portfolio optimization and asset allocations using dea and dea/ahp

portfolio optimization and asset allocations using dea and dea/ahp

ISSN : 0976-2876 (Print)
ISSN : 2250-0138 (Online)
Indian J.Sci.Res. 4(2) : 81-86, 2013
PORTFOLIO OPTIMIZATION AND ASSET ALLOCATIONS USING DEA AND DEA/AHP
a1
SHOKOOFEH BANIHASHEMI AND MASOUD SANEI
ab
b
Department of Applied Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran
ABSTRACT
The present study is an attempt toward evaluating the performance of portfolios and asset allocations usingData
Envelopment Analysis (DEA) and DEA/AHP (Analytic Hierarchy Process) ranking model. Among many evaluation methods,
DEA is one of the best methods for assessing the relative efficiency a group of homogenous Decision Making Units (DMUs) that use
multiple inputs to produce multiple outputs.The problem consists of choosing an optimal set of assets in order to minimize the risk
and maximize return. The purpose of this paper is to evaluate portfolio in two steps: asset selection using (DEA) and asset
allocations using DEA/AHP and ranking mutual funds in practical example. Thus, DEA/AHP ranking model is compared with
Anderson and Petersen (AP) ranking model. This method is illustrated by application in mutual funds and extremely weights are
obtained via DEA/AHP for making efficient portfolio. The finding could be used for constructing efficient portfolio in stock
companies, in various finance organization and public and private sector companies.
KEYWORDS : Portfolio, Data EnvelopmentAnalysis (DEA),Analytic Hierarchy Process (AHP)
1
Corresponding author
BANIHASHEMI AND SANEI : PORTFOLIO OPTIMIZATION AND ASSET ALLOCATIONS USING DEA AND DEA/AHP
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Indian J.Sci.Res. 4(2) : 81-86, 2013
BANIHASHEMI AND SANEI : PORTFOLIO OPTIMIZATION AND ASSET ALLOCATIONS USING DEA AND DEA/AHP
Indian J.Sci.Res.4(2) : 81-86, 2013
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BANIHASHEMI AND SANEI : PORTFOLIO OPTIMIZATION AND ASSET ALLOCATIONS USING DEA AND DEA/AHP
Structure comparison matrix is as follows:
B.The use of a two-level AHP method to find weights
(Asset Allocation)
84
Indian J.Sci.Res. 4(2) : 81-86, 2013
BANIHASHEMI AND SANEI : PORTFOLIO OPTIMIZATION AND ASSET ALLOCATIONS USING DEA AND DEA/AHP
Table 1 : Descriptive Statistics of The Mutual Funds
Mutual
fund
ACEFX
ACEGX
ACEMX
AELAX
AELGX
AGTHX
ARCGX
AVLFX
BJBIX
CUCAX
FAGIX
FAIAX
FAICX
FDEGX
FEURX
FIUIX
FSUTX
GEGTX
HRCPX
IDETX
Expected
return
2.671
2.734
2.668
1.241
1.287
1.902
2.017
1.615
1.506
1.990
0.533
1.404
1.420
2.445
1.696
1.398
1.697
1.727
2.376
2.356
Vari ance
64.173
64.254
64.098
22.976
22.970
23.445
30.697
19.817
33.203
24.858
5.471
39.099
39.095
53.059
30.655
13.813
18.829
19.483
34.856
35.331
Mutual
fund
IDEUX
IGLBX
IGLCX
JAMRX
JAOSX
JAVLX
JAWWX
LMVTX
MAFGX
MBFGX
MCFGX
MCOBX
MCOFX
MDFGX
MGCAX
MSEQX
NAWCX
NAWGX
POVBX
POVSX
Expected
return
1.874
1.858
2.488
1.991
1.870
2.237
1.946
1.735
1.849
1.923
2.463
1.959
1.875
1.942
1.789
1.842
1.318
1.384
2.579
1.619
Variance
24.913
25.178
39.982
35.740
23.264
30.771
20.705
19.463
20.490
20.626
60.247
19.729
18.821
18.833
31.720
31.348
24.631
24.676
149.234
21.647
Mutual
fund
RYOSX
SCGEX
SRGFX
SSGWX
TALGX
TRGEX
TWIEX
UMBIX
USBOX
VGHCX
VPMCX
WAGEX
WBIGX
FMAGX
JANSX
VFINX
VWNDX
Expected
return
2.690
1.656
2.224
2.044
1.368
1.786
1.773
1.823
2.093
1.334
1.513
1.625
0.979
1.681
2.643
1.690
1.889
Variance
42.951
18.530
40.412
26.771
30.664
25.739
23.208
12.379
24.542
26.919
20.243
17.619
25.015
14.225
35.453
27.731
21.968
Table 2 : Efficiency Measure of 57 Mutual Funds
Mutual funds
ACEFX
ACEGX
ACEMX
AELAX
AELGX
AGTHX
ARCGX
AVLFX
BJBIX
CUCAX
FAGIX
FAIAX
FAICX
FDEGX
FEURX
FIUIX
FSUTX
GEGTX
HRCPX
IDETX
MV efficiency
measure
0.62
1.000
0.62
0.37
0.38
0.62
0.58
0.55
0.31
0.69
0.66
0.24
0.25
0.56
0.38
0.69
0.61
0.60
0.86
0.77
Indian J.Sci.Res.4(2) : 81-86, 2013
Mutual funds
IDEUX
IGLBX
IGLCX
JAMRX
JAOSX
JAVLX
JAWWX
LMVTX
MAFGX
MBFGX
MCFGX
MDFGX
MGDAX
MSEQX
MCOBX
MCOFX
NAWCX
NAWGX
POVBX
POVSX
MV efficiency
measure
0.55
0.53
0.78
0.48
0.59
0.78
0.77
0.61
0.64
0.74
0.50
0.82
0.74
0.84
0.38
0.41
0.36
0.38
0.23
0.51
Mutual funds
RYOSX
SCGEX
SRGFX
SSGWX
TALGX
TRGEX
TWIEX
UMBIX
USBOX
VGHCX
VPMCX
WAGEX
WBIGX
FMAGX
JANSX
VFINX
VWNDX
MV efficiency
measure
1.000
0.61
0.59
0.69
0.30
0.47
0.52
1.00
0.81
0.34
0.51
0.63
0.27
0.80
1.000
0.41
0.65
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BANIHASHEMI AND SANEI : PORTFOLIO OPTIMIZATION AND ASSET ALLOCATIONS USING DEA AND DEA/AHP
Table 3 : Mutual funds selections, DEA model is
used to analyze given 57 mutual funds and
four efficient mutual funds is obtained
Mutual
funds
ACEGX
RYOSX
UMBLX
JANSX
86
Expected
return(Output)
2.739
2.690
1.823
2.643
Variance(Input)
64.254
42.951
12.379
35.453
Table 4 : Weights And Rankings
Mutual
Weights
DEA/AHP AP ranks
funds
(eigenvector)
ranks
ACEGX
0.132
4
infeasible
RYOSX
0.18
3
3
UMBLX
0.45
1
1
JANSX
0.23
2
2
Indian J.Sci.Res. 4(2) : 81-86, 2013