HEDGE FUND INDICES USING CLASSIFICATION BASED ON FUZZY SOFM NETWORK. Abstract

Transcription

1 HEDGE FUND INDICES USING CLASSIFICATION BASED ON FUZZY SOFM NETWORK Nandita Das Wilkes University Ratan Das ABB Inc. Abstract Hedge fund databases vary with the types of funds included and the classification system used. Classification systems are based on investment strategy and/or investment style. Considerable variation occurs in definitions, method of return calculation, and assumptions. The result is a myriad of classifications, some overlapping and some mutually exclusive. This calls for an alternative approach to hedge fund classification to deal with the lack of pure hedge fund types. Hedge fund literature relies almost completely on existing hedge fund classifications. Research results on hedge fund performance may differ depending on the database, making them difficult to compare. Indeed, the numerous classifications likely contribute to the disparities in values reported by different organizations and researchers measuring hedge fund performance. From an investor s perspective, information on hedge fund style is important for several purposes, namely, portfolio construction, performance attribution, and risk management. With numerous classifications, a particular hedge fund could belong to two different categories depending on the database used. Such heterogeneity, along with the fact that the classifications are self-reported, adds to the difficulty in understanding the characteristics of any hedge fund. This paper presents a hedge fund classification technique using neural network. Neural networks are modeled on the logical associations made by the human brain. Neural network based classifiers make weaker assumptions concerning the shapes of underlying distributions as compared to the traditional statistical classifiers. This research uses a self-organizing feature map (SOFM) neural network. The hedge funds in different groups using the new classification scheme are further analyzed to identify the attributes that represent the group membership. Group index is developed using the equal-weighted and value-weighted methodologies. Out-ofsample hedge fund data is used to classify hedge funds based on the group attributes of the fuzzy SOFM classifier. These benchmarks can be used to evaluate hedge fund performance. This classification method leaves no room for arbitrary style-allocation of a hedge fund by the manager. The investor will have a better idea as to the attributes of the hedge fund in question. From an academic perspective, this should lead to easy comparison of research outcomes using different databases and help in performance attribution of hedge funds. The performance of these hedge funds can be compared with the group index.

2 Hedge funds have enjoyed healthy growth through the years and continue to increase in popularity especially among high net worth individuals. Recently, an increasing number of institutions have allocated a small portion of their assets to these alternative investments owing to their long-term success. But the term hedge fund is used to describe a wide range of investment vehicles that can vary substantially in terms of size, strategy, and organizational structures. One commonality surrounding hedge funds is the limited amount of information provided to potential investors. Typically information is limited to periodic (monthly, quarterly, or annual) returns. Even the leading hedge-fund databases provide incomplete information drawn from the fund-offering documents such as contractual provisions (fee structure, minimum investment size, and withdrawal provisions), descriptions of investments, styles of investment, and the periodic return. Unfortunately, what constitutes a hedge fund is debatable and an industry standard for their classification schemes does not exit. There appears to be a myriad of classifications in existence. Investment strategy and/or investment styles are the basis of classification. Among these various classifications, there are some core strategies followed by the hedge fund managers. There is a need for a unified approach to the classification of hedge funds. The paper presents a hedge fund classification technique using fuzzy neural network. The classification is based on the asset classes the hedge funds invest in, the incentive fee, the risk, and liquidity of the investment strategy, and the size of the hedge funds. The results are compared with the existing classification in the CISDM database for the US and the Non-US funds. The paper proceeds as follows: Section I gives a brief history of the hedge fund industry. Section II provides a review of the literature. Data, modeling, and results are outlined in Section III. Section IV summaries our findings and contributions. 2

3 I. HEDGE FUND INDUSTRY In 1949, A.W. Jones introduced the concept of a hedge fund by combining a leveraged long stock position with a portfolio of short stocks in an investment fund with an incentive fee structure. Hedge fund investment practices and strategies have evolved from this simple concept. Moreover, hedge funds are no longer unique to the U.S. markets, but exist in many areas around the world. In the United States, they normally offer their shares in private placements and have less than 100 high networth investors, in order to make use of regulatory exemptions provided under the Securities Act of 1933, the Securities Exchange Act of 1934, and the Investment Company Act of l940. Interest in hedge funds and their performance has waxed and waned over time. Hedge funds have enjoyed healthy growth recently. For instance, the high-net-worth investors created through the bull market of the late 1980s started to invest in hedge funds as a means of enhancing their returns. In 1990, there were about 600 hedge funds worldwide with assets of approximately $38 billion. According to industry publications, at the end of 1998, despite the publicized collapse of Long Term Capital Management (LTCM), there were some 3,300 hedge funds with assets of approximately $375 billion. Additional investments at the turn of the century have pushed the hedge fund industry over the $600 billion mark. The true size of the hedge fund industry is not known, but present size is estimated to be anywhere from $600 billion to over $1 trillion. Although hedge funds invest in a variety of liquid assets similar to mutual funds, they are quite different. Under current federal law, hedge funds have no limitations on management, virtually no limits on the composition of the portfolios, and no mandatory disclosure of information about holdings or performance. 3

4 II. LITERATURE REVIEW Hedge Fund. The systematic study of hedge funds is a recent phenomenon, encouraged primarily by the availability of data. Most of the literature is less than a decade old, and focuses on performance attribution, performance evaluation, characteristics, and the impact on the financial markets. When modeling hedge fund performance as a group, researchers typically model hedge fund performance by treating all the hedge funds in a database as a single group. Examples include Schneeweis and Spurgin (1998), Ackermann et al. (1999). Researchers have also attempted to extract strategies from observed returns to reclassify hedge funds based on observed return characteristics. Examples include Fung and Hsieh (1997), Brown and Goetzmann (2001). The second research focus, performance evaluation, is essentially concerned with comparing the return earned on a hedge fund with the return earned on some other standard investment asset. Research in this area can be divided into three groups: benchmarking, performance persistence, and performance in a portfolio context. Key benchmarking research supports the fact that hedge funds outperform mutual funds, even on a risk adjusted basis. See, for instance, Ackermann et al. (1999), Brown et al. (1999), Edwards and Liew (1999), Agarwal and Naik (2000), Edwards and Caglayan (2001), Kat and Menexe (2002), Amin and Kat (2003) and Malkiel and Saha (2005). The third research area focuses on hedge fund characteristics. This area is the broadest focus group, starting with general characteristics and progressing to performance attributes, as in Brown et al. (2001). Characteristics of the hedge fund industry, including the fee structure, data conditioning biases, and the risk/return characteristic of various hedge fund strategies have been studied. For instance, see Park and Staum (1998), Schneeweis and Spurgin (1998), and Ackermann et al. (1999) for a thorough discussion of hedge fund characteristics. Returns are summarized in Amin (2002) Edwards (1999), 4

5 Fung and Hsieh (1999), and Lamm et al. (1999). Goetzmann et al. (1998) evaluate compensation issues. Several conclusions can be reached from this extensive set of empirical work on hedge funds. For instance, hedge funds consistently outperform mutual funds but not standard market indices. Hedge funds returns typically are more volatile then mutual funds, but hedge funds offer diversification effects when added to a portfolio due to their low correlation with traditional asset classes. Hedge funds have been shown to have risk-adjusted performance persistence, but not any direct role in precipitating risk in the financial market. Research has also shown that there may be diminishingreturn-to-scale in the hedge fund industry; that the incentive fee structure does not lead hedge fund managers to take more risk because of the possibility of non-survival, and that hedge funds follow a very dynamic strategy. Neural Network Applications in Finance. Neural Networks have become increasingly popular in the financial industry. Typical applications in finance include assessing the risk of mortgage loans [Collins, Ghosh, and Scofield (1988)], rating the quality of corporate bonds [Dutta and Shekhar (1988)], predicting financial distress [Salchenberger, Cinar and Lash (1992), Coats and Fant (1993), and Altman, et. al. (1994)], risk rating of mortgages and fixed income investments, index construction, simulation of market behavior, portfolio selection, identification of economic explanatory variables and economic forecasting [Trippi and DeSieno (1993)], predicting bond re-ratings [Hatfield and White (1996)]. According to Shandle (1993), companies such as General Electric, American Express, and Chase Manhattan Bank are using neural networks to screen credit applications, spot stolen credit cards, detect patterns which may indicate fraud and predict commodity and stock prices, bond ratings, and currency trading trends. 5

6 III. HEDGE FUND CLASSIFICATIONS IN DIFFERENT DATABASES The databases popular among researchers and investment community include: Center for International Securities and Derivatives Markets (CISDM) database (formerly, ZCM and MAR/hedge) which provides a comprehensive coverage of global hedge funds; the Hedge Fund Research (HFR) database which contains more equity-based hedge funds; and TASS, the information and research subsidiary of Credit Suisse First Boston Tremont Advisers. The database providers all offer hedge fund classifications and indices, unfortunately without much in common. Hedge fund categories listed in a particular database are based on the self-reported style classifications of the hedge fund managers. In addition, none of the databases provides information on the complete hedge fund universe. The databases also differ on their definition of a hedge fund. For example, TASS is the only database that includes managed futures fund which limit their activities to futures market. Since hedge fund managers employ a diverse array of investment strategies, the database providers must provide some sort of classification scheme. Although all the major databases rely on the voluntary information provided by the hedge fund managers, style definitions and the number of hedge fund categories differ among the database providers. For instance, the CISDM database used in this research classifies hedge funds into four general classes and ten broad categories of investment styles. The classes are onshore hedge fund (HF-US), offshore hedge fund (HF-NON), onshore fund-offunds (FOF-US), and offshore fund-of-funds (FOF-NON). Some of the categories have subclassifications. The CISDM database categories are shown in Figure 1. < Insert Figure 1 about here > 6

7 Hedge fund literature shows an almost complete reliance on the existing hedge fund classifications. Performance comparison of various hedge funds with the existing hedge fund indices return data is not appropriate as a particular hedge fund could be classified in two or more classes depending on the database. Table 5 compares the classifications of the CISDM, HFR, TASS and VanHedge databases. <Insert Table 1 about here> It appears from Table 1 that research on hedge fund performance may produce different results, based on the database used. There seems to be no common comparison basis for the existing literature on hedge funds. The disparity that is observed in the numbers produced between different organizations measuring hedge fund performance could be attributed to the varied classification of hedge funds. Much variation exists in the definitions, calculation methodologies, assumptions, and data employed by the different managers and databases. It is necessary to benchmark hedge fund manager practices relative to their peers as hedge funds follow diverse strategies. There is a need for an alternative approach to hedge fund classification given the lack of pure hedge fund types that exist in the industry. IV. DATA ORGANIZATION AND METHODOLOGY The unregulated nature of the hedge fund industry leads to the lack of transparency in hedge fund operations. It is this characteristic that has allowed hedge fund managers to seek economic returns from non-traditional investment strategies. It is imperative to bring some kind of uniformity between the different databases in existence and also within the same database. The classification schemes provided by different database providers are overlapping and many-a-times confusing from the perspective of the investor. 7

8 Hedge funds have all the characteristics of a complex ill-defined system, namely, inadequate a-priori information, a great number of variables that are not measurable, noisy and short data sample and many fuzzy characteristics. Classification of such ill-defined objects can be done using fuzzy neural networks. Unlike mathematical models, in neural network, the relationship between the independent and dependent variable(s) is estimated by selecting a suitable architecture of the neural network. A neural network is a mapping process for transforming inputs into desired outputs using highly connected networks of relatively simple processing units (neurons or nodes). Neural networks are modeled after the neural activity in the human brain. Kaastra and Boyd (1996) provide a simplistic understanding of the neural network and its relationship to the conventional regression analysis. Neural networks can model non-linear functions. This capability makes them suitable for pattern classification, where complex relationship exists between the input variables and the grouping of hedge funds. Generalization capabilities of neural networks help them process the data that broadly resembles the data they were trained-on. A neural network that is trained to recall non-noisy patterns may recognize noisy patterns, as well as data with desired segments missing and/or undesired segments added. Neural network based classifiers make weaker assumptions concerning the shapes of underlying distributions as compared to the traditional statistical classifiers. They may, therefore, prove to be more robust when distributions are generated by non-linear processes and are non-gaussian (Lippman, 1987). Neural networks can handle non-gaussian noise, which is quite often found in the parameters that are used to characterize a hedge fund. A neural network consists of simple computing elements connected in a network. Although a single neuron can handle simple function approximation problems, 8

9 the strength of neural computation comes from the neurons connected in a network (Lippman-1987, Dayhoff-1990, Tarassenko-1998, Haykin-1999). The hedge fund classification technique presented in this paper uses self-organizing feature maps for grouping hedge funds based on the fuzzified attributes. A Self-Organizing Feature Map (SOFM) is a neural network that trains itself to produce the output based on the inputs. It is ideally suited for classification purpose where the grouping of data is not known a-priori. Data characteristics, attributes, class membership, and other such properties describe the data for classification. These descriptors collectively are the attributes of the problem. Attributes that are highly correlated add little in terms of distinguishing the data units, and including attributes that have large variation among data units, but are not relevant to the problem at hand will provide misleading results. Hedge funds domiciled in the US and those domiciled outside the US are analyzed separately. Many hedge fund managers have two simultaneous operations, one domiciled in the US and another domiciled outside the US, but with same characteristics in terms of their investment strategy and investment style. A. Attributes used for Classification Asset Class: The asset class defines the market in which the fund operates. This attribute is subdivided into four different sub-attributes: stocks, bonds, currency, and derivatives. Each of these subdivisions is considered as a separate attribute for the clustering purpose. The attribute derivative is composed of options, futures, and warrants. No specific ordering is given to any of these three derivatives. In fact, they are taken as derivative 1, derivative 2, and derivative 3. If a hedge fund uses all three types of derivatives, proper weight is assigned to represent the use of all types of derivatives. 9

10 Size 1 : The minimum purchase is used as a proxy for size. It represents the size of a unit share in the particular hedge fund. Fee 2 : Incentive fee is used as an attribute for classification. Leverage: Leveraging and other higher-risk investment strategies are a hallmark of hedge fund management. Leverage varies from 0 to 70 times the asset value. Liquidity: There is no direct measure of liquidity that could be calculated for hedge funds. Redemption frequency that varies from daily to annually is considered as a measure of liquidity. B. Data Organization The attributes considered for the classification have different scales of measurement (quantitative and qualitative). The attributes for asset class are of the qualitative type, giving information as to whether the hedge fund invests in a particular asset class or not (no portfolio composition). All the attributes are converted to qualitative type, while taking care to minimize the loss of information in the conversion process. Evolutionary fuzzy logic 3 is used to convert the quantitative variables into qualitative variables with an ordinal measurement scale using a two-stage process. In Stage 1, the data is examined to estimate the ranges of each of the quantitative attributes. Table 6 lists the available ranges for each of the attributes along with the number of funds in each range. In Stage 2, groups are formed using different ranges of the attributes. The new ranges are than assigned a state, using ordinal scale. Table 6 provides the assigned states and the number of funds in each state for the attributes of incentive fee, leverage, redemption frequency, and minimum purchase. The asset class is subdivided into four attributes: stocks, bonds, currency, and derivatives. Hedge fund managers in the CISDM database used three types of derivatives. No distinction is made as to the type of derivative used for 10

11 assigning states to this attribute, but due consideration is given to the number of derivatives used by a hedge fund manager. For example, if a hedge fund manager uses two of the derivative instruments (options and futures, future and warrants, etc.) the fund is assigned to the State 2 for the derivatives attribute. The selection criteria provides eight attributes; four for the asset class, and one each for incentive fee, leverage, redemption frequency, and minimum purchase. These eight attributes are used to find the similarities between the hedge funds in the database. Since the derivatives can have a maximum state of +3, the other attributes of the asset class are also given a state of +3 if they invest in the particular asset class and a state of -3 if they do not invest in that asset class. A State of zero (0) is assigned to hedge funds that do not have any information as to their use or lack of use, concerning the attribute in question. Finally, all attributes are converted to uniform logical states of +3 to -3 while maintaining the number of states related to each attribute. This assigns equal importance to each of the eight attributes used for the classification. All logical states are represented by a decimal number which is used for the computation of distance measure. <Insert Table 2 about here> C. Methodology The ability to learn from training patterns is one of the most important characteristics of the neural network. The learning mechanisms which are used for neural network models update the weights as per a learning rule or algorithm, so that the network responds in a desired manner. These learning rules determine optimum weights by minimizing certain performance index. In unsupervised learning, used in the present research, the desired response is not known and it involves analyzing the cross- 11

12 correlation between the input and the output variables. A stronger correlation would result in increasing the weights, whereas a weaker correlation would result in decreasing the weights. The hedge fund classification technique uses various attributes of hedge funds, described above, to reach a decision and tends to emulate the conventional function approximation problem. An equation of the function describing the hedge fund classification return is embedded in the Self-Organizing Feature Maps Neural Network by training the network using an appropriate learning algorithm and suitable training data. The development process for the hedge fund classifier consists of the following steps: Preparation of training data Selection of a neural network architecture Training of the neural network Evaluation of the trained network using test data The development process is iterative. A particular neural network architecture selected may not be trained as desired. In that situation, the architecture and parameters must be changed and the network retrained. Important development issues and various aspects of training a neural network for the classification of hedge funds are discussed here. Training Data: The selection of suitable training data is an issue of prime importance for a neural network. The training data should contain all the necessary information to generalize the problem of hedge fund classification. Otherwise, it could lead to incorrect results, non-optimized solutions, and unpredictable behavior. Two separate networks are trained: one for hedge funds domiciled in US (HF-US) and the other for hedge funds domiciled outside US (HF-NON). For HF-US, eight attributes of randomly selected 1060 funds are used to train the network from the 1590 funds that 12

13 are available, leaving one-third fund data for testing purpose. Random selection is done to eliminate any bias that may be introduced based on the classification provided by the database provider. Similarly, the attributes of 892 randomly selected funds are used to train the network for the HF-NON hedge funds which has a total number of 1338 funds. SOFM Neural Network Architecture: The architecture of a neural network is applicationspecific. A Self-Organizing Feature Map 4 is used to classify hedge funds based on the above mentioned fuzzified attributes. Detailed discussion about the Self-Organizing Feature Map is available in Kohonen (2001). The attributes selected are such that the characteristics of a hedge fund represented with this set of attributes should not change with time unless the very structure of the hedge fund is changed. The market conditions, which have an impact on the return of the hedge fund, will not change the group membership of the hedge fund. Proper care is taken to ensure that the attributes selected represent the structure and not the return characteristics of the hedge fund. In this research, the MATLAB software along with the Neural Network Toolbox (The Mathworks Inc.,2006) is used. The built in topology function randtop, is used to initialize the locations of neurons in an N-dimensional random pattern which continuously changes during the training two such positions are shown in Figure 2. At the end of the training, the final location of the neurons could be very different from the initial location, depending on the dataset, and some neurons may end up as dead neurons (not associated with any group) depending on the data characteristics. The linkdist function in MATLAB is used to compute the distance between two neurons, which is the number of links, or steps, that must be taken to get to the neuron under consideration. The advantage of this measure is that it is always an integer and results in improved computation speed. 13

14 < Insert Figure 2 about here > The training process is started with 27 neurons, arranged in 3-dimensions, which has the ability to organize the data into twenty-seven groups a large number of possible groups is selected initially to allow the neural network enough degrees of freedom in grouping the hedge funds. It is observed that the dataset (both HF-US and HF-NON) primarily contains six groups of funds, based on the selected attributes. In the second stage, 8 neurons (arranged in three-dimensions) are selected for both the SOFM neural network used for the classification of HF-US and HF-NON hedge funds. However, it is observed that the dataset is again organized into six groups, although the architecture selected had the option of organizing the dataset into eight groups. Training and Adaptation: The neural network is trained using the training data and the Kohonen algorithm (Kohonen, 2001). Neurons close to the winning neuron are updated along with the winning neuron. One can chose from various topologies of neurons. Similarly, one can choose from various distance expressions to calculate neurons that are close to the winning neuron. Thus, when a vector is presented, the weights of the winning neuron and its close neighbors move together. Consequently, after many presentations, neighboring neurons will have learned vectors similar to each other. This process of training minimizes the dead neurons. The results obtained from training the fuzzy neural network for the hedge funds domiciled in the US (HF-US) and hedge funds domiciled outside US (HF-NON) are presented in Table 7 and Table 8 respectively. The training process is repeated five times each time the training is done for 2000 epochs. The reason for training the network five times with the same dataset is to check the robustness of the trained network. During each of the training process, the randtop function will initialize the neuron position differently as shown in Figure 2. It is observed from the training 14

15 results that three sets of grouping are very similar and other two sets follow closely with less than 10% variation of funds grouping. However, data is organized into six groups for both HF-US and HF-NON funds, although it was possible to organize the data into eight groups. This (an important finding of this research), indicates that there are six possible grouping of the hedge funds, irrespective of their domicile, based on the attributes selected. Table 3 and Table 4 present the grouping from one of the training set out of the five sets. <Insert Table 3 and 4 about here> It is important to identify the distribution of funds from the original CISDM classification to the new classification scheme for different numbers of Groups. Table 3 and Table 4 show the cross-tabulation of the CISDM classification versus the six-group classification for HF-US hedge funds and HF-NON hedge funds using the SOFM neural network. It is clear from Table 3, for hedge funds domiciled in the US, Group 5, the largest group in terms of total number of funds, consists of hedge funds from all of the categories. Similar results are obtained for hedge funds domiciled outside US. It is interesting to note that the hedge fund classification has not kept intact any of the original classifications of the CISDM database. It can be inferred that the hedge fund categories of the CISDM database consist of heterogeneous hedge funds, with regard to the attributes that are considered in the present study. Out of the six groups, Group 5 has about one-third of the funds from each category. It appears that most of the hedge funds are very similar to each other, even if they belong to different categories of the database for funds domiciled in the US. The results are similar for hedge funds domiciled outside US. The largest group here is Group 2, which contains approximately 30% of the total hedge funds, as is shown in Table 4. 15

16 Testing Trained Neural Network Performance: For neural learning to be considered successful, it is essential that the network performs correct approximation of test data, i.e. the data on which the network has not been trained. This capability of a network is an index of the generalization the performance of trained HF-US and HF-NON fuzzy neural networks with test data is listed in Table 5 and Table 6 respectively. The test data for HF-US funds consists of 530 funds and the test data for HF-NON consist of 446 funds. The testing process is also repeated five times with the corresponding weights of neural connections obtained from the trained network. It is interesting to note that the randomly selected test data for HF-US and HF-NON funds are also distributed into six groups. Table 5 and Table 6 present the grouping from the corresponding test set, for which training results are presented in Table 3 and Table 4 respectively. The distribution of hedge funds into different groups using the test data is very similar to the distribution obtained using the training data. This is noteworthy since the two data-sets are non-overlapping and the hedge funds for each data-set are selected randomly. <Insert Table 5 and 6 about here> The idea of classification is to come up with a manageable number of groups of hedge funds, without having hedge funds with very different characteristic grouped together. It should be noted that the choice of six groups was not determined a-priori. The data attributes lead the network to classify the hedge funds into six groups in spite of using eight neurons. V. TESTING THE VALIDITY OF THE CLASSIFICATION SCHEME In addition to the checking of performance of the SOFM network using (out-of-sample) test data described above, the validity of the classification scheme was also verified using the dummy variable regression. The return of all the hedge funds belonging to a particular group is regressed on dummy 16

17 variables that indicate the membership of the fund to the category of the CISDM classification. The purpose here is to test the null hypothesis of no difference in the mean return of hedge funds of different categories, as long as these hedge funds are members of the same group. The regression model is as follows: [ Ri ] = α [] ι + β [ D1 i ] + β 2[ D2i ] + β 3[ D3i ] β m [ Dmi ] + ε i 1 (1) where: R i is the (N x1) vector of monthly return of hedge fund i for the study period ι is the (N x 1) vector of ones, and D 1 i, D 2 i,., D mi, is the (N x1) vector of dummy variables indicating membership of the hedge fund to a particular category respectively. For example, D 1=1 if the hedge fund belongs to the Event Driven category, it takes a value of zero otherwise. There are m categories, and so the number of dummy variables is (m-1). This avoids the dummy variable trap of perfect multicollinearity. The mean return of hedge funds from group 1 that belong to category m is given by: E ( Ri D i = D2i =... = D( m 1) i = 0) = α + β m 1 (2) Similarly, the mean return of hedge funds from Group 1 that belong to the control category (Global Regional Established) is: ( R D = D =... = D = 0) = α E (3) i 1i 2i mi If the null hypothesis of no difference in mean return of Group 1 hedge funds belonging to different categories is true, then the estimated betas obtained from the regression of Equation (1) should be statistically insignificant. The results of the regression of hedge fund return on dummy 17

18 variables indicating category membership using the training data are given in Table 7 and Table 8 for hedge funds domiciled in the US and domiciled outside US respectively. < Insert Table 7 and 8 about here > The highlighted values are the betas that are statistically insignificant. For hedge fund domiciled in US, only three categories of Group 1 have betas that are statistically significant. The result of the regression is quite impressive. In general, the individual betas are insignificant for all groups except Group 5 which has mixed results. This in general lends support to the hypothesis that category membership does not influence return, as long as the funds belong to the same group. However, the result of Group 5 does not lead to any specific conclusion. This apparent discrepancy in result is due to the large number of funds in Group 5. The result of the regression of hedge fund return on dummy variables indicating category membership for hedge funds domiciled outside US is slightly different than those obtained using hedge funds domiciled in US. Table 9 and Table 10 have the result of the regression analysis, using the test data, for hedge funds domiciled in the US and domiciled outside US respectively. All the groups have statistically insignificant betas. It should be noted that the results are slightly different for before-fee and after-fee returns. It appears from the result that fees do make a difference in the overall analysis. Since investors are concerned with after-fee return and fees vary from hedge fund to hedge fund, it is important to consider after-fee return in the analysis. < Insert Table 9 and 10 about here > The same approach is used to test the difference in return of hedge funds of the same category, but having membership in different groups. If the group-membership represents the expected return 18

19 characteristics of the hedge funds, then the betas obtained from the regression of group-fund return on the dummy variables should be statistically insignificant, indicating category membership. Similarly, the betas obtained from the regression of category-fund return on the dummy variables should be significant, indicating group membership. The results are similar and are not provided here for the sake of brevity, but are available from the author on request. In general, the betas obtained from the regression of category-fund return on the dummy variables are statistically significant; leading to the conclusion, that group-membership influence return characteristics. VI. DEVELOPMENT OF HEDGE FUND INDEX Performance Evaluation is concerned with comparing the return earned on a hedge fund with the return earned on some other standard investment asset. It is thus necessary to develop appropriate benchmarks for the new classification scheme. An investment benchmark is a passive representation of a manager s investment process. It represents the prominent financial characteristics that the investment would exhibit in absence of active investment judgment. The new classification scheme is used to develop equal-weighted and value-weighted benchmarks for the groups. The benchmarks are developed on a monthly basis. The annual results are the average of the monthly results. These benchmarks can be used to evaluate hedge fund performance. Table 11 provides the equal-weighted and value-weighted benchmarks, before fee basis, for each group in each year of study along with the three market indices for the hedge funds domiciled in the US. Table 12 show similar results for the hedge funds domiciled outside the US. Tables also show the average number of funds in each cluster in each year. < Insert Table 11 and 12 about here > 19

20 VII. SUMMARY AND CONCLUSION Investment strategy and/or investment style are the basis of the classification schemes of hedge funds employed by different database providers. This classification varies from database to database. There is considerable variation in the definitions, return calculation methodologies, and assumptions. There exists a myriad of classifications, some overlapping and some mutually exclusive. The source of information for the classification scheme is the questionnaire filled by the hedge fund manager. It is important to note that the strategy definitions themselves are sometimes not clear. At a certain time, a hedge fund manager may think that the fund s investment strategy matches with a particular category; the same manager may think otherwise at a different time-period, although there may not have been any fundamental change in the strategy followed by the manager. This paper discusses a hedge fund classification technique using SOFM neural network for the CISDM database. The attributes used for classification are those that influence the return characteristics of the hedge funds. These attributes will affect the hedge fund return, but the return will not affect the classification scheme. The classification is based on asset class, the size of the hedge fund, incentive fee, risk-level, and the liquidity of the hedge funds. All attributes are converted into a uniform scale of measurement using evolutionary fuzzy logic. Similarities in attributes of interest are the basis of the formation of groups for the hedge funds. The new classification obtained using the hedge fund classification technique using SOFM neural network is compared with the existing classification of the CISDM database. The new classification has not kept intact any category of the existing classification. This suggests that the existing classification does not consider the attributes that are used for classification in this paper. The attributes used in this paper do not have any subjective criteria that would change from manager to manager. 20

21 The validity of the classification scheme is tested using the dummy variable regression approach. The result of the regression is quite impressive. The new classification is used to develop benchmarks for evaluating the performance of hedge funds. Hedge funds from other databases can be classified using this classification scheme. The group indices can be used to compare performance of hedge funds belonging to that group. Further work needs to be done to determine the representative characteristics of a typical hedge fund for membership to a particular group, which will help in the identification of hedge funds to this new classification approach. ENDNOTES 1. The net asset value could be a measure of size. However, the net asset value will change from year to year and will depend on the method of calculation. Mutual funds are valued daily with a published net asset value (NAV). There are no specific rules governing hedge fund pricing. U.S. hedge funds provide investors only a monthly estimate of percentage gain or loss. 2. In general, hedge funds charge two types of fees: an asset management fee and an incentive fee. The asset management fee is based on percentage of assets in the fund, usually 1 or 2 percentage points per year. This includes legal, audit, administrative, and other expenses. It is paid monthly or quarterly and may be due at the beginning or end of each period. The fee is automatically deducted pro rata from each investor s account. The asset management fee is almost same for all hedge funds. Therefore, the asset management fee is not considered as an attribute for this classification system. The incentive fee or the carried interest is the hedge fund manager s share in the fund s profit. This incentive fee is what differentiates hedge funds from mutual funds. Usually the fee is 20 percent, but it could vary from 0 percent to 50 percent. 3. The evolutionary fuzzy logic, a form of multi-valued logic is based on the notion of graded truth and falsity, similar to other multi-valued logical systems. However, it allows the researcher to change the number of states without changing the membership of already classified members. It also incorporates a state of unknown where truth and falsity merge. This feature helps to address missing information in the data set for any attribute. In the context of this paper, this logical system allows to convert the quantitative variable into qualitative variable with ordinal measurement scale. For example, a hedge fund that identifies 21

22 itself as using a leverage of 10% has membership in State 3 which encompasses State 1 (up to 1% leverage) and State 2 (1%-2% of leverage). 4. Self-organizing in networks is one of the most interesting areas in the neural networks field. Such networks can learn to detect regularities and correlations in their input and adapt their future responses to that input accordingly. The neurons of competitive networks learn to recognize groups of similar input vectors. Self-Organizing Feature Maps (SOFM) learn to classify input vectors according to the data grouping in the input space. Neighboring neurons in the self-organizing map learn to recognize neighboring sections of the input space. Thus, selforganizing maps learn both the distribution (as do competitive layers) and the topology of the input vectors they are trained on. The neurons in the layer of a SOFM are arranged originally in physical positions according to a topology function. Distances between neurons are calculated from their positions with a distance function. A self-organizing feature map network identifies a winning neuron as is normally employed by a competitive layer. However, instead of updating only the winning neuron, all neurons within a certain neighborhood of the winning neuron are updated using the Kohonen rule. After many presentations of training data neighboring neurons will have learned vectors similar to each other. When a new data set (not used for training the network) is presented to the trained network it will be able group the data with one of the pre-classified group. REFERENCES Altman, E., M. Giancarlo and F. Varetto (1994), Corporate Distress Diagnosis: Comparisons Using Linear Discriminant Analysis and Neural Networks (the Italian experience), Journal of Banking and Finance, Vol Brown Stephen J., William N. Goetzmann and James Park (2000), Hedge funds and the Asian Currency Crisis of 1997, The Journal of Portfolio Management, Summer, Caldwell Ted, Classifying Hedge Funds:What s in a Name?, Investment Policy, 1, Coats, Pamela K. and L. Franklin Fant (1993), Recognizing Financial Distress Patterns Using a Neural Network Tool, Financial Management, Vol. 22(3), Collins E., S. Ghosh, and C. Scofield (1988), An Application of a Multiple Neural Network Learning System to Emulation of Mortgage Underwriting Judgements, Proceedings of the IEEE International Conference on Neural Network, July, Das, Nandita and Das, Ratan (2005): Hedge Fund Classification Technique using Self Organizing Feature Map Neural Network, Presented at the Annual Meetings of the Financial Management Association International, Chicago, IL, October Das, Nandita (2003a): Essays on Hedge Fund, Doctoral Dissertation, Lehigh University,

23 Das, Nandita (2003b): Development of an Analytical Framework for Hedge Fund Investment, A Research Paper Submitted to The Foundation for Managed Derivatives Research. Das, Nandita (2003c): Hedge Fund Classification using K-means Clustering Method, Presented at the 9th International Conference on Computing in Economics and Finance, July 11-13, U of Washington, Seattle. Das, Ratan (2001): Evolutionary Fuzzy Logic: A New Paradigm, Proceedings of the IASTED International Conference on Artificial Intelligence and Applications (AIA 2001), Marbella, Spain, Sept. 4-7, Paper No , p Dayhoff, Judith E. (1990), Neural Network Architectures: An Introduction, Van Nostrand Reinhold< New York. Dutta S. and S. Shekhar (1988), Bond Rating: A Non-Conservative Application of Neural Networks, Proceedings of the IEEE International Conference on Neural Network, July, Franklin R. Edwards (1999), Hedge Funds and the Collapse of Long Term Capital Management, Journal of Economic Perspectives, Vol.13, Fung, William and David A. Hsieh (2001), Benchmarks of hedge fund performance: Information content and measurement bias, Financial Analyst s Journal. Fung, William and David A. Hsieh (1997), Empirical Characteristics of Dynamic Trading Strategies: The Case of Hedge Funds, The Review of Financial Studies, Vol. 10, Goldman Sachs & Co. & FRM (2000), Hedge Funds Revisited, Pensions and Endowment Forum. Goldman Sachs & Co. & FRM (1998), Hedge Funds Demystified: Their Potential Role in Institutional Portfolios, Pensions and Endowment Forum. Hatfield, Gay B., and A. Jay White, Bond Rating Changes: Neural Net Estimates for Bank Holding Companies, 1996, Working Paper. Haykin Simon (1999), Neural Networks: A Comprehensive Foundation, Second Edition, Prentice Hall. Hoppner Frank, Frank Klawonn, Rudolf Kruese and Thomas Runkler (1999), Fuzzy Cluster Analysis, John Wiley and Sons Ltd. Johnson Richard A. and Dean W. Wichern (1998), Applied Multivariate Statistical Analysis, Prentice Hall. Kaastra I, and Milton Boyd (1996), Designing a neural network for forecasting financial and economic time series, Neurocomputing, Vol. 10, Kohonen, T (2001), Self-Organizing Maps, Third Extended Edition, Springer Series in Information Sciences, Vol. 30, Springer, Berlin, Heidelberg, New York.. Kuo R. J., L. M. Ho and C. M. Hu (2002), Cluster Analysis in Industrial Market Segmentation through Artificial Neural Network, Computers and Industrial Engineering, Vol. 42, Lippmann, R.P. (1987), An Introduction to Computing with Neural Nets, IEEE ASSP magazine, Salchenberger, L. M., E. M. Cinar and N. A. Lash (1992), Neural Networks: A New Tool for Predicting Thrift Failures, Decision Sciences, Vol. 23,,

24 Shandle, J., Neural Networks are Ready for Prime Time (1993), Electronic Design, Vol. 18, February, The Mathworks Inc. (2004), MATLAB and, Neural Network Toolbox, Natick, MA. Tarassenko Lionel (1998): A Guide to Neural Computing Applications, John Wiley and Sons Inc. Trippi, Robert R. and D. DeSieno (!993), Neural Networks in Finance and Investing: Using Artificial Intelligence to Improve Real-World Performance, Probus, Chicago. Yago Glenn, Lalita Ramesh and Noah E. Hochman (1999), Hedge Funds: Structure and Performance, The Journal of Alternative Investments. 24

25 Figure 1. CISDM Classification of Hedge Funds Category Subcategory 1 Event Driven 1a Risk Arbitrage 2 Fund of Funds 1b Distressed Securities 3 Diversified 4 Niche 5a 5b International Regional Established 5 6 Global Macro Opportunistic 5c Regional Emerging 7 Long Only/ Leveraged 8a Long/Short 8 Market Neutral 8b Arbitrage Convertible 9 Sector 8c Arbitrage Stocks 10 Short Sellers 8d Arbitrage Bonds. 25

26 Table 1. Comparison of CISDM, HFR, TASS, and VanHedge Classifications Item CISDM Strategies HFR Strategies TASS Strategies VanHedge Strategies 1a 1b Event Driven: Risk Arbitrage Event Driven: Distressed Securities Event Driven Merger Arbitrage Distressed Securities Event Driven: Risk Arbitrage Event Driven: Distressed Securities Special Situation Distressed Securities 2 Fund of Funds Fund of Funds None Fund of Funds 3 Diversified Fixed Income Diversified 4 Niche Fixed Income: High Yield Regulation D None Event Driven: Regulation D Event Driven: High Yield Several Strategies 5 Global Emerging Markets Emerging Markets Emerging Markets 6 Macro Opportunistic Macro Market Timing Relative Value Arbitrage Statistical Arbitrage 7 Long Only / Leveraged 8a 8b 8c 8d Market Neutral: Long/Short Market Neutral: Arbitrage Convertible Market Neutral: Arbitrage Stock Market Neutral: Arbitrage Bond 9 Sector Sector: Energy Sector: Financial Sector: Health Care/ Biotechnology Sector: Metals/Mining Sector: Real Estate Sector: Technology Global Macro None Equity Nonhedge None None Opportunistic Value Managers Equity Hedge Long/Short Equity Market Neutral: Securities Hedge Convertible Arbitrage Convertible Arbitrage Market Neutral: Arbitrage Equity Market Neutral Equity Market Neutral Market Neutral: Arbitrage Fixed Income Arbitrage Fixed Income Arbitrage Market Neutral: Arbitrage None Financial Services Health Care Income Media/ Communications Technology 10 Short Selling Short Selling Dedicated Short Bias Short Selling 26

27 Table 2. Logical States for Incentive Fee, Leverage, Redemption Frequency and Minimum Purchase Values Grouping Logical State Panel A. Incentive Fee 0% 0.2-8% 9-10% Less than equal to 10% % Greater than 10% & less than equal to % 20% % Greater than 20% 3 Panel B. Leverage No leverage Less than equal to 1X Less than equal to 0.8X 1 Greater than 0.8X and less than equal to 1X Greater than 1X and less than equal to 1.25X Greater than 1X & less than equal to 2X 2 Greater than 1.25X and less than equal to 1.5X Greater than 1.5X and less than equal to 2X Greater than 2X and less than equal to 9X Greater than 2X & less than equal to 10X 3 Greater than 9X and less than equal to 10X Greater than 10X and less than equal to 25X Greater than 10X & less than equal to 30X 4 Greater than 25X and less than equal to 30X Greater than 30X and less than equal to 35X Greater than 30X & less than equal to 50X 5 Greater than 35X and less than equal to 50X Greater than 50X and less than equal to 70X Greater than 50X & less than equal to 70X 6 Not known Not declared 7 Panel C. Redemption Frequency Daily Weekly 1 Less than equal to monthly Bimonthly Monthly Quarterly Semiannually Annually More than Annual Greater than monthly & less than equal to semiannually 2 Greater than semiannually 3 Panel D. Minimum Purchase <=$100 $101-$5,000 Less than equal to $25,000 1 $5,001-$25,000 $25,001-$50,000 Less than equal to $50,000 2 $50,001 - $100,000 Less than equal to $100,000 3 $100,001-$500,000 Less than equal to $500,000 4 $500,001-$1 million Less than equal to $1 million 5 $1 million -$5 million $5 million -$25 million Less than equal to $25 M 6 More than $25 million Greater than $25 million 7 27