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Frontiers of Computer Science

ISSN 2095-2228

ISSN 2095-2236(Online)

CN 10-1014/TP

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2018 Impact Factor: 1.129

Front Comput Sci Chin    2010, Vol. 4 Issue (2) : 237-253    https://doi.org/10.1007/s11704-010-0503-7
RESEARCH ARTICLE
Evaluation of mutual funds using multi-dimensional information
Xiujuan ZHAO1(), Jianmin SHI2()
1. School of Economics and Management, Beijing University of Posts and Telecommunications, Beijing 100876, China; 2. Department of Computer Science and Systems Engineering, Muroran Institute of Technology, Muroran 050-0071, Japan
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Abstract

To make better use of mutual fund information for decision-making we propose a coned-context, data envelopment analysis (DEA) model with expected shortfall (ES) modeled under an asymmetric Laplace distribution in order to measure risk when evaluating performance of mutual funds. Unlike traditional models, this model not only measures the attractiveness of mutual funds relative to the performance of other funds, but also takes the decision makers’ preferences and expert knowledge/judgment into full consideration. The model avoids unsatisfying and impractical outcomes that sometimes occur with traditional measures and it also provides more management information for decision-making. Determining input and output variables is obviously very important in DEA evaluation. Using statistical tests and theoretical analysis, we demonstrate that ES under an asymmetric Laplace distribution is reliable and we therefore propose the model as a major risk measure for mutual funds. At the same time, we consider a fund’s performance over different time horizons (e.g., one, three and five years) in order to determine the persistence of fund performance. Using the coned-context DEA model with ES value under an asymmetric Laplace distribution, we also present the results of an empirical study of mutual funds in China, which provides significant insights into management of mutual funds. This analysis suggests that the coned context measure will help investors to select the best fund and fund managers in order to identify the funds with the most potential.

Keywords mutual fund      data envelopment analysis (DEA)      performance evaluation      expected shortfall (ES)      cone-ratio     
Corresponding Author(s): ZHAO Xiujuan,Email:xjzhao@iss.ac.cn; SHI Jianmin,Email:shi@mmm.muroran-it.ac.jp   
Issue Date: 05 June 2010
 Cite this article:   
Xiujuan ZHAO,Jianmin SHI. Evaluation of mutual funds using multi-dimensional information[J]. Front Comput Sci Chin, 2010, 4(2): 237-253.
 URL:  
https://academic.hep.com.cn/fcs/EN/10.1007/s11704-010-0503-7
https://academic.hep.com.cn/fcs/EN/Y2010/V4/I2/237
Fund codeInvestment styleMeanStandard deviationSkewnessKurtosis
999001Equity0.483.860.376.09
999002Equity0.403.460.456.14
999003Equity0.383.360.056.00
999004Equity0.494.110.146.01
999005Equity0.484.070.406.11
999006Balanced0.313.060.176.02
999007Balanced0.362.950.086.00
999008Equity0.383.280.216.03
999009Bond0.261.760.466.14
999010Equity0.343.100.326.07
999011Balanced0.393.720.096.01
999012Equity0.353.410.276.05
999013Bond0.100.500.666.30
999014Equity0.393.000.516.17
999015Equity0.393.180.466.14
999016Equity0.333.000.196.03
999017Equity0.494.600.106.01
Tab.1  Descriptive statistics on mutual funds in China
Fund codeInvestment styleJarque-Bera statisticsFund codeInvestment styleJarque-Bera statistics
999001Equity507.58**999010Equity495.65**
999002Equity535.87**999011Balanced456.09**
999003Equity453.86**999012Equity483.24**
999004Equity460.85**999013Bond635.62**
999005Equity519.03**999014Equity559.23**
999006Balanced464.31**999015Equity537.78**
999007Balanced455.30**999016Equity468.12**
999008Equity470.32**999017Equity456.81**
999009Bond540.79**
Tab.2  Normality tests for mutual funds in China
Fig.1  Density functions for asymmetric Laplace distributions
Fig.1  Density functions for asymmetric Laplace distributions
Fund codeInvestment styleμpσA2
999001Equity0.000.480.921.06#
999002Equity-0.060.450.880.34#
999003Equity0.000.480.922.10#
999004Equity0.000.470.931.05#
999005Equity-0.130.430.970.56#
999006Balanced0.000.480.810.88#
999007Balanced0.000.470.821.33#
999008Equity0.000.470.840.81#
999009Bond-0.020.450.380.36#
999010Equity0.000.470.831.31#
999011Balanced0.000.481.010.71#
999012Equity-0.090.440.920.45#
999013Bond0.000.450.111.03#
999014Equity-0.100.430.810.77#
999015Equity-0.090.440.890.39#
999016Equity-0.030.460.850.32#
999017Equity0.000.490.981.58#
Tab.3  Maximum likelihood estimation for asymmetric Laplace distribution
Fund codeAsymmetric Laplace distributionAsymmetric Laplace distributionNormal distribution
ESExceeding possibility/%VaRExceeding possibility/%VaRExceeding possibility/%
999001-2.640.58-2.390.70-2.041.05
999002-2.250.83-2.181.05-2.061.16
999003-2.530.44-2.390.70-2.031.16
999004-2.930.37-2.400.81-2.061.28
999005-2.810.68-2.330.93-2.141.28
999006-2.200.62-2.130.70-1.801.16
999007-2.210.56-2.080.81-1.791.39
999008-2.290.30-2.180.46-1.861.63
999009-1.100.55-0.940.58-0.841.74
999010-2.160.37-2.140.46-1.840.93
999011-2.660.33-2.640.46-2.240.93
999012-2.410.63-2.271.16-2.061.28
999013-0.380.80-0.272.67-0.291.63
999014-2.010.76-1.920.93-1.781.39
999015-2.160.48-2.150.70-1.970.81
999016-2.170.52-2.160.70-1.911.74
999017-3.280.29-2.600.46-2.180.81
Tab.4  ES efficiency test
Fig.2  Conceptual model of the empirical study.
Fig.2  Conceptual model of the empirical study.
Fund codeInput 1Output 1Output 2Output 3
ES in 5 yearsLong-term returnMid-term returnShort-term return
9990012.644.021.913.93
9990022.252.891.252.88
9990032.532.611.672.59
9990042.934.121.004.03
9990052.813.891.633.83
9990062.201.781.081.74
9990072.212.271.062.24
9990082.292.511.432.48
9990091.101.400.501.39
9990102.162.111.292.08
9990112.662.662.022.60
9990122.412.231.312.18
9990130.260.370.300.37
9990142.012.681.322.67
9990152.162.590.772.53
9990162.172.011.082.01
9990173.284.031.013.97
Tab.5  Input data and output data
Context-dependent DEAConed-context DEA
E1 = {999001, 999013};E2 = {999004, 999005, 999011, 999014};E3 = {999002, 999003};E4 = {999008, 999009};E5 = {999010, 999015, 999017};E6 = {999007, 999012};E7 = {999016};E8 = {999006}.E1 = {999001};E2 = {999013, 999004};E3 = {999005};E4 = {999014};E5 = {999002, 999009, 999017};E6 = {999015};E7 = {999008};E8 = {999003};E9 = {999007};E10 = {999011};E11 = {999010};E12 = {999016};E13 = {999012};E14 = {999006}.
Tab.6  Comparison of levels of division between the context-dependent model and the coned-context model.
ModelScoreInput 1Output 1Output 2Output 3
Weights in coned-context model1.003.912.612.610.00
Weights in context-dependent model0.983.910.00539.130.00
Original data0.260.370.300.37
Tab.7  Differences in outputs for fund 999013 between the two models
Fund codeContext (efficient frontier)
2nd level3rd level4th level5th level6th level
1st level1-degree2-degree3-degree4-degree5-degree
999001102.93%109.51%113.02%117.28%127.50%
2nd level1-degree2-degree3-degree4-degree
999013107.29%①109.93%①114.15%①125.27%①
999004101.25%②104.49%②108.43%②117.81%②
3rd level1-degree2-degree3-degree
999005103.21%107.10%116.75%
4th level1-degree2-degree
999014103.83%113.95%
5th level1-degree
999002109.74%①
999009108.16%②
999017103.74%③
Tab.8  Preferred attractiveness information for a subset of mutual funds analyzed.
Fund codeContext (Efficient frontier)
1st level2nd level3rd level4th level
2nd level1-degree
99901398.25%①
99900492.57%②
3rd level2-degree1-degree
99900591.63%93.99%
4th level3-degree2-degree1-degree
99901489.37%91.24%97.60%
5th level4-degree3-degree2-degree1-degree
99900286.12%①87.93%①93.99%①96.37%①
99900984.94%②86.73%②92.70%②95.05%②
99901781.52%③83.38%③88.97%③91.55%③
6th level5-degree4-degree3-degree2-degree
99901578.58%80.78%85.94%88.69%
7th level6-degree5-degree4-degree3-degree
99900872.90%74.57%79.61%81.88%
8th level7-degree6-degree5-degree4-degree
99900368.85%70.23%75.18%77.11%
9th level8-degree7-degree6-degree5-degree
99900768.07%69.73%74.33%76.56%
Tab.9  Preferred progress information for a subset of the mutual funds analyzed
Fund code(PPD)(ES)(LT)(MT)(ST)
2nd level9990131-degree5.37%13.10%0.00%0.00%
9990041-degree5.43%5.43%0.00%0.00%
3rd level9990051-degree11.23%17.55%0.00%0.00%
9990052-degree5.85%5.85%0.00%0.00%
4th level9990041-degree14.20%21.33%0.00%0.00%
9990042- degree7.35%7.35%0.00%0.00%
9990043-degree3.53%3.53%0.00%0.00%
5th level9990021-degree17.24%23.59%0.00%0.00%
9990091-degree17.06%17.06%0.00%0.00%
9990171-degree8.78%8.78%0.00%0.00%
9990022-degree12.44%12.44%0.00%0.00%
9990092-degree8.80%8.80%0.00%0.00%
9990172-degree11.69%11.69%0.00%0.00%
9990023-degree6.88%6.88%0.00%0.00%
9990093-degree4.35%4.35%0.00%0.00%
9990173-degree16.58%16.58%0.00%0.00%
9990024-degree3.48%3.48%0.00%0.00%
9990094-degree22.08%26.28%0.00%0.00%
9990174-degree0.80%0.80%0.00%1.73%
6th level9990151-degree27.16%29.45%0.00%0.00%
9990152-degree20.68%20.68%0.00%5.00%
9990153-degree13.36%22.51%0.00%12.01%
9990154-degree7.81%16.96%0.00%20.01%
9990155-degree5.67%17.87%0.00%18.01%
7th level9990081-degree23.97%25.34%0.00%0.00%
9990082-degree17.15%17.15%0.00%0.00%
9990083-degree12.92%12.92%0.00%0.00%
9990084-degree10.48%10.48%0.00%0.00%
9990085-degree7.82%7.82%0.00%0.00%
9990086- degree0.64%0.64%0.00%0.00%
8th level9990031-degree25.51%29.07%0.00%0.00%
9990032-degree20.05%20.05%0.00%0.00%
9990033-degree15.47%15.47%0.00%0.00%
9990034-degree12.73%12.73%0.00%0.00%
9990035-degree9.76%11.34%0.00%0.00%
9990036- degree4.16%4.16%0.00%0.00%
9990037-degree2.03%5.19%0.00%0.00%
9th level9990071-degree34.97%36.37%0.00%0.00%
9990072-degree29.24%29.24%0.00%0.00%
9990073-degree25.59%25.59%0.00%0.00%
9990074-degree23.47%23.47%0.00%0.00%
9990075-degree21.04%23.37%0.00%0.00%
9990076- degree12.58%12.58%0.00%0.00%
9990077-degree9.96%10.43%0.00%9.96%
9990078-degree7.62%7.62%0.00%0.00%
Tab.10  Improvement for the 11 mutual funds from E2 to E9.
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