Classification of Open-End Investment Funds Using Artificial Neural Networks. The Case of Polish Equity Funds
and | Nov 07, 2021
Published Online: Nov 07, 2021
Page range: 269 - 284
DOI: https://doi.org/10.2478/ceej-2021-0020
Keywords
© 2021 Katarzyna Perez et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Open-end investment funds are publicly offered and classified in practice by ranking agencies such as Morningstar. The classification of these funds consists in assigning a given fund to a group of funds having the same investment style, which reflects the investment policy declared in the fund's prospectus and determines the level of investment risk taken by the fund manager. The style is visible in the name of the fund, so that the potential investor can identify and select a fund with an acceptable risk level for investment. Thus, the classification of funds facilitates their distribution and sale.
The current literature shows that managers of open-end investment funds often perform so-called style drift (K. C. Brown et al., 2015; S. J. Brown & Goetzmann, 1997; Chua & Tam, 2020; DiBartolomeo & Witkowski, 1997; Sha, 2020; Wermers, 2012). This means that they add financial instruments representing a different investment style to a fund's portfolio (for example, they may buy shares for a debt fund, or they may buy bonds into an equity fund) in order to increase this fund's profitability. The higher return is sought in order to increase the competition against peers and to attract new potential investors to such a fund. However, such action often causes the risk level of the fund to be different than declared (higher or lower), and the fund itself becomes misclassified (S. J. Brown & Goetzmann, 1997). Inaccurate fund classification produces the wrong signals and misleads investors, who become lost in the very rich offerings of these funds nowadays. This especially concerns individual investors, who are the dominant group of fund participants, characterised by different levels of risk tolerance and financial education that influence their investment decisions (Jiang et al., 2020; Müller & Weber, 2010). For this reason, there is a need for deep diagnosis of the methods of classifying open-end investment funds, which are key in their sale. New technologies come with help, including machine learning, which can be used as an objective tool for classifying open-end investment funds. It can be offered through robo-advisory, which is cheaper and less error-prone than stationary advisory (Jung et al., 2019). Thus, it can provide tangible benefits for both the demand and supply sides of this market.
The purpose of this study is twofold. First, it utilises machine learning tools to confirm the classification of open-end mutual funds, which is based on fund styles, reflected in funds’ names and designation of investment risk levels and prepared by rating agencies. Second, it verifies whether any other attributes, such as historical returns, age, size, cash flow or the channel of distribution and the current economic conditions, may influence this classification in addition to investment risk. In this article, we are going to answer these questions in the case of open-end mutual funds representing one style: equity. The justification for this choice is as follows. Equity funds are the dominant subject of research on open-ended mutual funds in general, and certainly research on investment style. This is because these funds have the greatest volatility and the highest management activity among open-end funds, and therefore, the greatest possible temptation for management to change the style. Moreover, equity funds constitute almost half of the population of open-end investment funds in the world (Investment Company Institute (2020)], Fig. 1.1). In this study, we focus on equity funds from Poland. Contrary to the mature and widely investigated fund market of the USA, this market is an emerging one and it still has a low share of stock market capitalisation and the net asset value in GDP (Investment Company Institute [(2020)], Figure 1.10). Nonetheless, its growth potential is very high, if only because of the PLN 1.3 trillion (EUR 0.3 trillion) in local household savings, which, due to the zero interest rate on bank deposits, has been transferred richly to open-end investment funds. Growing individual investors’ attention to the growing emerging fund market that consists of a wide offer of open-end investment funds justifies the need to verify whether these funds are classified correctly.
We base our study on a sample taken from the Morningstar Direct database. The sample consists of 4,645 monthly observations of 37 equity funds from the largest fund families registered in Poland from December 1995 to March 2019. We allocated funds to one of the classes generated using Multilayer Perceptron (MLP) and Radial Basis Function (RBF), used to solve classification problems. Risk measures—that is, standard deviation and beta coefficient—are our classifiers. The results of the study allow us to confirm the legitimacy of using machine learning as a tool for classifying open-ended equity investment funds. Artificial neural networks provided more applicable results in the case of standard deviation as a classifier than did beta ratio. In addition to the level of investment risk, the sigma classification is supported by the fund distribution channel, the fund name and the current economic situation, as well as the fund age and its size. We find historical returns (apart from the last-month return) and the net cash flows of the fund as insignificant for the fund classification.
To our knowledge, this study is the first in which neural networks are used to verify the correctness of the classification of open-end investment funds. The literature is dominated by two approaches to studying the style drift. The first, proposed by Sharpe (1992), is the return-based analysis, which considers the volatility of fund returns and shows the manager's actions regarding the investment risk. The second, described by Daniel et al. (1997), is the holding-based analysis, which examines the detailed composition of a fund portfolio in terms of its changes and volatility. Our study complements the results obtained using both methods by classifying mutual funds according to risk measures and, additionally, various fund characteristics that may be significant for this classification. We classify funds using artificial neural networks, one of the methods of machine learning which is an effective research tool implemented lately in the area of financial markets and asset pricing (Gandhmal & Kumar, 2019; Gu et al., 2020; Pandurang & Kumar, 2019). However, in the case of studies on open-end investment funds, machine learning is still a niche utilised so far only to examine the quality of an open-end fund price prediction and not to study the quality of fund classification. For example, Indro et al. (1999) extend the pioneer research of Chiang et al. (1996) by predicting 1-factor Jensen's alpha of funds with different styles using multilayer perceptrons (MLP) and the GRG2 nonlinear optimiser. Wang & Huang (2010) predict the Sharpe index by comparing the backpropagation neural network (BPN) to the fast adaptive neural network classifier (FANNC). Pan et al. (2019) investigate the possibility of predicting the net asset value (NAV) of equity funds by use of the functional link artificial neural network (FLANN), and Rout et al. (2020) add technical extensions to it. They confirm that machine learning techniques generate better open-end investment fund price forecasting results than commonly used linear models. We hypothesise similar results, this time, though, as far as the classification of open-end investment funds is concerned.
Finally, in this study, the research gap is filled regarding the classification of investment funds from emerging European economies. There is much evidence of the style drift on the mature American market (Bams et al., 2015; S. J. Brown & Goetzmann, 1997; Cremers & Petajisto, 2009; M. Kim et al., 2000; T. H. Kim et al., 2005; Mason et al., 2012; Sensoy, 2009). Researchers provide some evidence of the style drift in emerging fund markets in China (Chua & Tam, 2020; Sha, 2020; Zhou et al., 2018). For India, Mohanti & Priyan (2018) show that the fund managers exhibit some level of active management and a good selection capability. However, the literature on the classification of European funds is fragmentary. Castellanos and Alonso (2004), and Moreno, Marco and Olmeda (2006) demonstrated manipulation of the risk of a portfolio of funds by a large proportion of investment fund managers registered in Spain. On the other hand, Zamojska-Adamczak (2005) showed similar behaviour for Poland, unlike Białous and Truszkowski (2009)'s research on Polish funds. They used Sharpe's (1992) methodology and indicated that the equity funds studied by them invested the accumulated capital in line with the declared investment policy, maintaining approximately 86% of shares in the portfolio. In this study we hypothesise a similar result: not shifting the style of equity funds, but carrying out an up-to-date investigation utilising a novel method to classify open-end investment funds. We also investigate which fund attributes are important to this classification. Our findings support retail investors who might not be equipped with the tools to track the possible style drift, but who may deduce which funds deviate from the defined fund classification by analysing the funds’ names, channels of distribution, age, size and returns, as well as the current economic conditions.
The remainder of the article is organised as follows: in section 2 we characterise artificial neural networks. In section 3 we present the data, variables and research procedure for classifying mutual funds using artificial neural networks. In section 4 we discuss the results and in section 5 we conclude.
In order to classify mutual funds according to their investment style, the method of artificial neural networks (ANN) is applied. Artificial neural networks are information (data) processing systems. The main idea behind the operation of ANN is to reproduce the operation of the human nervous system, where signals are transmitted between neurons. Artificial neural networks are made up of layers of artificial neurons (see Figure 1). The input layer contains the number of neurons equal to the number of dependent (explanatory) variables used in the analysis.
Figure 1
Diagram of an artificial neural network
Source: own elaboration
Next, in the artificial neural network, there are hidden layers of neurons (there may be one, several or a dozen of these layers, depending on the complexity of the analysed problem). Neurons in the input layer are connected to the neurons in the first hidden layer by means of a weight system, and the neurons in the adjacent hidden layers are also connected. Thanks to weights, signals (values) coming from neurons are transformed before being transferred to other neurons. As each neuron obtains signals from many other neurons, these signals are aggregated in the neurons (see Figure 2). The most common types of aggregation are:
linear aggregation, where the aggregate value is a linear combination of the inputs:
radial aggregation, based on the distance of the vector of variables x from the vector of weights in:
Figure 2
Neuron diagram
Source: own elaboration
As this aggregation is a measure of the similarity between weights and values of the variables, it is often used in classification problems.
The output value of the neuron is determined by an activation function, which can be any kind of function. S-shaped, linear, or Gaussian are the most commonly used.
The final layer is output, which provides output that is the result of multiple transformations. In regression problems, there is only one neuron in the output layer, which gives 1 output value. In classification problems, the number of neurons in the output layer is equal to the number of classes into which we want to divide the analysed objects.
The strength of artificial neural networks lies in the possibility of applying various activation functions that transform signals into the terms of the problem analysis (linear, s-shaped, Gaussian) and aggregation (linear, radial). Thanks to this, artificial neural networks are used in the analysis of problems where the algorithm for solving the problem is not fully known or must be frequently or quickly modified. They solve problems in the area of little-known phenomena and processes; the user does not have to declare any form of model in advance, and does not even have to be sure that any mathematical relationship can be modelled at all.
The network operation process consists of 3 stages:
The learning stage, to adjust weights in order to obtain the most correct results. This stage takes place on the training set, extracted from the entire data set. It usually contains 50–80% of the observations. The testing stage, used to check the correct operation of the network on a new data set (approximately 10–30% of observations). If the correctness is not satisfactory, the network returns to the learning stage. The validation stage, in which final assessment regarding the correct operation of the network is made. Validation is performed on new data that was not used in the learning or testing stages. Most often, 10–30% of observations are allocated for validation.
Our dataset is formed using database of the Morningstar Direct for the local open-end investment fund. This local database is Poland. We find this market a representative setting from various reasons. In 1989 Poland started its period of transition from communism to capitalism and in 2004, 15 years later, together with a few other countries from Central Eastern Europe (CEE), Poland joined the European Union (EU). Since then, the country's gross domestic product (GDP) has always been positive—from a minimum of 1.4% to a maximum of 6.8% (see Table 1). In 2009, Poland was categorised by the World Bank as a mature economy and in 2018, by FTSE Russell, as a mature capital market. The Polish mutual fund market is the biggest amongst CEE countries and one of the most dynamically growing in the EU. On average, in 2005–2020, the open-end investment fund NAV has been growing there more than 20% p.a.; while, at the same time, on average in the EU it was 8.7%, and in the US, 6.5% (see Table 1). However, together with China, Poland is still among the countries with much lower ratios of stock market capitalisation to GDP than the most developed countries in the world; therefore, they tend to have fewer total net assets in regulated long-term funds that are relative to GDP (Investment Company Institute, 2020, see Figure 1.10). In other words, the open-end investment fund market in Poland is still much closer to that of an emerging market than it is to a mature one.
Macro and investment fund market data for USA, European Union and Poland
| 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 | |
| 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 | |
| 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 | |
| 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% | |
| 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% | |
data for stock market capitalisation as a percentage of GDP of UK in 2004–2014 comes from the World Bank database and in 2015–2018 from the CEICdata.com.
Source: Eurostat, World Bank, Investment Company Institute, European Fund and Asset Management Association, Polish Chamber of Fund and Asset Management
The Polish open-end investment funds are called “capital market funds” and they are offered mainly to retail investors. The style structure of the Polish open-end fund market is much more diversified than what is seen in the US or EU. Unlike in the US or EU, where taking NAV into account, the 2004–2018 equity funds counted for an average of 50.2% and 36.4%, respectively, in Poland, it was 17.9% (see Table 1). Polish multi-asset funds held, on average, 19%. Bond and money market funds accounted for 16.7% and 12.4%, respectively. This fund style structure suggests that the many Polish fund unitholders prefer to keep funds in their portfolios that are classified as moderate- or low-risk (at least lower than for their average American or European Union peers).
For the purposes of our study, we included data from the Morningstar Direct database on funds valued in PLN and funds belonging to large families of capital market funds registered in Poland, the net assets of which exceeded PLN 3 billion at the end of the research period. This condition was met by 12 out of 35 fund families, with a total market share of 87%. Ultimately, 37 equity funds were included in the sample (additionally, one fund was eliminated due to its short operation period of 2 months, thus yielding only 2 observations). The data on the funds start in December 1995 and go through March 2018, on a monthly basis. December 1995 was the first month of quoting the first equity fund operating on the Polish market and March 2018 was the last month of data availability. In total, the sample consisted of 4,645 observations (see Figure 3).
Figure 3
Number of observations in the studied period (12.1995-03.2018)
Source: own elaboration
The following data were used as explanatory variables ( logarithmic monthly return ( lagged logarithmic monthly returns by: 1 month R(-1), 3 months R(-3) and 6 months R(-6), calculated using quotations of the funds at the end of the given month, logarithm of fund operation time counted in months ( logarithm of fund size ( the value of financial flow (cash flow, distribution method - dichotomous variable
The descriptive statistics of these data are shown in Table 2. The diversity of returns and cash flow is very large but the values of
Descriptive statistics of quantitative independent variables
| 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 |
Source: own research
Additionally, the following input variables were introduced into the analysis:
These variables were introduced because of the additional information they contain. We recognise that this information may prove important in the classification process. The variable
The classification of funds was carried out on the basis of the following two
1. BETA ratio, which determines the degree of dependence regarding the fund's return rate and the return rate on the market portfolio, represented in our study by the WIG index.
According to the values of the beta coefficient, the observations were assigned to 3 classes:
This is justified in the interpretation of the value of this indicator. When a fund's beta is greater than 1, the fund is said to be aggressive and has systematic risk greater than the market portfolio. A fund with a beta value of less than 1 and greater than 0 is defensive and reacts poorly to market changes. A fund with a beta below 0 is a fund whose returns are opposite to those of the market portfolio. This is a very rare but occurring case, thus it has been included. It should be noted that the
According to these classification rules, there are 89.8% of all observations in class with BETA values between 0 and 1, 5.6% in class of negative BETA value and 4.6% in the third class – BETA more than 1. This uneven division is the result of only one style of funds being analysed. We expect a better distribution when more fund styles are taken into account in further research. The descriptive statistics of observations in each class based on BETA classifier are shown in Table 3.
Descriptive statistics of quantitative independent variables in classes of BETA classifier
| 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 |
Source: own research
According to the
The cut-off value of 0.75 corresponds to a variation of approximately 80%. This is a very high coefficient of variation; however, since we take into account equity funds, such high volatility is warranted. The
According to those rules, there are 49.9% of all observations in class with SIGMA values less than 0.75 and 50.1% ones in the class with SIGMA more than 0.75. The descriptive statistics of observations in each class based on BETA classifier are shown in Table 4.
Descriptive statistics of quantitative independent variables in classes of SIGMA classifier
| 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 |
Source: own research
The
From all possible combinations of parameters, 50 networks were selected, of which the best 5 (providing the best classification correctness) were selected for the final classification.
The classification was made on the basis of the network set – that is, the observations of a given fund were allocated to the class indicated by the largest number of networks.
As a result of building ANN procedure, there are 45 neurons in the input layer and 3 neurons in the output layer for each out of 5 of the best network. The number of neurons in the hidden layer vary from 6 to 13. All finally chosen networks are multilayer perceptrons with linear aggregation functions. The activation functions are logistics sigmoid in two networks, exponential in two networks and one hyperbolic tangent in hidden layer neurons. In the output layer there are hyperbolic tangents in three cases, logistics sigmoid and softmax (see Table 5).
Description of the network set used in classification based on BETA classifier
| 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 |
Source: own research
The adoption of the values 0 and 1 as the classifier's cut-off values was substantively justified; however, it resulted in the defensive funds class (
Classification matrix based on
| 225 | 0 | ||||
| 23 | 3 | ||||
| 0 | 205 | ||||
Source: own research
Based on the values of the input variables, neural networks correctly classified 4,189 observations (90.2%). There was a significant improvement in the quality of the classification within the class of defensive funds, where the networks correctly classified 99.4% of the observations. The percentage of correct classifications in the
The results show that many of the surveyed equity funds were defensive in their nature. After equity funds, we should expect an aggressive rather than defensive investment policy. This perhaps resulted from a very long research horizon, which smoothed out the volatility regarding the returns of these funds over time. This could be overlapped with the defensive actions of managers (let us bear in mind that they are from the companies managing the oldest funds of the largest size), who prefer allocating the funds’ assets in the value stocks that are less volatile than the growth stocks. Such approach to management meets the preferences of Polish individual investors—the structure of the fund market shows that in general they are rather risk averse, not risk takers.
The procedure of building of ANN resulted with the set consisting of 5 networks of MLP type (the aggregation function is linear). There are 45 neurons in the input layer and 2 neurons in the output layer. The number of neurons in the hidden layer varies from 6 to 13. In the hidden layer there is logistics sigmoid in three networks as well as the exponential function and the hyperbolic tangent in the two remaining ones. In output layers the softmax appears three times and the hyperbolic tangent twice. The final set of the neural network used in this classification can be seen in Table 7.
Description of the network set used in classification based on SIGMA classifier
| 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 |
Source: own research
The cut-off value of the
The observations classified in the first group (
The classification made with the use of artificial neural networks provides 79.8% of correct classifications (Table 8). The quality of the network operation can be considered to be satisfactory. This means that the assumed input variables that were the fund characteristics can be used to determine the fund's operating style and, to some extent, replace the standard deviation as a commonly accepted measure of risk.
Classification matrix based on
| 395 | ||||
| 543 | ||||
Source: own research.
The correctness of the classification in the group of observations for which the
The results confirm the legitimacy of using artificial neural networks as a tool for classifying equity investment funds. Overall, standard deviation turns out to be a better classifier than the beta ratio. Standard deviation is the most recognised measure of risk that is published in the Key Information for Investors Document (KIID) obligatory for open-end investment funds operating in the European Union. Therefore our results confirm that it can be used in practice by investors as an indicator of the open-end investment funds classification.
Artificial neural networks are a method of analysis known as a ‘black box’, which means that we enter input and get the result of the network, but we cannot fully control or analyse the rules producing the result or the rules that the network has detected. Therefore, the interpretation of the relationship between the characteristics of the funds used in the study as input variables, and the applied risk measures, is not easy and obvious. Part of this interpretation is possible thanks to the global sensitivity analysis, which allows comparison of the quality of the network classification with the given variable for each input variable used in the network and after its removal. A value higher than 1 obtained in such an analysis proves that the network works better with this variable than without it—thus, it is important for the quality of the classification. It is related to the investment risk taken by the funds. A value close to 1 proves that the network works just as well with this variable as without it—this variable adds nothing to the classification. A value lower than 1 indicates that the network without this variable provides better correctness of the classification than with this variable—it is a variable disturbing the classification.
The mean results of the overall sensitivity analysis obtained for the network group we investigated are presented in Table 9. The sensitivity analysis shows that the characteristics important for the fund classification based on the sigma risk taken by funds are primarily the distribution channel, the name of the fund and the current economic situation. Especially the last characteristic has not yet been considered and found important by the literature in the classification of open-end investment funds. Qureshi et al. (2019) prove that investors choose to invest in equity-based funds when economic conditions are good, but when they are poor, investors move to the income-type funds. Therefore the fund flows forecast the economic conditions (Ferson & Kim, 2012; Jank, 2012; Kopsch et al., 2015). We find the other side of the fund-macroeconomy relation—the economic conditions may be considered as the open-end fund classification guide—depending on the business cycle, the equity funds may be more or less tempted to drift the style in order to rescue the fund flows balance.
Global analysis of network sensitivity (
| 1.03 | 1.02 | 1.01 |
Source: own research.
Slightly less crucial, but still important for the classification, are the age and the size of the fund, as well as the current and last-month return. The less important variables turned out to be the 3 and 6 month lagged returns and the cash flows of the funds. Investors should pay attention to these characteristics when they make investment decisions about the funds. Presumably older and bigger funds with more stable short-term returns follow the classification reflected in their names more than funds that are younger, smaller and more volatile. It does not mean investors should avoid the latter funds. They should simply be aware such funds may be more exposed to the style drift.
Our results confirm the findings of Cao et al. (2017) in the case of the fund size, and of Herrmann et al. (2016) in the case of the one-month lagged return. The other results concerning other characteristics that we found essential to the classification of open-end investment funds based on the standard deviation seem to be pioneering. They should be further investigated in expanded research with the same (or similar) methodology in order to support their meaning for the investment fund style analysis.
The need for in-depth diagnosis of the classification of open-end mutual funds, of which so many are on offer nowadays, has been recently increasing mainly for two reasons. First, financial advisors have increased responsibility to offer funds objectively tailored to the capabilities of an individual investor. This investor has little knowledge of the financial market and has to invest her savings there because the current pension systems are not able to provide her with funds for old age. Second, the need to reduce the costs of management and distribution of actively managed funds, which, for example, is imposed by a competitive market in the US, and the MiFID II Directive in the EU, means that accurate classification is needed. New technologies come with help, including machine learning tools, which, in this article, were used to verify the correctness of the classification of equity funds managed by the largest investment fund companies in an emerging fund market in Europe. Classification based on artificial neural networks allowed us to partially confirm the standard class identification of the researched funds. Artificial networks provided more applicable results in the case of standard deviation as a classifier, where the classification was evenly distributed over 2 groups and was correct in about 87%. This result is quite similar to that achieved by Białous and Truszkowski (2009). In the case of the
The obtained results are sufficient to confirm the validity of using machine learning as a tool for classification (and further, for grouping) of open-end investment funds. To bolster the credibility of these results, further research should expand the sample to include other styles of funds in Polish and other markets, including the emerging fund market of China or the mature fund markets of Europe or the USA. Other risk measures, such as the Synthetic Risk and Reward Indicator (SSRI) published in the Key Information for Investors may be investigated as a risk measure as well. It is also worth considering other features of funds, such as those characterising the investors, the teams managing funds, or those describing the entire family of funds.