Strategy of global asset allocation using extended classifier system Expert Systems with Applications 37 (2010) 6611–6617 Contents lists available at ScienceDirect Expert Systems with Applications j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e s w a Strategy of global asset allocation using extended classifier system Wen-Chih Tsai, An-Pin Chen * National Chiao-Tung University, Institute of Information Management, Hsinchu 30050, Taiwan a r t i c l e i n f o Keywords: Extended classification system Learning classifier system Exchanged traded funds Finance predication 0957-4174/$ - see front matter � 2010 Elsevier Ltd. A doi:10.1016/j.eswa.2010.03.001 * Corresponding author. Tel.: +886 911296906. E-mail addresses: miktsai@gmail.com, wctsaie@t iim.nctu.edu.tw (A.-P. Chen). a b s t r a c t There are several studies about extended classification system (XCS) in past years. XCS model can dynam- ically learn and adapt to the change of environments for maximizing the desired goals. This paper con- ducts simulation to apply XCS to global asset allocation in the country-specific exchanged traded funds (ETFs). Since international stock price trend is influenced by unknown and unpredictable surround- ings, using XCS to model the fluctuations on global financial market allows for the discovery of the pat- terns of the future trends. As such, the benefits of international asset diversification can be achieved in a tax-efficient way with country-specific ETFs at a low transaction cost with minimized tracking error. These empirical results indicate that XCS is capable of evolving over time, and thus XCS can provide a good indicator for future global asset allocation decision-making aiming at maximized profit. � 2010 Elsevier Ltd. All rights reserved. 1. Introduction Recently, exchanged traded funds (ETFs) have become very popular investment products for index trading all over the world since their first introduction at the beginning of last decade. ETFs are the leading financial innovation of the last decade (Fuhr, 2001). ETFs closely track the performance of corresponding indices. ETFs offer the benefits of diversification and index tracking at a low cost. The first ETF, SPDR, was launched on AMEX in 1993 and was designed to passively mimic the S&P500 index. Furthermore, at the end of 2007, there were 837 ETFs with 1324 listings with assets of USD $1212 billions and managed by 107 managers on 56 ex- changes across the world. Most days, two or three ETFs are on the list of the top five most actively traded stocks on the AMEX. Additionally, since the trend of fund price is affected by many man-made and natural elements using dynamic machine-learning tool for the fund analysis is more suitable and adaptive than tradi- tional methods. Learning classifier system (LCS) consists of a set of steps and classifiers for discovering rules of genetic and non-genet- ic operators (Miffre, 2007). In LCS bibliography, a wide range of re- sources has been covered (Karpoff & Jonathan, 1987; Kovacs, 2000); however, the applications of XCS on financial issues (Lanzi, Stolzmann, & Wilson, 2000; Leigh, Modani, Purvis, & Robert, 2002) are much fewer when compared with its LCS counterpart. The fol- lowing are reasons to use XCS on dynamic and noisy environments: ll rights reserved. smc.com (W.-C. Tsai), apc@ � XCS is capable of making real-time and accurate responses. � XCS has been shown to properly learn from noisy, complex, and non-linear environments when the outside information contin- uously changes. � XCS is able to evaluate rules that are ideal for modeling prob- lems without retraining all data. � XCS, generalized under predefined conditions, can discover gen- erally accurate rules to perform on a variety of problem domains. � XCS can adjust itself to strengthen its inward knowledge step by step. � XCS assigns rule fitness based on the accuracy of the rule rather than on the reward payoffs. Recently there have been several investigations into applying LCS to machine learning and data mining classification problems, (Amin & Kat, 2003; Andrea, 1995; Trippi & DeSieno, 1992). This pa- per continues this investigation by applying an adaptation of a re- cently developed XCS, Wilson’s XCS, to a large multi-class benchmark data set available at the 24 iShares MSCI (Morgan Stan- ley Capital International) country funds. This paper is structured as follows: Section 1 to introduce the study’s motivation and goals, Section 2 to examine the literature, Section 3 to briefly describe XCS in our model, Section 3 to describe the data set and the exper- imental procedure adopted, Section 5 to present the results, and Section 6 to conclude the result and future study direction. 2. Literature review On basis of analysis of past studies, we divide the related stud- ies into four parts, which include literature on ETFs, artificial http://dx.doi.org/10.1016/j.eswa.2010.03.001 mailto:wctsaie@tsmc.com mailto:apc@ http://www.sciencedirect.com/science/journal/09574174 http://www.elsevier.com/locate/eswa 6612 W.-C. Tsai, A.-P. Chen / Expert Systems with Applications 37 (2010) 6611–6617 intelligence and portfolio, technical analysis and technical indica- tors and classifier systems. 2.1. International ETFs In the past, studies by Cumby and Glen (1990); Shukla and Singh (1997), Redman, Gullett, and Manakyan (2000) analyzed mutual fund performance and showed evidence that international mutual funds can outperform the US stock market. Cumby and Glen examined the performance of 15 US-based internationally diversified mutual funds from 1982 to 1988. The findings showed that mutual funds outperformed the US Index. Enu, Kolodny, and Resnick (1991) investigated 19 US-based international mutual funds from 1977 to 1986, and concluded that majority of interna- tional mutual funds outperformed the US stock market. However, Shukla and Singh (1997), Redman et al. (2000), of- fered distinct conclusions. Shukla & Singh, 1997 evaluated the per- formance of the US-based global equity mutual funds during 1988–1995 including a total of 20 global and 76 domestic funds. They showed that both global funds and US domestic funds under- performed the S&P 500 Index. Redman also showed that the inter- national portfolio underperformed the US equity portfolio. Bhargava (2001) suggested both the international equity managed funds and mutual funds underperformed the S&P500 Index. De- spite the significance associated with their studies, they might have problem making real-time decisions while incorporating tra- ditional models into their models. This paper is thus based on a dynamical and real-time model in order to optimize global asset allocation. 2.2. Global asset allocation The country-specific ETFs global asset allocation is an invest- ment strategy that attempts to exploit short-term international market inefficiencies by establishing positions in an assortment of markets with a goal to profit from relative movements across those international markets. These decisions can usually be broken down briefly into two processes. First, select a list of countries that have growth potential or are currently undervalued. The process is called portfolio selection. Secondly, investigate these ETFs price movements of each selected countries, and execute correct trading strategies at appropriate timing. This paper focuses on 24 iShare MSCI country-specific funds. Like country-specific open and closed-end index funds, country- specific iShares increase mean–variance efficiency. On the other hand, unlike country index funds, which could only be transacted at a cut-off time (such as 4 pm) everyday, the ETFs can be bought or sold at any time during the trading day, offering one or more flexibilities compared to their country-specific index fund counterparts. 2.3. Sharpe ratio This paper starts by testing whether the returns of 24 iShares MSCI country-specific ETFs are normally distributed and better than the XCS model in the dynamic environment. Skewness and Kurtosis are statistics that very often are used to describe the height and the symmetric of distribution of data test for normality (Amin & Kat, 2003; Wachter & Warusawitharana, 2008). This Sharpe ratio measures are used to test the ETF’s performance. Sharpe (1992) proposed the ratio that is mainly used to rank alternative portfolios based on their historic reward-to-variability ratio: SRi ¼ Ri � Rf ri ð1Þ where Ri is the historic mean return on ETF-i over the interval con- sidered, ri is the historic standard deviation of the return on ETF-i over the interval considered and Rf is the average risk-free rate over the interval considered. 2.4. Risk free rate In theory, the risk-free rate is the minimum return an investor expects for any investment unless the potential rate of return is greater than the risk-free rate. In practice, however, the risk-free rate does not exist since even the safest investments carry a very small amount of risk. The interest rate on a three-month US Trea- sury bill is often used as a risk-free rate (Allen & Karjalainen, 1999; Kashima, 2007; Shukla & Singh, 1997). In this study, we also use the US three-month Treasury bill as the risk-free rate. The US three-month Treasury bill historically is obtained from the Board of Governors of the Federal Reserve database. Since we try to view from US investors’ standpoints, the US domestic Treasure bill can be used to measure the risk-free rate. 2.5. XCS XCS is based on the Learning Classifier System (LCS) (Holland, 1992; Karpoff, 1987; Kovacs, 2000), which is a general and inde- pendent machine learning system. LCS, which was proposed by John H. Holland (Andrea, 1995; Butz & Wilson, 2000), is an online step-by-step rule base because it includes both genetic algorithm and strength learning. LCS can be classified as an extended genetic algorithm or an algorithm of strength learning. In LCS, strength learning element is used to distinguish suitable or unsuitable rules and solve the rule conflict problem while genetic algorithm is used to find good and new rules, and eliminate the unsuitable rules. XCS retains the main frames of LCS, but also makes some changes. Firstly, XCS uses precision as the rate of fitness. Secondly, it changes the rule discovery component from acting on the whole population to the population having the same states and actions. Thirdly, it uses Q-learning-like algorithm to substitute the Bucket brigade algorithm. And lastly, it removes the message board. 2.6. Knowledge integration Knowledge integration can be considered as a multi-objective optimization problem (Sakai & Masuyama, 2008; Yuan & Zhuang, 1996). Due to the huge searching space, the optimization problem is often very difficult to be solved. A genetic algorithm is usually used to discover a desirable optimal set of rules. The application of a GA in search of the optimal rule set for machine learning is known as Genetic Based Machine Learning (GBML). A well-known GBML architecture is the so-called LCS developed by Andrea (1995); Holland (1986) and Holland, Holyoak, Nisbett, and Thagard (1986). More recent GBML architectures are the Extended Classifier System (XCS) developed by Butz and Wilson (2000), the Anticipa- tory Classifier System by Lanzi et al. (2000), and EpiCS by Butz and Wilson (2000). 3. System architecture This paper implements the system architecture shown in Fig. 1. This is based on the Wilson’s XCS classifier system (Butz & Wilson, 2000). XCS retains the main frames of LCS, but also makes some changes. Firstly, XCS uses precision as the rate of fitness in the transaction data-encoding module. Secondly, it changes the rule discovery component from acting on the whole population to the population having the same states and actions. Thirdly, it uses Q- learning-like algorithm to substitute the Bucket brigade algorithm Fig. 1. Architecture of XCS. Fig. 2. Algorithm of XCS. W.-C. Tsai, A.-P. Chen / Expert Systems with Applications 37 (2010) 6611–6617 6613 in the knowledge extraction module. And lastly, it rewards the re- sult to the knowledge integration module. In this section we tries to elaborate more on the contents of the various models of the architecture as implemented in XCS and illustrated in Fig. 1. 3.1. Transaction data-encoding model Fig. 1 shows a transaction data-encoding module, a group of financial indices of the country whose stock index is tracked by that country’s specific ETF, with same syntax form a classifier pop- ulation. The group consists of: 1. Detecting condition section C1 ^ C2 ^�� �^ Cn; Ci 2f0; 1;�g L ; 1 6 i 6 n ð2Þ That is composed of at least one condition. The condition may include a state of positive (1), negative (0), or do not-care (–). And for the entry of the condition, the associated state must be satisfied. Eq. (2) stands for conditions 1–n are satisfied and in a predetermined sequence. The sequence could be condition 1 is followed by condition 2, which is followed by condition 3, until condition n takes place. 2. Action section A 2fa1; . . . ; amg ð3Þ Action section to represent the candidate classifiers action. 3. Rule prediction p to evaluate classifiers utility. 4. Prediction error standing for the difference between actual ben- efit and prediction p. 5. Fitness F to evaluate the precision of prediction p from predic- tion error. 3.2. Knowledge extraction model This model consists of: � Execution section. XCS interacts with environment at discrete time t in terms of environment states St, utilizes St to compare with population [P]’s conditions, and copies the matched classifiers to match set [M]. XCS further computes the weighted averages of each action in the match set [M], so as to build up a system prediction PA(a). With PA(a), XCS further selects an action ai, and classifiers that have action ai from match set [M], and puts them in action set [A]. The system then executes ai, and receives a delay reward rt�1 in discrete time t + 1. The same process continues until the objective problem is solved. � Reinforcement section. XCS uses reward r to update parameters of strength learning of classifier in action set [A]. The update of prediction value p may be as follows: C � p C � p þðR � C � pÞ� k ð4Þ R ¼ rt�1 þðE � sÞ ð5Þ C is the classifier, k is the learning rate (0 < k 5 1), rt�1 is the re- ward of previous step, E is the max system expected value and s is the discount factor. The update of predicted error value e: C � e C � e þðjR � C � pj� C:eÞ� k ð6Þ The equation of fitness F: C � F C � F þðC � l0 � C � FÞ� k ð7Þ C � l0 C � lP x2½A�C � lx ð8Þ C � l 1 if C � e < e0 aðe0=C � eÞ b otherwise � ð9Þ e0 is the tolerance of predicted error value (e0 > 0), a, b is the con- stant of precision control l (0 < a < 1; b > 0). From fitness function F in Eq. (5), we know that the fitness of classifier in XCS evaluates precision of classifier in the same ac- tion set [A], and has an invert function relationship with pre- dicted error e. Table 3 iShare MSCI Japan Index (EWJ) from 2003/1/2 to 2009/5/30. Symbol Date Open High Low Close Volume EWJ 2003/1/2 7 7.1 7 7.08 1,529,000 6614 W.-C. Tsai, A.-P. Chen / Expert Systems with Applications 37 (2010) 6611–6617 3.3. Knowledge integration model This XCS model focuses on the genetic algorithm (GA) in Fig. 2. Genetic algorithm is used to eliminate unsuitable classifiers in ac- Table 2 iShare FTSE/Xinhua China 25 Index (FXI) from 2004/10/12 to 2009/05/30. Symbol Date Open High Low Close Volume FXI 2004/10/12 53.6 53.85 53.38 53.7 248,200 FXI 2004/10/13 53 53.31 52.2 52.32 369,100 FXI 2004/10/14 51.96 52.1 51.45 51.62 119,800 FXI 2004/10/15 52.05 52.64 52.03 52.4 234,500 FXI .. . .. . .. . .. . .. . .. . EWJ 2003/1/3 7.05 7.09 7 7.07 360,400 EWJ 2003/1/6 7.15 7.23 7.08 7.2 2,614,900 EWJ 2003/1/7 7.02 7.05 6.96 6.97 890,700 EWJ .. . .. . .. . .. . .. . .. . Table 1 Sample data list. ETFs region Extend-traded funds name Symbol Inception date Asia Pacific iShares MSCI Australia Index EWA 1996/3/12 North American iShares MSCI Canada Index EWC 1996/3/12 European iShares MSCI Sweden Index EWD 1996/3/12 European iShares MSCI Germany Index EWG 1996/3/12 Asia Pacific iShares MSCI Hong Kong Index EWH 1996/3/12 European iShares MSCI Italy Index EWI 1996/3/12 Asia Pacific iShares MSCI Japan Index EWJ 1996/3/12 European iShares MSCI Belgium Index EWK 1996/3/12 European iShares MSCI Switzerland Index EWL 1996/3/12 Asia Pacific iShares MSCI Malaysia Index EWM 1996/3/12 European iShares MSCI Netherlands Index EWN 1996/3/12 European iShares MSCI Austria Index EWO 1996/3/12 European iShares MSCI Spain Index EWP 1996/3/12 European iShares MSCI France Index EWQ 1996/3/12 Asia Pacific iShares MSCI Singapore Index EWS 1996/3/12 Asia Pacific iShares MSCI Taiwan Index EWT 2000/6/20 European iShares MSCI United Kingdom Index EWU 1996/3/12 North American iShares MSCI Mexico Index EWW 1996/3/12 Asia Pacific iShares MSCI South Korea Index EWY 2000/5fi South American iShares MSCI Brazil Index EWZ 2000/7/10 South American iShares MSCI South Africa Index EZA 2003/2/14 Asia Pacific Xinhua China 25 Index Fund FXI 2004/10/15 North American iShares S&P 500 Index IVV 2000/5/26 North American iShares Dow Jones US Industrial IYJ 2000/7/21 Table 4 Data coded. EITs region Symbol Date Open Hi Asia Pacific EWA 2003/1/2 19.91 1 Asia Pacific EWH 2006/3/2 13.42 1 Asian Pac& EWJ 2006/3/2 13.75 1 Asia Pacific EWM 2006/3/2 7.36 Asia Pacific EWS 2006/3/2 8.65 Asia Pacific EWT 2006/3/2 13.01 1 Asia Pacific EWY 2006/3/2 47 4 Asia Pacific FXI 2006/3/2 73.34 7 European EWD 2006/3/2 24.05 2 European EWG 2006/3/2 22.12 2 European EWI 2006/3/2 27.24 2 European EWK 2006/3/2 20.65 2 European EWL 2006/3/2 20.58 2 European EWN 2006/3/2 21.8 2 European EWO 2006/3/2 29.8 3 European EWP 2006/3/2 40.3 4 European EWQ 2006/3/2 27.88 2 European EWU 2006/3/2 19.6 1 North American EWC 2006/3/2 23.72 2 North American EWW 2006/3/2 39.05 3 North American IVV 2006/3/2 129.04 12 North American IYJ 2006/3/2 61 6 South American EWZ 2006/3/2 42.96 4 South American EZA 2006/3/2 19.91 1 tion set [A] rather than the whole population. In doing so, genetic algorithm starts when action set [A] have not been executed by ge- netic algorithm for an average time value. When genetic algorithm executes, two classifiers and crossover at a v probability might be randomly selected. Also, it will mutate at probability. 4. Experiment 4.1. Data This paper targets 24 iShares MSCI country-specific ETFs from the iShares web database (http://www.ishares.com). The data in- clude daily opening price, close price, maximum price, minimum price and trade volume over the period from Jan 2003 to June 2009, resulting in 76 monthly observations shown in Tables 2–4. As previously mentioned, the reason for choosing iShares MSCI country-specific ETFs is to achieve international diversification. Table 1 indicates the basic information of these ETFs including the region, symbol, name, and inception date. The inception date for most of the ETFs is 12 March 1996, and the latest inception date, for iShares MSCI-Xinhua China 25 (FXI), falls on 15 October 2004. Thus, our sample period covers all ETFs historical data. All of these ETFs belong to Barclays Global Investors Group, known as iShares. We use 24 iShares MSCI country funds measured by the MSCI individual country index. These ETFs include eight iShares from Asia Pacific countries (Australia, Hong Kong, Japan, Malaysia, Singapore, South Korea, Japan, and China), 10 iShares from European countries (Austria, Belgium, France, Germany, Italy, Netherlands, Spain, Sweden, Switzerland, and UK), four iShares gh Low Close Volume Coded 9.95 19.75 19.91 204,400 –0010 3.47 13.36 13.45 392,000 10111 3.75 13.61 13.72 18,600,300 01111 7.4 7.33 7.38 497,600 10010 8.66 8.59 8.62 467,900 10101 3.04 12.9 13.03 2,354,700 11011 7.08 46.57 46.86 762,500 01101 3.37 72.8 73.31 379,600 00111 4.34 23.98 24.34 49,000 11000 2.23 22.01 22.23 603,000 10010 7.26 27.04 27.26 66,600 10010 0.84 20.62 20.84 90,800 10000 0.68 20.4 20.67 71,500 10010 1.86 21.61 21.86 86,900 10000 0.16 29.62 30.16 158,600 –––000 0.43 40.02 40.43 28,000 11000 7.99 27.8 27.98 559,000 10010 9.76 19.56 19.75 88,400 10100 3.9 23.61 23.88 488,500 10000 9.17 38.8 39.03 459,400 10–00 9.6 128.81 129.48 863,100 10100 1.15 60.84 61.06 22,600 11011 3.18 42.57 43.14 2,135,000 10000 9.95 19.75 19.91 204,400 11011 http://www.ishares.com W.-C. Tsai, A.-P. Chen / Expert Systems with Applications 37 (2010) 6611–6617 6615 form North American countries (S&P500, Dow Jones, Canada and Mexico) and two iShares from countries in Southern hemisphere (Brazil and South Africa). 4.2. Data coded and portfolio optimizer In the experiment, we codify the daily information of the cho- sen countries’ ETF into a five-code string. The daily information in- cludes opening price (‘‘open”), maximum price (‘‘high”), minimum price (‘‘low”), closing price (‘‘close”), and trade volume (‘‘volume”). Table 5 Daily global asset allocation portfolio. Extend-traded fund name Ticker Date iShares Dow Jones US Industrial IYJ 200 iShares Goldman Sachs Technology Index IGM 20O iShares MSCI Australia Index EWA 200 iShares MSCI Austria Index EWO 200 iShares MSCI Belgium Index EWK 200 iShares MSCI Brazil (Free) Index EWZ 200 iShares MSCI Canada Index EWC 200 iShares MSCI E AFE Index Fund EFA 200 iShares MSCI EMU Index EZU 200 iShares MSCI France Index EWQ 200 iShares MSCI Germany Index EWG 200 iShares MSCI Horn Kong Index EWH 200 iShares MSCI Italy Index EWI 200 iShares MSCI Japan Index EWJ 200 iShares MSCI Malaysia (Free) Index EWM 200 iShares MSCI Mexico (Free) Index EWW 200 iShares MSCI Netherlands Index EWN 200 iShares MSCI Singapore (Free) Index EWS 200 iShares MSCI South Africa Index EZA 200 iShares MSCI South Korea Index EWY 200 iShares MSCI Spain Index EWP 200 iShares MSCI Sweden Index EWD 200 iShares MSCI Switzerland Index EWL 200 iShares MSCI Taiwan Index EWT 200 iShares MSCI United Kingdom Index EWU 200 iShares Russell 1000 Index IWB 200 iShares S&P 500 Index IVV 200 Xinhua China 25 Index Fund FXI 200 NASDAQ 100 Trust Shares QQQ 200 Table 6 Traditional Sharpe ratio asset allocation. ETFs region Extend-traded funds name Symbol Asia Pacific iShares MSCI Australia Index EWA Asia Pacific iShares MSCI Hong Kong Index EWH Asia Pacific iShares MSCI Japan hides EWJ Asia Pacific iShares MSCI Malaysia Index EWM Asia Pacific iShares MSCI Singapore Index EWS Asia Pacific iShares MSCI Taiwan Index EWT Asia Pacific iShares MSCI South Korea Index EWY Asia Pacific iShares FTSE/Xinhua China 25 Index FXI European iShares MSCI Sweden Index EWD European iShares MSCI Germany Index EWG European iShares MSCI Italy Index EWI European iShares MSCI Belgium Index EWK European iShares MSCI Switzerland Index EWL European iShares MSCI Netherlands Index EWN European iShares MSCI Austria Index EWO European iShares MSCI Spain Index EWP European iShares MSCI France Index EWQ European iShares MSCI United Kingdom Index EWU North American iShares MSCI Canada Index EWC North American iShares MSCI Mexico Index EWW North American iShares S&P 500 Index IVV North American iShares Dow Jones US Industrial IYJ South American iShares MSCI Brazil Index EWZ South American iShares MSCI South Africa Index EZA US T-Bill The daily information for the chosen ETF on 3/2/2006 and its coded strings are shown in Table 4. It is worth noting that the coded string is configured to represent the differences in the daily infor- mation, and we further determine whether the differences fall into predetermined ranges or not before assigning the state code (0, 1, or –) to them. It is also worth noting that the ranges could be open- ended. The difference in daily information could be the differences of different day’s averaged price moving and averaged trade vol- ume (Brock, Lakonishok, & LeBaron, 1992). In order to simplify the experiment, the experiment uses 1 for positive and 0 for Coded As-is (%) To-Be (%) 6/3/2 11011 6 5 6/3/2 10000 2 1 6/3/2 –0010 2 2 6/3/2 ––000 2 2 6/3/2 10000 2 2 6/3/2 10000 1 2 6/3/2 10000 2 2 6/3/2 10000 2 2 6/3/2 –0111 5 6 6/3/2 10010 2 2 6/3/2 10010 2 2 6/3/2 10111 8 9 6/3/2 10010 2 1 6/3/2 01111 11 12 6/3/2 10010 3 3 6/3/2 10–00 2 2 6/3/2 10000 1 0 6/3/2 10101 2 2 6/3,2 11011 13 14 6/3/2 01101 4 5 6/3/2 11000 1 0 6/3/2 11000 1 0 6/3/2 10010 1 0 6/3/2 11011 5 6 6/3/2 10100 1 1 6/3/2 00–10 0 0 6/3/2 10100 2 2 6/3/2 00111 9 10 6/3/2 11000 6 5 Annual return (%) Annual std. deviation (%) Sharpe ratio (%) 14.72 17.47 63.8237 2.15 22.06 9.7461 11.26 19.45 57.8920 17.96 19.65 91.3995 6.95 22.49 30.9026 10.66 34.11 31.2518 31.55 33.81 93.3156 56.00 38.10 146.9816 10.73 32.57 32.9444 4.73 33.69 14.0398 6.89 22.94 30.0349 9.12 23.16 39.3782 5.43 17.71 30.6606 2.15 26.08 8.2439 26.31 19.91 132.1447 14.21 24.15 58.8406 3.70 23.90 15.4812 0.74 16.26 4.5510 10.61 16.92 62.7069 4.14 24.62 16.8156 �0.50 17.90 �2.7933 2.50 18.25 13.6986 20.07 49.14 40.8425 27.10 45.42 59.6653 3.57 Fig. 4. Accumulated portfolio. 6616 W.-C. Tsai, A.-P. Chen / Expert Systems with Applications 37 (2010) 6611–6617 negative in terms of the difference in the daily information. And we further use 1 to associate with ‘‘buy” and 0 to associate with ‘‘sell.” In other words, the system will adjust the weight in the global iShares. The daily rules discovery is shown in Table 5, the column of ‘‘as-is” is indicative of information at day t � 1 while the column of ‘‘to-be” is reserved for day t (today). 4.3. Traditionally Sharpe ratio The traditional portfolio model used the ‘‘Sharpe ratio” to eval- uate the optimal asset allocation. Hence we compare the monthly Sharpe ratio global asset allocation with the XCS model global asset allocation in Table 6. This Sharpe ratio measures are used to test the ETF’s performance (Sharpe, 1992) 4.4. International global asset allocation In this paper, we implement the integration knowledge model with XCS expert system to study the global markets that include the US, China, Taiwan, Japan, South Africa, and Malaysia. In Fig. 3, the iShares track the indices of international capital markets before any global asset allocation strategies tracking those indices could be implemented for our international global asset allocations. The global allocation element of ETFs contributes to the global risk diversification and generates sufficient gains in a transparent and low cost manner that is not easily achievable by global index funds. 4.5. Experiment result The results of the experiments are summarized in Fig. 4. Fig. 4 shows the profit accumulation result. The average of the cumu- lated profit is better than the traditional Sharpe ratio, and the high- est profit is about 840,888 units after 1300 days, which is about 6.5% per day. Therefore, it is a good performance when the index ended up lower at the end of the 120-day period than the start thereof. Our XCS model is about 74.45% better than the asset alloca- tion strategy on the basis of Sharpe ratio. Fig. 3. International markets analysis from XCS exports system. 5. Conclusion As we know, the country-specific ETFs offer the benefits of international portfolio diversification at a lower cost with a lower tracking error in a more tax-efficient way than passive open or closed-end county funds. This paper focuses on the soft computing algorithm, XCS, and compares with the traditional asset allocation model, according to Sharpe ratio. The statistical shows that dy- namic artificial intelligence model is better than the non-efficiently monthly Sharpe ratio model. Additionally, using a limited numbers of factors from the real international market this paper has shown some promise using extended classifier trading mechanism in country-specific ETFs. The XCS experts system consists of Wilson’s XCS technique, which provides a good online learning system for our model. In the fast changing security market, Genetic algorithm, rule base, neural network etc. do not satisfy our needs. Rather, XCS’s online learning is generally perceived as a more suitable op- tion. XCS can give trader or investor a real-time advice to make rel- atively more accurate trading decisions in the international markets. In the future, although the experiment has shown good results, the model proposed by the current paper may still have some rooms to improve by having the inputted factors changed. Especially, this work does not include the commodities ETF. In addition, this study includes no short ETF either. Hence, the study could be further developed after having the above-mentioned inputted factors considered. The next step would be to verify XCS in different products such as commodities ETFs, and actively man- aged ETF. 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Strategy of global asset allocation using extended classifier system Introduction Literature review International ETFs Global asset allocation Sharpe ratio Risk free rate XCS Knowledge integration System architecture Transaction data-encoding model Knowledge extraction model Knowledge integration model Experiment Data Data coded and portfolio optimizer Traditionally Sharpe ratio International global asset allocation Experiment result Conclusion References