Strategic Decision Making in Portfolio Management with Goal Programming Model
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1 American Journal of Operaions Managemen and Informaion Sysems 06; (): hp:// doi: 0.648/.aomis Sraegic Decision Making in Porfolio Managemen wih Goal Programming Model Lam Weng Siew,, *, Lam Weng Hoe, Faculy of Science, Universii unku Abdul Rahman, Kampar, Malaysia Cenre for Mahemaical Sciences, Cenre for Business and Managemen, Universii unku Abdul Rahman, Kampar, Malaysia address: (L. W. Siew), (L. W. Hoe) * Corresponding auhor o cie his aricle: Lam Weng Siew, Lam Weng Hoe. Sraegic Decision Making in Porfolio Managemen wih Goal Programming Model. American Journal of Operaions Managemen and Informaion Sysems. Vol., o., 06, pp doi: 0.648/.aomis Received: Ocober 3, 06; Acceped: ovember, 06; Published: December, 06 Absrac: Enhanced index racking is a popular ype of porfolio managemen which aims o consruc he opimal porfolio in order o generae higher porfolio mean reurn han he benchmark index mean reurn. Enhanced index racking is a dual obecive opimizaion problem which can be represened by a goal programming model o deermine he rade-off beween maximizing he porfolio mean reurn and minimizing he racking error. he obecive of his paper is o apply he goal programming model in consrucing he opimal porfolio o rack he echnology Index in Malaysia. In his sudy, he daa consiss of weekly reurn of he companies from echnology secor in Malaysia sock marke. he resuls of his sudy indicae ha he opimal porfolio is able o ouperform echnology Index by generaing weekly excess mean reurn % a minimum racking error.0980%. he significance of his sudy is o idenify and apply he goal programming model as a sraegic decision-making ool for he fund managers o rack he benchmark echnology Index effecively in Malaysia sock marke. Keywords: Goal Programming Model, Enhanced Index racking, Opimal Porfolio, Mean Reurn, racking Error. Inroducion A he operaional level, many decisions are made in order o achieve he desired oucome ha conribue o he achievemen of a company s overall sraegic goal. In operaions managemen, here are quaniaive models, opimizaion models and oher echniques available which help he managers o make beer decisions scienifically. In porfolio managemen, he fund managers have o deermine he opimal porfolio which can generae higher reurn a minimum risk of loss. Enhanced index racking is a popular ype of porfolio managemen which aims o consruc he opimal porfolio in order o generae higher porfolio mean reurn han he benchmark index mean reurn a minimum racking error []. racking error is a risk measure of how closely he porfolio reurn follows he benchmark index reurn []. racking he secorial index is imporan because he index represens he overall performance of he economic secors in a counry such as echnology secor, consrucion secor and indusrial produc secor. In racking he benchmark index, he opimizaion model wih goal programming approach has been developed o deermine he rade-off beween minimizing he racking error and maximizing he mean reurn of he porfolio [3]. he opimizaion model has been sudied by differen researchers as a sraegic decision-making ool in porfolio managemen [4-9]. racking error and mean reurn of he opimal porfolio are wo elemens in enhanced index racking problem [0, ]. he obecive of his paper is o apply he opimizaion model wih goal programming approach in consrucing he opimal porfolio o rack he echnology Index in Malaysia. he performance of he opimal porfolio is hen compared wih he benchmark echnology Index. he res of he paper is organized as follows. he nex secion describes he maerials and mehods used in his sudy. Secion 3 presens he empirical resuls of his sudy. Secion 4 concludes he paper.. Maerials and Mehods.. Daa In his sudy, he daa consiss of weekly reurn of he
2 American Journal of Operaions Managemen and Informaion Sysems 06; (): socks from echnology secor which are lised on he Malaysia sock marke as shown in able []. able. Lis of Socks from echnology Secor on Malaysia Sock Marke. Socks CUSCAPI D&O DAAPRP DIGISAR DEX GHLSYS GPACKE GROIC MPI MSIAGA OIO OMESI PAPAGE PEA HEA RIVE UISEM he sudy period is from January 0 unil December 05. his daa is applied in he opimizaion model wih goal programming approach for porfolio consrucion o rack he echnology Index in Malaysia. In porfolio consrucion wih he goal programming model, he decision variables represens he opimal porfolio composiion ha can be deermined by solving he model [3]. he reurn of he socks is deermined as below []. R P, P, is he reurn of sock a ime, is he closing price of sock a ime, is he closing price of sock a ime -. he reurn of he benchmark index is deermined as below [4]. R I I I is he reurn of index a ime, is he index value a ime, is he index value a ime -. he mean reurn of he sock is calculaed as below [3]. r R is he mean reurn of sock, P, = ln P, is he reurn of sock a ime, R R r I I = ln I = R = () () (3) is he number of observaions. Figure shows he consrucion process of he opimal porfolio in racking he benchmark echnology Index wih an opimizaion model [4]. Figure. Consrucion Process of he Opimal Porfolio Composiion wih Opimizaion Model. In his sudy, he opimizaion model wih goal programming approach is solved wih LIGO sofware [5]... Goal Programming Model In enhanced index racking, here are wo goals o be achieved, which are minimizing he racking error and maximizing he mean reurn of he opimal porfolio. Reference [3] proposed he dual obecive opimizaion model for enhanced index racking problem which is formulaed as follow. Minimize Maximize subec o = x R = r = (4) (5) (6)
3 36 Lam Weng Siew and Lam Weng Hoe: Sraegic Decision Making in Porfolio Managemen wih Goal Programming Model r 0 is he mean reurn of sock in he opimal porfolio, is he number of socks, is he racking error of sock, is he porfolio racking error, R is he porfolio mean reurn, Equaion (4) is he firs goal which minimizes he porfolio racking error. Equaion (5) is he second goal which maximizes he porfolio mean reurn. Consrain (6) ensures ha he oal weighs of socks invesed equal o one. Consrain (7) ensures ha he weigh of each sock in he opimal porfolio are posiive. he dual obecive opimizaion model above is solved wih goal programming approach [3]. Goal programming is able o handle decision problems ha involve muliple goals [6]. he goal programming model is formulaed as follow. Minimize z = d d (7) (8).3. Porfolio Performance racking error and mean reurn of he opimal porfolio are wo elemens in enhanced index racking problem [0, ]. racking error is he sandard deviaion of he difference beween he reurns of he porfolio and he reurns of he benchmark index [7-9]. he formula for racking error is as follows. E is he racking error, is he number of periods, is he mean reurn of he opimal porfolio a ime, R P R I E = is he mean reurn of he benchmark index a ime. (3) he mean reurn of he opimal porfolio is formulaed as follow [4, 0]. r P ( R P R I ) i= = i= r x (4) subec o d d = m (9) r P r is he mean reurn of he opimal porfolio, is he mean reurn of sock in he opimal porfolio. R d d = n = (0) () Excess reurn is defined as he difference beween he porfolio mean reurn and benchmark index mean reurn which is formulaed as follow [3, 0]. α = rp r I (5) 0 d is he exen of underachievemen for racking error, d is he exen of overachievemen for racking error, d is he exen of underachievemen for porfolio mean reurn, d is he exen of overachievemen for porfolio mean reurn, is he porfolio racking error, R is he porfolio mean reurn, m is arge value for porfolio racking error, n is arge value for porfolio mean reurn, is he number of socks, () Equaion (8) is he obecive funcion of he model which minimizes he sum of deviaions of all decision goals. Equaion (9) is he firs goal which minimizes he porfolio racking error. Equaion (0) is he second goal which maximizes he porfolio mean reurn. Consrain () ensures ha he oal weighs of socks invesed equal o one. Consrain () ensures ha he weigh of each sock in he opimal porfolio are posiive. α r P r I is he excess reurn, is he mean reurn of he opimal porfolio, is he mean reurn of he benchmark index. he performance of he opimal porfolio is measured wih informaion raio [0, ]. he informaion raio is defined as he raio of porfolio s excess mean reurn o he porfolio s racking error which is formulaed as below. (6) IR is he informaion raio, α is he excess mean reurn of he opimal porfolio over he mean reurn of he benchmark index reurn, E is he racking error. Higher informaion raio indicaes higher performance of he opimal porfolio. 3. Empirical Resuls α IR = E able displays he summary saisics of he socks reurns in his sudy.
4 American Journal of Operaions Managemen and Informaion Sysems 06; (): able. Summary Saisics of he Socks Reurns. Socks Mean Sandard Deviaion CUSCAPI D&O DAAPRP DIGISAR DEX GHLSYS GPACKE GROIC MPI MSIAGA OIO OMESI PAPAGE PEA HEA RIVE UISEM As repored in able, he socks reurns show ha he values of mean and sandard deviaion are differen for each sock in his period of sudy. GROIC gives he highes mean reurn a whereas GHLSYS gives he highes sandard deviaion a able 3 presens he sock selecion in opimal porfolio which is consruced by solving he goal programming model. able 3. Sock Selecion in Opimal Porfolio. Socks Weighs (%) CUSCAPI 0.3 D&O.8 DAAPRP 0.48 DIGISAR 0.00 DEX 4. GHLSYS.68 GPACKE 0.00 GROIC 9.4 MPI.0 MSIAGA 0.00 OIO 0.00 OMESI 0.00 PAPAGE 0.00 PEA 4.53 HEA 0.00 RIVE.65 UISEM 3.88 As shown in able 3, he lis of socks wih posiive weighs indicae ha hose socks are seleced by he goal programming model in consrucing he opimal porfolio o rack he echnology Index in Malaysia. he opimal porfolio consiss of 0 socks wih differen weighs in racking he echnology Index. DIGISAR, GPACKE, MSIAGA, OIO, OMESI, PAPAGE and HEA are no seleced in he opimal porfolio because hese socks give he weighs of 0.00%. Figure presens he opimal porfolio composiion wih goal programming model. Figure. Opimal Porfolio Composiion wih Goal Programming Model. As shown in Figure, he opimal porfolio consiss of CUSCAPI (0.3%), D&O (.8%), DAAPRP (0.48%), DEX (4.%), GHLSYS (.68%), GROIC (9.4%), MPI (.0%), PEA (4.53%), RIVE (.65%) and UISEM (3.88%). his implies ha he opimal porfolio composiion are he opimal soluion of he goal programming model. GROIC is he mos dominan sock in he opimal porfolio wih 9.4% of he allocaed fund. On he oher hand, CUSCAPI is he smalles sock in he opimal porfolio wih 0.3% of he allocaed fund. able 4 and Figure 3 presen he summary saisics and reurn disribuion of he opimal porfolio of he goal programming model respecively. able 4. Summary Saisics of he Opimal Porfolio. Goal Programming Model Summary Saisics Porfolio Mean Reurn Porfolio Sandard Deviaion Porfolio Skewness Porfolio Kurosis Figure 3. Porfolio Reurn Disribuion of he Goal Programming Model. Based on able 4 and Figure 3, he opimal porfolio of goal programming model gives he mean reurn (0.6068%) wih sandard deviaion Besides ha, he skewness and kurosis value of he opimal porfolio are and respecively. able 5 displays he performance of he opimal porfolio consruced using he goal programming model.
5 38 Lam Weng Siew and Lam Weng Hoe: Sraegic Decision Making in Porfolio Managemen wih Goal Programming Model able 5. Performance of he Opimal Porfolio of Goal Programming Model. Porfolio echnology Index Goal Programming Model Mean Reurn (%) Excess Reurn (%) racking Error (%) Informaion Raio As shown in able 5, he weekly mean reurn for echnology Index is 0.70% based on he sudy period. he opimal porfolio racks he echnology Index wih weekly mean reurn % which is higher han he mean reurn of echnology Index. his implies ha he opimal porfolio consruced by he goal programming model is able o ouperform he echnology Index wih weekly excess mean reurn % a minimum racking error.0980%. Besides ha, he informaion raio 0.80 indicaes ha he opimal porfolio can generae weekly excess mean reurn 0.80% over he mean reurn of echnology Index a % racking error. herefore, he goal programming model is suiable o be used as a sraegic decision-making ool for he fund managers and invesors in Malaysia. 4. Conclusion his paper discusses abou he sraegic decision-making ool in porfolio managemen by using he goal programming model o rack he echnology Index in Malaysia. In conclusion, he opimal porfolio consruced by he goal programming model is able o ouperform echnology Index by generaing weekly excess mean reurn % a minimum racking error.0980%. he significance of his sudy is o idenify and apply he goal programing model as a sraegic decision-making ool for he fund managers and invesors o rack he benchmark echnology Index effecively in Malaysia. References [] J. E. Beasley,. Meade, and. J. Chang, An evoluionary heurisics for he index racking problem, European Journal of Operaional Research, vol. 48, pp , 003. [] R. Roll, A mean variance analysis of racking error, he Journal of Porfolio Managemen, vol. 8, pp. 3-, 99. [3] L. C. Wu, S. C. Chou, C. C. Yang, and C. S. Ong, Enhanced Index Invesing Based on Goal Programming, he Journal of Porfolio Managemen, vol. 33, pp , 007. [4]. A. Canakgoz, and J. E. Beasley, Mixed ineger programming approaches for index racking and enhanced indexaion, European Journal of Operaional Research, vol. 96, pp , 008. [5] G. Guasaroba, and M. G. Speranza, Kernel Search: An applicaion o index racking problem, European Journal of Operaional Research, vol. 7, pp , 0. [6] W. S. Lam, J. Saiful, and I. Hamizun, he impac of differen economic scenarios owards porfolio selecion in enhanced index racking problem, Advanced Science Leers, vol., no. 5, pp , 05. [7] W. S. Lam, J. Saiful, and I. Hamizun, An empirical comparison of differen opimizaion models in enhanced index racking problem, Advanced Science Leers, vol., no. 5, pp. 78-8, 05. [8] W. S. Lam, J. Saiful, and I. Hamizun, he impac of human behavior owards porfolio selecion in Malaysia. Procedia of Social and Behavioral Sciences, vol. 7, pp , 05. [9]. Meade, and J. E. Beasle, Deecion of momenum effecs using an index ou-performance sraegy, Quaniaive Finance, vol., no., 33-36, February 0. [0] L. C. Wu, and L. H. Wu, racking a benchmark index using a spreadshee-based decision suppor sysem as he driver, Exper Sysems, vol. 30, pp , 0. [] W. S. Lam, and W. H. Lam, Porfolio opimizaion for index racking problem wih mixed ineger programming model, Journal of Scienific Research and Developmen, vol., no. 0, pp. 5-8, 05. [] Bursa Malaysia, n.d.. Company Announcemens Bursa Malaysia Marke. [online] Available a: < hp:// es/#/?filer=bs08&board=mai- MK&secor=ECHOLOGY&page=> [3] L. J. Giman, M. D. Joehnk, and L. J. Smar, Fundamenals of Invesing, h ed, Pearson, 0. [4] W. S. Lam, and W. H. Lam, Selecion of mobile elecommunicaions companies in porfolio opimizaion wih mean-variance model, American Journal of Mobile Sysems, Applicaions and Services, vol., no., pp. 9-3, 05. [5] LIGO, Version. Chicago: LIDO Sysems Inc, 00. [6] H. A. aha, Operaions Research:An Inroducion. 9h ed, ew Jersey, Prenice Hall, 0. [7] W. S. Lam, J. Saiful, and I. Hamizun, Comparison beween wo Sage Regression Model and Variance Model in Porfolio Opimizaion, Journal of Applied Science and Agriculure, vol. 9, no. 8, pp , 04. [8] W. S. Lam, J. Saiful, and I. Hamizun, Index racking modelling in porfolio opimizaion wih mixed ineger linear programming, Journal of Applied Science and Agriculure, vol. 9, no. 8, pp , 04. [9]. Meade, and G. R. Salkin, Developing and Mainaining an Equiy Index Fund, Journal of Operaion Research Sociey, vol. 4, no. 7, pp , 990. [0] F. K. Reilly, and K. C. Brown, Invesmen Analysis and Porfolio Managemen. 0h Ed, Mason, Souh Wesern Cengage Learning, 0. [] C. L. Israelsen, A Refinemen o he Sharpe Raio and Informaion Raio, Journal of Asse Managemen, vol. 5, no. 6, pp , 005.
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