>chi2 Prob>chi2
Reject H0 Reject H0 Reject H0 Reject H0
Alfred B. Gambak Delphi Norge Eika Norge Odin Norge C
adj chi2 adj chi2 adj chi2 adj chi2
Prob>chi2 Prob>chi2 Prob>chi2 Prob>chi2
Alfred B. Aktiv Fondsfinans Norge KLP AksjeNorge Norge Norge Verdi
93 Appendix 6
Calculations of the Durbin-Watson statistic to test for autocorrelation in Carhart’s 4-factor model.
94 Appendix 7
Estimated test statistic and p-value in the skewness/kurtosis test for normality in Carhart’s 4-factor model generated by Stata.
Active funds:
0.9200 5.0800 4.5400 2.0500
0.6321 0.0789 0.1035 0.3592
No No No No No No No No
6.4900 5.8000 11.5500 4.5100
0.0389 0.0550 0.0031 0.1046
Yes No No No Yes Yes No No
6.7800 1.9500 3.4100 0.2300
0.0337 0.3781 0.1818 0.8892
Yes No No No No No No No
1.4600 3.8900 1.0900 6.3000
0.4830 0.1430 0.5795 0.0429
No No No No No No Yes No
2.1700 7.3100 0.7900 48.0400
0.3387 0.0258 0.6730 0.0000
No No Yes No No No Yes Yes
Index funds:
Reject H0 on % level:
7.7200 5.9900 10.0800 95% 99%
0.0211 0.0501 0.0065
Yes No No No Yes Yes
2.8500 0.7600 0.3200
0.2401 0.6845 0.8503
No No No No No No
Reject H0 Reject H0 5%/1% Reject H0
adj chi2 adj chi2 adj chi2
Prob>chi2 Prob>chi2 Prob>chi2
Reject H0 Reject H0 Reject H0
DNB Norge Indeks Storebrand Indeks Norge Nordnet Superfondet Norge
adj chi2 adj chi2 adj chi2
Prob>chi2 Prob>chi2 Prob>chi2
Reject H0 Reject H0 Reject H0 Reject H0
Alfred B. Indeks Classic KLP AksjeNorge Indeks Pluss Indeks
adj chi2 adj chi2 adj chi2 adj chi2
Prob>chi2 Prob>chi2 Prob>chi2 Prob>chi2
Reject H0 Reject H0 Reject H0 Reject H0
Danske Invest Norge I DNB Norge IV Nordea Avkastning Storebrand Norge
adj chi2 adj chi2 adj chi2 adj chi2
Prob>chi2 Prob>chi2 Prob>chi2 Prob>chi2
Reject H0 Reject H0 Reject H0 Reject H0
Alfred B. Norge Classic Nordea Kapital Holberg Norge Pareto Investment Fund
adj chi2 adj chi2 adj chi2 adj chi2
Prob>chi2 Prob>chi2 Prob>chi2 Prob>chi2
Reject H0 Reject H0 Reject H0 Reject H0
Alfred B. Humanfond C WorldWide Handelsbanken Norge Pareto Aksje Norge B
adj chi2 adj chi2 adj chi2 adj chi2
Prob>chi2 Prob>chi2 Prob>chi2 Prob>chi2
Reject H0 Reject H0 Reject H0 Reject H0
Alfred B. Gambak Delphi Norge Eika Norge Odin Norge C
adj chi2 adj chi2 adj chi2 adj chi2
Prob>chi2 Prob>chi2 Prob>chi2 Prob>chi2
Alfred B. Aktiv Fondsfinans Norge KLP AksjeNorge Norge Norge Verdi
95 Appendix 8
Calculations of the Durbin-Watson statistic to test for autocorrelation in Treynor-Mazuy’s unconditional model.