An Application of Revised Fuzzy AHP Modeling on Taiwan High-Tech Stock Portfolio Strategy 1

Transcription

1 A Applcato of Revsed Fuzzy AHP Modelg o Tawa Hgh-Tech Stock Portfolo Strategy P. Wu * ad Y. H. Che ** * Departmet of Idustral Egeerg ad Maagemet I-Shou Uversty, Kaohsug Couty, Tawa, ROC. Emal: pwu@su.edu.tw Phoe: ext 550 ** Departmet of Iformato Maagemet ad Commucato Kao-Yua Isttute of Techology, Kaohsug Couty, Tawa, ROC. Abstract The Aalytc Herarchy Process (AHP) has bee appled may areas wth ts smple theory ad easy of use. I ths research, we combe Buckley s fuzzy AHP model wth the approach of deletg attrbutes based o the method of Brach Freezg Rule (BFR) proposed by Harker. Ths revsed model helps mprovg the effcecy by reducg the umbers of parwse comparsos the questoare whe the sze of the herarchy creases. I order to mprove the amablty ad relablty of the system, we use Icomplete Parwse Comparso Matrx (IPC) proposed by Harker. Fally, we apply the revsed model o Tawa Hgh-tech stock portfolo strategy to provde the vestors a referece for stock purchasg. By comparso wth Buckley s fuzzy AHP model, our revsed model shows great savg o the performace of decreasg the expert s questoare. Keywords:Stock portfolo, Fuzzy AHP, BFR, IPC.. Itroducto Decsos play decsve role huma lfe. Whe cofrot to the fuzzy complex stuato, how to make the decso smart effectve uder rsk s a mportat ssue. Tools for decso supportg are prolferated, such as, expert system, group decso system (GDSS), Artfcal Neural Networks (ANN), Aalytc Herarchy Process (AHP), Decso Tree, Geetc Algorthm (GA), Data Mg etc. Amog the lsted methods, AHP stads out for ts smplcty theory, easess operatg, avalablty dfferet problems. However, tradtoal AHP method oly deals wth the determstc pheomeo. To exted the techque to cover the cases wth ucertaty ad cope wth the trsc vagueess, researchers beg to employ the fuzzy theory to tradtoal AHP method. More ad more fuzzy AHP studes have bee vestgated later o. The tradtoal AHP method has some drawbacks as follows: () rato scale problems; () decso attrbutes terdepedet problems; (3) mprecse problems; (4) group decso problems; (5) the herarchy umbers creasg problems [,]. Curretly most AHP methods address the frst four ssues. Few researches have covered the 5th problem [6,7,8]. I dealg wth complex problems such as stock selecto strategy, matag the hgh effcecy requres Ths research s sposored by the Natoal Scece Coucl of Tawa, R.O.C., ( NSC H-4-0).

2 more supplcated treatmets whe the sze becomes larger. I ths paper, we revse Buckley s fuzzy AHP model [] wth Brach Freezg Rule (BFR) ssued by Harker [5]. Ths revsed model helps to mprove executg effcecy by reducg the umbers of parwse comparsos whe the sze of the herarchy creases. The desg of the expert s questoare ot oly uses lgustc varable stead of Saaty's -9 rato stadard but also combes Icomplete Parwse Comparso Matrx (IPC) by Harker [3] to mprove the system s amablty ad relablty whe the questo s ot aswered.. The Revsed Fuzzy AHP Model I our AHP process, we use fuzzy umbers to represet the measuremet of experts vew toward the preferece of assessmet by formg the parwse comparso matrx. Ad called the matrx the fuzzy postve recprocal matrx, M = [ R j ]. Here M represets the fuzzy postve recprocal matrx ad R j fuzzy umber of experts preferece. Ad R =,, j =,, Λ. R j, j s the I tradtoal AHP process, the rato of the parwse comparso for each etry must be ozero. Whe the questoares are ale or ukow to the decso maker, Haker [4] suggested that the etry s left uaswered. Therefore we employ the cocept of complete parwse comparso matrx to our recprocal matrx. The llustrato of the complete parwse matrx s show as follow. Cosder a recprocal matrx C as: C = w3 w w w3 () Let B= (b j ) be the complete parwse matrx correspodg to C. We set () b j = c j, where c j > 0 s a real umber; () the rest etres, whose aswers are ukows, to be 0; ad (3) b = m, where m s the umber of uaswered questos row, where =,,3,,. Thus we obta the matrx B as: B = () We further defe A = (I + B), ad obta the complete par wse comparso matrx A. A = 0 0 (3) Ad matrx A becomes our ew recprocal matrx. Aother approach we used the study s to elmate the small weghts the AHP process. Whe the weghts are too small (less mportace), we employ Haker s cocept, the BFR (Brach Freezg Rule), as the rule for elmatg small weghts. Furthermore, we modfy the cocept wth fuzzy umbers as follows: W < (4), ( Kut) where W s the total weght of the dvdual elemet of a partcular key factor, s the umber of the elemets of a partcular key factor the same herarchcal layer ad K ut s the fuzzy umber for the cut value (threshold value). Typcal value of K ut s (,.5, 4) whch drop /3 of the key factors. Whe total weght of the key factor s less tha the value that s seekg

3 (calculatg), the the value s dropped alog wth the factor tself. As for the rakg order method, we adopt the -cut rakg method descrbed below: Gve M α = [ a, b ]] M α = [ a, b ], () Adam s Approach M ( > ) M at α - level ff b > b (5) () Buckley ad Chas' Approach M ( > ) M at α - level ff a > b (6) For the lgustc terms for fuzzy umber, we adapt Che ad Hwags scaled coverso measuremet []. We use measure 3 ths study. The expert s preferece s traslated Fgure. very low a b a b X=R low medum hgh very hgh Fgure. Measure 3, Sematc Coverso Graph 3. Methodology Combe the ew approaches metoed prevous secto, we ca start the fuzzy AHP process the followg ways: Step. Create the herarchy layers: Based o the characterstcs decomposed by each attrbute, the herarchcal structure of our model s costructed Fgure. The Layer 0 represets the ultmate goal, the etry Layer represets the factors whch affect the ultmate goal, the etry Layer s the sub-factors for each factor Layer, ad the etry the last layer represets the alterate choces of polcy. Layer 0 Decso Factors Layer Goal C C C m K K K m K m Alterate Polcy Bottom layer A A A3 Fgure Herarchy Layers Step. Desg expert questoares: Followg the structure bult Step, we desg the expert questoares by covertg the decso factors to the sematc format. Ths step s dvded to two parts: Frstly, we ask the expert to aswer the questoare, ad decde whether the key factors Layer ad the sub key factors layer are mportat or ot? Secodly, we ask aother set of experts to fll the revsed questoare, whose key factors wth extreme low weghts calculated by the revsed fuzzy AHP procedure Layer are elmated, wth the alteratve choces Layer 3 (see Fgure 3). Step 3. Group tegrato: After the pollg process, we ca obta the weghts of each key factors ad ts descedet layer. By usg the sematcs Table, we ca trasform these to correspodg fuzzy umbers. We the covert the experts opo to fuzzy umbers by the followg formulas: ( M j = mj mj Λ mj ) (7), where M j s the tegrated tragle fuzzy k umber; m j s the -th to the j-th factor par comparso by expert k. Step 4. Buld the fuzzy recprocal matrx: Follow step 3, we may obta the fal calculated fuzzy umbers for each layer accordg to equatos (), (), ad (3). Step 5. Calculate the key factors fuzzy weghts:

4 A modfed formula for the fuzzy weghts s show below. ( a ) = Λ a Z, w = Z ( Z Λ Z ) =,, Λ, Step 6. Elmatg factors wth small weghts: Use equato (4) to elmate those factors wth small weghts Layer, the recalculate the overall weghts. Step 7. Repeat Steps - 6 utl all the fuzzy weghts are calculated. Step 8. Herarchy layer sequecg: Calculate the fuzzy weght values for the alteratve polcy as follow: where U = j= w r j j (9), U s the alteratve polcy fuzzy weghts; w j s the fuzzy weght for the key factor; r j s the score for the selectve alteratve polcy A to the key factor X j. Step 9. Fuzzy orderg: Rak the fuzzy umbers accordg to the rakg polcy. 4. Illustrated Example ad Aalyss I ths secto, we use the Tawa IC Idustry Stocks as our example to further exemplfy the suggested process ad aalyze ts results of our theory ad algorthms. Our purpose s to fd the best stock selectg strategy for IC dustry the log term (from several moths to oe year). Accordg the L (988) ad Che (999), the factors that may affect the dvdual stock prce, but ot the overall stock fluctuatos s establshed Fgure 3. I ths fgure, Layer 0 s the ultmate goal whch s to get best stock selectg polcy, ad Layer cotas the key factors that mostly fluece selectg polcy such as: Eterprse stuato; Idustry stuato; ad Ivestmet Captals categores. Layer cotas the sub-factors that affect the key factors Layer, ad Layer 3 s the optos for the IC dustry (see Fgure 3). These optos clude the upstream IC desg (VIA), mdstream IC maufacturg (Fab: TSCM, ad Flash: MXIC) ad dowstream IC packagg (ASE). The frst questoare s set out to the maagers of the securty ad trust fud compaes. Total te questoares were collected. After calculatg the total weghts of sub-factors, the sub-actors: Maager Atttude, Govermet Polcy, Trust Fud Stock Holders, Idvdual Stock Holders, ad Securty Broker Holders were elmated, ad ew weghts were recalculated. After elmatg the umportat factors the category, the revsed questoare wth the selectg optos (VIA, TSMC, MXIC, ad ASE) s delvered to the stock aalysts ad brokers. Total 7 out of 30 set pollsters were collected. Recalculatg the fuzzy recprocal matrx, we obta the fal weghts for all key factors. Sequecg the dfferet layers by equato (9), we obta the correspodg weght for each opto (stock selecto) Table. Ad the order of prorty as follows: VIA > TSMC > MXIC > ASE. From Table, we exame total weghts of the four optos, ad ormalze the weghts to scale betwee 0 to. The results suggest that the vestmet ratos for these optos are VIA 43%, TSMC 6%, MXIC 4%, ad ASE 7%. 5.Coclusos ths study, we have vestgated the

5 U ltmate Goal Evaluate Key Fact Sub Factors Selectg Polcy Operatg status Proftablty Eterprse Stuato Competetvess Compay Sze Compay Image Upstream VIA Facal structure Maager atttude Optmal Stock selectg Polcy Idustry Stuato Mmarket cycle Idustry future R & D Market Demad Govermet Polcy mdstream MXIC mdstream TSCM Board Share Ivestmst Captals Trust Fud Share QFII Share Idvsual Share Dowstream ASE Broker Share Fgure 3 Herarchy Level Structo revsed fuzzy AHP method for the use of stock selectg strategy. Not lke the tradtoal fuzzy AHP method uses all factors to evaluate the decso factors, the revsed method uses the BFR (Brach Freezg Rule) techque to 985. [] S. J. Che ad C. L. Hwag, Fuzzy Multple Attrbute Decso Makg Method ad Applcato, A State-of-the-Art Survey, 99, New York:Sprg-Verlag. elmate those factors wth extreme small [3] P. T. Harker, Icomplete parwse weghts. Our results dcates that the total parwse comparsos of revsed method s 3++*0+6* = 6 tmes whch s less tha those of Buckley s Fuzzy AHP method, comparsos the aalytc herarchy process, Mathematcal Modellg, vol 9, pp , 987. [4] P. T. Harker, Alteratve modes of (3++*0+6*7=46 tmes). Ths s 0% questog the aalytc herarchy savg computato. Whe the umber of layers creases, the savg s eve more. process, Mathematcal Modellg, vol 9, pp , 987. [5] I. Mllet ad P. T. Harker, Globally effectve Referece [] J. J. Buckley, Fuzzy Herarchcal Aalyss, Fuzzy Sets ad Systems 7, pp.33-47, questog the Aalytc Herarchy Process, Europea Joural of Operatoal Research, vol 48, pp.88-97, 990. Table, sematcally statemets coverso table Extremely Extremely Umportat Ordary Importat Sematc Statemets Umportat Importat Very Bad Bad Normal Good Very Good Fuzzy Numbers (/0,/9,/8) (/7,/5,/3) (,,) (3,5,7) (8,9,0) Table The Fuzzy Weghts of Selectable Optos Selecto Optos VIA MXIC TSMC ASE Fuzzy Weghts (0.0,0.48,8.53) (0.0,0.38,4.7) (0.04,0.54,5.08) (0.005,0.075,.397)