Figure 1
Figure 2
Figure 3
Classification matrix based on BETA classifier
| Observed class | Percentage of correct classification | Predicted class | TOTAL | ||
|---|---|---|---|---|---|
| <0 | <0 ; 1> | > 1 | |||
| < 0 | 14% | 36 | 225 | 0 | 261 |
| <0 ; 1> | 99% | 23 | 4143 | 3 | 4169 |
| > 1 | 5% | 0 | 205 | 10 | 215 |
| TOTAL | 90% | 59 | 4573 | 13 | 4645 |
Descriptive statistics of quantitative independent variables
| N | Mean | Median | Minimum | Maximum | Std. Deviation | |
|---|---|---|---|---|---|---|
| R | 5055 | 0.33426 | 0.61367 | −36.5010 | 23.49568 | 5.560999 |
| R(-1) | 5018 | 0.36612 | 0.64163 | −36.5010 | 23.49568 | 5.566170 |
| (R-3) | 4944 | 0.37174 | 0.64123 | −36.5010 | 23.49568 | 5.572185 |
| (R-6) | 4835 | 0.39409 | 0.66000 | −36.5010 | 23.49568 | 5.613492 |
| AGE | 5055 | 4.10926 | 4.34381 | 0.0000 | 5.59099 | 0.975071 |
| SIZE | 5055 | 18.93488 | 19.09698 | 12.7528 | 22.53559 | 1.596097 |
| CF | 5054 | 0.05861 | −0.00184 | −0.3542 | 70.10703 | 1.094054 |
Descriptive statistics of quantitative independent variables in classes of SIGMA classifier
| Variable | Class of SIGMA | N | Mean | Median | Minimum | Maximum | Std. Dev. |
|---|---|---|---|---|---|---|---|
| R | 0 | 2480 | 1,33224 | 1,29754 | −11,4557 | 13,83502 | 3,403976 |
| 1 | 2575 | −0,62690 | −0,65290 | −36,5010 | 23,49568 | 6,904846 | |
| R(-1) | 0 | 2460 | 0,90702 | 0,81168 | −16,7491 | 21,52702 | 3,267253 |
| 1 | 2558 | −0,15406 | 0,22143 | −36,5010 | 23,49568 | 7,069031 | |
| (R-3) | 0 | 2432 | 0,82333 | 0,89965 | −18,8818 | 21,52702 | 3,877995 |
| 1 | 2512 | −0,06547 | 0,21742 | −36,5010 | 23,49568 | 6,795085 | |
| (R-6) | 0 | 2393 | 0,86726 | 0,91793 | −16,7867 | 21,52702 | 4,400762 |
| 1 | 2442 | −0,06958 | 0,35119 | −36,5010 | 23,49568 | 6,556710 | |
| Size | 0 | 2480 | 4,25810 | 4,46591 | 0,0000 | 5,58350 | 0,903739 |
| 1 | 2575 | 3,96591 | 4,18965 | 0,6931 | 5,59099 | 1,018972 | |
| WAN | 0 | 2480 | 18,98222 | 19,03036 | 12,7528 | 22,38194 | 1,376150 |
| 1 | 2575 | 18,88927 | 19,25083 | 13,0466 | 22,53559 | 1,781540 | |
| CF | 0 | 2479 | 0,08046 | −0,00222 | −0,3542 | 70,10703 | 1,534043 |
| 1 | 2575 | 0,03757 | −0,00124 | −0,3415 | 9,09067 | 0,288631 |
Classification matrix based on SIGMA classifier
| Observed class | Percentage of correct classification | Predicted class | TOTAL | |
|---|---|---|---|---|
| < 0.75 | > 0.75 | |||
| < 0.75 | 82.9% | 1921 | 395 | 2316 |
| > 0.75 | 76.7% | 543 | 1786 | 2329 |
| TOTAL | 79.8% | 2464 | 2181 | 4645 |
Global analysis of network sensitivity (SIGMA classifier)
| DISTRIBUTION | FUND | DATE | AGE | R(-1) | SIZE | R | R(-6) | R(-3) | CF |
|---|---|---|---|---|---|---|---|---|---|
| 2.90 | 2.75 | 1.51 | 1.35 | 1.20 | 1.19 | 1.12 | 1.03 | 1.02 | 1.01 |
Descriptive statistics of quantitative independent variables in classes of BETA classifier
| Variable | Class of BETA | N | Mean | Median | Minimum | Maximum | Std. Dev. |
|---|---|---|---|---|---|---|---|
| R | 0 | 304 | 1.20025 | 1.30403 | −14.628 | 20.05664 | 5.348625 |
| 1 | 4522 | 0.40023 | 0.67158 | −36.501 | 23.49568 | 5.441381 | |
| 2 | 229 | −2.11814 | −2.0185 | −31.0289 | 20.50384 | 7.296892 | |
| R(-1) | 0 | 300 | 1.10756 | 1.76688 | −36.501 | 13.66871 | 5.552314 |
| 1 | 4491 | 0.40151 | 0.63795 | −34.4015 | 23.49568 | 5.483564 | |
| 2 | 227 | −1.31399 | −0.84962 | −30.8209 | 14.91146 | 6.782666 | |
| (R-3) | 0 | 292 | 1.82123 | 1.6856 | −24.7961 | 21.52702 | 5.655938 |
| 1 | 4426 | 0.32228 | 0.65432 | −36.501 | 23.49568 | 5.533347 | |
| 2 | 226 | −0.53241 | −0.48742 | −30.8209 | 12.79057 | 5.91571 | |
| (R-6) | 0 | 278 | 0.98586 | 0.937 | −24.6169 | 18.48296 | 5.07533 |
| 1 | 4336 | 0.38388 | 0.66353 | −36.501 | 23.49568 | 5.621471 | |
| 2 | 221 | −0.14981 | 0.42433 | −30.8209 | 12.49409 | 6.04421 | |
| AGE | 0 | 304 | 3.50819 | 3.85015 | 0 | 5.12396 | 0.942185 |
| 1 | 4522 | 4.13225 | 4.37574 | 0.6931 | 5.59099 | 0.961346 | |
| 2 | 229 | 4.45323 | 4.86753 | 0.6931 | 5.50533 | 0.979203 | |
| SIZE | 0 | 304 | 17.75238 | 17.77637 | 12.7528 | 19.95648 | 1.344688 |
| 1 | 4522 | 18.96870 | 19.12191 | 12.7671 | 22.53559 | 1.57812 | |
| 2 | 229 | 19.83668 | 19.83888 | 13.9245 | 22.51503 | 1.407123 | |
| CF | 0 | 303 | 0.06953 | 0.01405 | −0.3239 | 1.40754 | 0.189824 |
| 1 | 4522 | 0.06084 | −0.00249 | −0.3542 | 70.10703 | 1.154969 | |
| 2 | 229 | 0.00008 | −0.00713 | −0.1938 | 2.24313 | 0.157846 |
Description of the network set used in classification based on SIGMA classifier
| ANN No. | ANN type | Number of hidden neurons | Activation function (hidden layer) | Activation function (output layer) |
|---|---|---|---|---|
| 1 | MLP | 6 | Logistic sigmoid | Softmax |
| 2 | MLP | 9 | Exponential | Hyperbolic tangent |
| 3 | MPL | 7 | Hyperbolic tangent | Softmax |
| 4 | MLP | 13 | Logistic sigmoid | Hyperbolic tangent |
| 5 | MLP | 9 | Logistic sigmoid | Softmax |
Macro and investment fund market data for USA, European Union and Poland
| 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | average p.a. | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| GDP | |||||||||||||||||
| GDP (in %) | USA | 3.8 | 3.5 | 2.9 | 1.9 | −0.1 | −2.5 | 2.6 | 1.6 | 2.2 | 1.8 | 2.5 | 2.9 | 1.6 | 2.2 | 2.9 | 2.0 |
| EU | 2.4 | 2.3 | 2.2 | 3.1 | 0.5 | −4.3 | 2.1 | 1.8 | −0.4 | 0.3 | 1.8 | 2.3 | 2.0 | 2.5 | 2.0 | 1.2 | |
| PL | 5.3 | 3.5 | 5.8 | 6.8 | 4.2 | 2.8 | 3.6 | 5.0 | 1.6 | 1.4 | 3.3 | 3.8 | 3.1 | 4.8 | 5.1 | 4.0 | |
| Inflation | |||||||||||||||||
| CPI (in %) | USA | 3.3 | 3.4 | 2.5 | 4.1 | 0.1 | 2.7 | 1.5 | 3.0 | 1.7 | 1.5 | 0.8 | 0.7 | 2.1 | 2.1 | 1.9 | 2.1 |
| EU | 2.4 | 2.3 | 2.2 | 3.2 | 2.2 | 1.5 | 2.7 | 3.0 | 2.3 | 1.0 | −0.1 | 0.2 | 1.1 | 1.6 | 1.6 | 1.8 | |
| PL | 1.7 | 0.7 | 1.4 | 4.0 | 3.3 | 3.5 | 3.1 | 4.6 | 2.4 | 1.0 | −1.0 | −0.5 | 0.8 | 2.1 | 1.1 | 1.9 | |
| Stock market capitalisation as a percentage of GDP | |||||||||||||||||
| USA | 133 | 130 | 141 | 138 | 79 | 105 | 115 | 101 | 116 | 144 | 151 | 138 | 147 | 166 | 148 | 130 | |
| UK* | 117 | 121 | 140 | 125 | 64 | 116 | 108 | 110 | 122 | 142 | 116 | 106 | 108 | 117 | 97 | 116 | |
| PL | 38 | 31 | 43 | 49 | 17 | 34 | 40 | 26 | 35 | 39 | 31 | 29 | 29 | 38 | 25 | 37 | |
| Open-end investment fund NAV growth | |||||||||||||||||
| USA | 10.2% | 8.8% | 16.9% | 15.4% | −20.0% | 15.8% | 6.3% | −1.6% | 12.2% | 15.3% | 5.5% | −1.4% | 4.4% | 14.7% | −5.6% | 6.5% | |
| EU | 9.5% | 22.8% | 14.5% | 7.5% | −22.9% | 15.2% | 14.0% | −1.4% | 12.9% | 9.5% | 15.8% | 19.5% | 4.5% | 11.6% | −3.2% | 8.7% | |
| PL | 36.8% | 71.0% | 62.3% | 43.0% | −52.8% | 28.2% | 29.1% | −10.1% | 38.2% | 27.1% | 7.5% | 20.9% | −0.7% | 13.8% | −10.6% | 20.2% | |
| Open-end investment fund structure | |||||||||||||||||
| USA | equity | 49.4% | 53.7% | 55.0% | 56.1% | 53.5% | 38.0% | 43.9% | 47.3% | 44.8% | 45.5% | 51.6% | 52.4% | 52.0% | 52.4% | 54.9% | 50.2% |
| money market | 27.6% | 23.5% | 22.8% | 22.5% | 25.7% | 39.8% | 29.8% | 23.7% | 23.1% | 20.6% | 18.1% | 17.2% | 17.6% | 16.7% | 15.2% | 22.6% | |
| bond | 17.0% | 16.0% | 15.3% | 14.4% | 14.0% | 16.3% | 19.8% | 21.9% | 24.4% | 26.0% | 21.8% | 21.8% | 21.8% | 22.3% | 21.7% | 19.8% | |
| multi-asset | 6.0% | 6.8% | 7.0% | 7.0% | 6.8% | 5.8% | 6.5% | 7.1% | 7.6% | 7.9% | 8.5% | 8.7% | 8.6% | 8.6% | 8.2% | 7.4% | |
| EU | equity | 35.0% | 38.0% | 41.0% | 39.9% | 29.1% | 33.9% | 36.0% | 33.0% | 33.0% | 37.0% | 38.0% | 38.0% | 37.0% | 38.0% | 39.0% | 36.4% |
| money market | 21.0% | 18.0% | 16.0% | 16.5% | 25.8% | 21.1% | 20.0% | 19.0% | 16.0% | 13.0% | 13.0% | 14.0% | 13.0% | 12.0% | 2.0% | 16.0% | |
| bond | 27.0% | 25.0% | 23.0% | 21.7% | 22.9% | 23.0% | 23.0% | 27.0% | 29.0% | 28.0% | 28.0% | 26.0% | 27.0% | 27.0% | 23.0% | 25.4% | |
| multi-asset | 14.0% | 13.0% | 15.0% | 15.5% | 16.0% | 16.4% | 15.0% | 16.0% | 16.0% | 16.0% | 16.0% | 17.0% | 17.0% | 18.0% | 26.0% | 16.5% | |
| other | 3.0% | 6.0% | 5.0% | 6.4% | 6.3% | 5.6% | 6.0% | 5.0% | 6.0% | 6.0% | 5.0% | 5.0% | 6.0% | 4.0% | 10.0% | 5.7% | |
| PL | equity | 12.7% | 10.7% | 19.5% | 31.3% | 23.4% | 29.0% | 27.7% | 19.2% | 16.9% | 16.0% | 13.8% | 11.7% | 10.9% | 11.9% | 13.4% | 17.9% |
| money market | 14.4% | 13.2% | 8.2% | 6.5% | 10.3% | 9.3% | 13.2% | 16.1% | 9.5% | 11.1% | 13.5% | 11.9% | 12.4% | 14.8% | 21.9% | 12.4% | |
| bond | 21.2% | 17.4% | 7.2% | 5.6% | 14.6% | 13.6% | 14.4% | 17.1% | 28.3% | 23.1% | 20.1% | 16.2% | 16.8% | 17.1% | 17.4% | 16.7% | |
| multi-asset | 16.2% | 18.6% | 26.3% | 31.7% | 26.5% | 32.7% | 28.8% | 18.9% | 13.8% | 11.3% | 15.1% | 12.8% | 9.5% | 11.7% | 11.4% | 19.0% | |
| other | 35.5% | 40.1% | 38.8% | 24.9% | 25.2% | 15.4% | 15.9% | 28.7% | 31.5% | 38.5% | 37.5% | 47.4% | 50.4% | 44.5% | 35.9% | 34.0% | |
Description of the network set used in classification based on BETA classifier
| ANN No. | ANN type | Number of hidden neurons | Activation function (hidden layer) | Activation function (output layer) |
|---|---|---|---|---|
| 1 | MLP | 13 | Hyperbolic tangent | Hyperbolic tangent |
| 2 | MLP | 6 | Logistic sigmoid | Softmax |
| 3 | MPL | 11 | Exponential | Hyperbolic tangent |
| 4 | MLP | 13 | Exponential | Logistic sigmoid |
| 5 | MLP | 15 | Logistic sigmoid | Hyperbolic tangent |