運用基因演算法與粒子群演算法建構股票投資組合

  

  

  

  

Genetic Algorithms and Particle Swarm Optimization Used

to to Construct the Equity Portfolios



        
          

   Abstract

This research focuses on using the characteristics of the Genetic Algorithms (GA) and Particle Swarm Optimization (PSO) for efficiently sourcing solution to construct optimal equity portfolios. The internal equity portfolios’ monthly data from Jan. 2004 to Dec. 2006 was adopted. The data set were divided into three sub-periods for getting different stocks, and the experiment is divided into two stages. The first stage carries on the fund evaluation in view of the fund achievements target, constructing h value evaluation. There are 8 factors were taken into account in the portfolios performance evaluation, including Ratio of Return, Standard Deviation, Beta Coefficient, Shape Index, Jensen Index, Treynor Index, Information Ratio and Turnover which Republic of China investment trust on securities and consultant the trade association announce. Then selects top 15 funds to own stocks the proportion highest top five great stocks to carry on the stock evaluation once more, and selects its reward variation ratio highest stock. In the second stage, we apply the GA and PSO algorithms to these stocks in search for the optimal capital allocation for equity portfolios by using the moving interval windows. The research compared the returns of the equity portfolios with that of TWSI and that of the best return of equity fund.

The result shows that the ratio of return of our research is better than that of TWSI and that of the best return of equity fund. The result also displays that the investor must perform elastic operation the order to obtain the higher ratio of returns in demand.

Keywords



Equity portfolio, Fund Performance Evaluation, Genetic Algorithms,

1.








1983          200710    ! " #$ % & ' 2.2( ) *+, - .   / 0 " #1 2 3 45 6 7 89 : ; < $ % => ? @ 2 3 AB C; 8D  D E F +G H IJ K1 ; < L M N O P Q R S IT U VW J KX Y 82 3 Z [ \ 1 ] @ ^ _ *N ` R a 1 b c  d / 0 " #1 2 3 6 e R a f g h i 8; j < k l m n o 6 J Kp p q 2 3 r s R t 1 2 T U ] uv w xy z *Z { | 6 ; j < k } a 1 2 3 ~ C€ Q  ‚ J K1 ƒ„ " #* 3 … † ‡ ˆ ‰ Š ‹ 1 ŒŽ   ‘ A’ “ L ” • – —˜ ™ 1 š " › œ  ž ŸGenetic Algorithms,   ¡ GA¢£% ¤ ¥ ¦ ŸFuzzy Theory¢£§ ¨ © ª « ŸNeural Network,   ¡ NN¢£¬ ) ­ ® (Ant System)£¯ ° $ ± ž ŸGenetic Programming,  ¡ GP¢VŽ ² P ³ A’ 1 ´ µ ¶ ] · ¸ œ  ž (Particle Swarm Optimization,  ¡ PSO)*a • GA ¹ º ] · ¸ » ¼ ½¾ ^ _ ] —¿ À ” • Á ÂGA8¹ º ] · ¸ ^ _ Ã Ä • Å 1 Æ 3 … † ‡  ž Ç ” • x 2 » ¼ L 1 € . £C; È2 #½¾  É * PSO +Ê Ë ˆ ‰ Ì 1 ” • P ³ ³ Í Î8Ï Q a • “ ] · ¸ 1 œ  Q Ð Ñ Ò Ó Ô Õ Ö 8× Õ Ø Ù Ú 1 … Û 8 Ü ŒÝ Þ 1 ¾ ß *+àÜ Œá • Chang et al.(2007)C; â ã ä —å æ 2 » ¼ ç l è éê – GA ë PSO ì í œ  ž îO í 1 œ ¸ Q Ð ] · *~ ï ð   ï ½; ñ â ò ~ ó T U ô ê – - | Ü Œå æ 1 2 » ¼ Q õ ö ÷  2 3 ø Á L ] H ù 1 T U *

2.








Ü ¦ ú ŒÁ 1 —3 … † ‡ 1  ž å æ ; j 2 » ¼ 4C€ 2 #½¾  É 1 û ü *ý þ æ 2 » ¼ ^ _
Ú € . £C; V2 # É  Ø  M Ü Œ M1  —¹ º 2 #½¾  É ^ _ › àê – " › œ  ž V´ µ ¶ œ  ž 1 Ä  Q Ð 4    ; j " #—Œ~ ó ì Ø Ý Þ Ã   5 „ -  ~ ó Œ  ] · 2 #½¾ É  ~  S ] · 1 ; j 2 » ¼ *—  “  ó    ~ Îë  1   ï ½; ñ â ò T U ô V- ] · ; j " #T U ô ~ ó ê – - | Ü Œ1 ; j 2 » ¼ T U ô Q   x-; j " #ë  ï ½; ñ â ò T U ô *— Q Ñ Ò Ó 2 3 Ö 8" #© ¥ 3  § 1 2 … Û Vå æ  š ¥  T U 1 ; j 2 » ¼ Ü Œ Á 1 ¥ N î!1." #° ®   $% â ã å æ Ü Œ1 $% % *2. & a • " › œ  ž ë´ µ ¶ œ  ž É  2 #å æ ; j 2 » ¼ 4ê – O í å æ Q Ð  ` ] · *3. ' ( Ý Þ ) * 1 5 „ ê – + , ; 1 - . / 0 8Ï Q  x1 - 2 š 2 » ¼ 1 T U 3` *4.  " › œ  ž ë´ µ ¶ œ  ž ” • xÊ Ë ˆ ‰ Ì 1 4 5 6 *

3.  













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2 3 +ƒ„ " #1 C€ Ì Ç 7 8 ° ®   â ã 1 $% ä 9 :    Ç ; 8 ƒ„ " #  $% 1 3` ä —2 » ¼ 2 < É  1 Ù Ú ç l * 2 3 =  MC€  > Ë ? @ V  A  c  B 1 " #  C ] ¾ M8C€ D E" #- ä   1 F G *

TreynorŸ1965¢a • H I < k J(Security Market Line, SML)K L Œ1953 M 1962N  1 20E" #Ñ ÷ ƒ„ " #  â ã Treynorâ ã O â ã P " #1 T U Q = R J Ka ô S = ­ ® 6 J KTU + V W ­ ® 6 J KîÇ R t 1 T U *TreynorX D Il " #1   D · *ShapeŸ1966¢l 7 8 2 Ü < k J(Capital Market Line, CML)1954M 1963N  34E  " #1 2 Y VZ [ … × â ò —< k T U ô ~ ó   â ã 1 *  3` \ U @ ]  ƒ„ " #1   4^  x< k 2 » ¼ 1   *Shape_ —2 í ‹ ø 1 ” O 82 » ¼ 1 ` J K5 a 8­ ® 6 J K› àÑ ÷ Shapeâ ã ShapeX D @ T U O " #  D · *JensenŸ1968¢b c H I < k d e JÑ ÷ Jensenâ ã $ % +f g -   Š „ J Kz ç î" #  8Ï š IxÖ W xÁ ã 2 » ¼   TB *JensenŒ1945M 1964N  1 115E  " #3` \ U Ý Þ 1 ƒ„ " #h Ä   4^  x S&P â ò Z *  ÷ 1 T U ô *Eun, Kolodny and ResnickŸ1991¢i • Treynorâ ã £Shapeâ ã VJensenâ ã j N  19 E k " #1   TB *Œ3` \ U a • Treynor â ã £Shape â ã $%   š 11E" #   x< k 2 » ¼ i • Jensenâ ã $% l a š 5E " #   x< k 2 » ¼ *

3.2.    

























' ( » ¼ l Æ 5 „ 1 H I —2 » ¼ Ç i ! J Km W *n x9 o  C€ ; j 4¼ p 2 » ¼ Q i » ¼ J Km W *EvansÈArcher(1968) 8] , Œ9 o  ‚ ž (random diversification)1 J K ‚  ` _ —Ø & ; j 1 T U ô q 5 $ r 1 s t ]  Ç © #¼ p Š u v w '  ‚ J K1  ` * ] , 1 2 » ¼ ¥ ¦ 8#x y z © { Ô | t  Harry Markowitz+1952 Z Ñ ÷ *+. 4} š ~  1 X € J K* — Q å  2 » ¼ %  2 í
P J Ks ò ‚ ¸ *MarkowitzA’ ÷ " Ü 1 2 » ¼ % ƒ ÷ 2 < 2 » ¼ 1 „ - T U ô V„ - J KX *“  M¦ ß +xf g J Kî…  „ - T U ô † @ ¸ ‡+f g „ - T U ô î…  J K† ˆ ¸ *MarkowitzŸ1952¢

Ñ ÷ ‰Š ‹ ò -s Œ ò 2 » ¼ ¥ ¦ (Mean-Variance Model, MVç l )ॠ¦ Ž ~ 2 » ¼ ' M J K ‚ Ö 8T U ¥  î2 < É  1 ç l *GrubelŸ1968¢A B  2 < É  1 K L Ä • x k 2 < É   P 2 ã 1 ‘ ’  C H I < k  l O 2 » ¼ Ç ' M J K ‚ 1  ` à Q R t – · 1    ô ’ *Levy and SarnatŸ1970¢ Markowitz 1 2 » ¼ ¥ ¦ % ~ ó Œ4à “ ) R J Ka ô ” +"  • 5 „ a ô z ç î1 2 » ¼ 3¦ ë Grrbel Š „ " # k 2 < É    ‚ J KÃ Ñ IT U *Levy and LermanŸ1988¢Œ– — I 2 £ – H I 2 VH I ï — I ˜ ¼ 2  Æ  x ô ’ ~ ó ŒŒ3 ` \ U H I ï — I 1 ˜ ¼ 2 / 0 1  ô ’ ] · TU CS 2 » ¼ 2 < É  . Ç P H I < k ȗ I < k p ™ ð Ú *SiegelŸ1991¢Œâ ÷ 2 3 +š › œ  (business cycle)1 ž Ÿ ß ~ ó ; j ȗ I 2 ã 1   1 ž , Ç ~  1 Ñ I2 » ¼ T U ô *BriantonŸ1997¢â ÷ Markowitz 1 2 » ¼ ¥ ¦ Z  ÷ 1  ô ’ 8; 8 „ - 2 T U ô £ã ç ¡ ȃs Œ ò  Ø s ò à ¢ ð M£ 8Š ¤ ¥ 1  ð M£ š Z s t Ç Q ¦ t M ¡ Œ † @ 1  ô ’ § J*Clarke and SilvaŸ1998¢_ —P 5 „ ¨ © î2 » ¼ J KëT U a • ï ½ Š ‹ 1  Z R t 1 3` – i • ª « 2 Y Z t 1  ô ’ ¬ ï ­  à š  ô *

3.3.     































" › œ  ž ŸGenetic Algorithms‡GA¢1 " Ü ¥ ¦ 8#Hollandx1975® ¯ Ñ ° 8" x±  C€ ( ² 1 Æ ] · ¸ ³  o æ Ÿ´ µ ¶ È
· ¸ 1999¢* " Ü ­ ¨ +x% ¹ º   Õ L   » ¼€ £ ½ ¾ ¿ 1 ±  ~ ¸ ž l Q  C€   Æ L Û š – F À 6 1 Á  9 o 6 1 Š u à , Ä à1 " › 2 Å - Æ Q < º – Ì Á  ¬  Ç 1 µ  5 : È œ ¸ îÉ < º 4 ” 6 ] Ê 1 ] ·   Æ *" › œ  ž l 1  Ø  MÄ  µ —Ë Ì ŸReproduction¢£Ã É ŸCrossover¢£VÍ s ŸMutation¢*D ²  | 6 Ô í Î † Ï GA1 Œ ž ÐGoldberg(1989) Ñ a • " › œ  ž ä —o Ò Ô Ó Ô Õ ­ ® 1 Ö ¥ o × š 5 Ø Ô í Ñ ” • +š ‹ 2 » ¼ Ù  [ 1 ˆ ‰ (Orito, Yamamoto, 2003‡Xia, Liu, Wang, & Lai,2000)* Xia, Y., Liu, B., Wang, S. and Lai, K. K. (2000)Ñ ÷ 2 » ¼ C€ % ' ( „ € H I - Æ T U ô 1 Ú Û a • " › œ  ž    ] @ ¸ 2   *Ý H 3` \ U i • à% Z t M 1 2 » ¼   – ° ® 2 » ¼ · *Kyoung-jae Kim and Ingoo Han (2000)19891998  1 Ü  ; < —Œa • " › œ  ž Ý À Þ  ß Èº g „ € ; ñ 1 § ¨ © à 3½X Œ3` \ U ` ç  c ê i ° á § ¨ © ª « I÷ 10â11ã*R.J.Kuo,C.H.Chen & Y.C.Hwang (2001)1991 1997 1   ; < —Œä Ü á • GFNN(GA based FuzzyNeural Network)% 3 ¼ ¸ Èå ¸ › £ › “ _ —; j < k @ ]  æ i • ¸ 1 â ã 4} š Ú ç M å ¸ 1 › £ *Œ3` \ U GFNN % 1 3` Š F š  à è é ò ' 90 ãÌ *Orit, Y. and Yamazaki, G.(2001)ê ë ; < L ë@ . Š ‹ ² c – I1 Â

1100E; j  9» ; j » ¼ ä —C; ã 1 a • " › œ  ž xâ ò " #1 C ; Ì ³  – · 1 2 » ¼ *4 ” ì ò #Š ‹ ² c ë2 » ¼ J Kì s ò ï ½» ¼  Á 1   Š ‹ ² c ] @ à J K] ˆ 1 2 » ¼ *Ý H 3` \ U i • " › œ  ž + =t © CS â ò " #2 » ¼ 1   – f g  1 » ¼ · *J. Korczak and P. Roger(2002)Ä • " › œ  ž Ví t Š ‹ JÁ 1 —Œ; j 0 î ß 1 „ € ž  ; < —Œ#CAC40â ò L ï C÷ 24E; j *Œ -  #199712=19991110=“ L ð ñ - —261¼€ ò - —7¼*Œ 3` AB £" › œ  ž Z t / 0 @ ]  – 0 ð 2 š / 0 T U ô  t I‡ó£l ô õ T U  1 Š ‹ 6 ö x0*Rui Jiang and K. Y. Szeto(2002)Ä • " › œ  ž Ví t Š ‹ J Mä —; j 0 î ß 1 „ € *Œä Ü Microsoft£ Intel£DellVOracle1 ; ñ -  —199011=2002830=ƒ3305÷ à è 2 Y *Â2000÷ 2 Y Ý —ð ñ - u1305÷ 2 Y ä —€ ò - *Œ3` AB £ R a ~ \ Ix0 ð 2 š / 0 ‡ó£GAZ t ð ñ - T U ô W x€ ò “ T U ô *

3.4.      





































´ µ ¶ œ  ž (Particle Swarm Optimization, PSO)8# James Kenney È Russell Eberhart ì W Ô í x1995Z Ñ ÷ 1 ø ù _ —±  Õ L 1 | 6 B æ Ç Q —œ  ž A’ 1  ú  ₁₉₉₀ û a • ü ý ±  Õ L ¶ ! ó —A ’ ] · ¸ û ü þ —
y A’ ÷ º   ¶ ! ‰¦ ­ ® — š 1 *  û ü  ¦ ­ ® 8© #%    V Ø ! Z » 1 ¶ ! ë  VëØ !  1 u t ó —  8 a •  ] Å  Z < º 1 „ € ó —  ¹ º ^ _ * 8  Æ œ ¸ *  (Evolutionary computation)ú ± x ¶ 1 º Ó 6 ó —Œ%  º   í t V  1 ( ²  MK L —º   Ø ! Û š Ô Ó V  Q Ð C€ ±  Ü  š ] @   1 © Þ ä —Ø ! í t ( ² 1 9 : ç l (Chang, Chu, Roddick & Pan 2005)*Shi and EberhartŸ1998¢Ñ ÷  6 ½¾ › µ (w)•   s ´ µ 1  c  4à S t  ‰ ³  ë ‰ ³   1 Š j ß ¬  È  M  ‰ ] · ¹ *“ ¥ ¦ "  8a • ´ µ ¶ @   ³  u 6 › µ  û  Ø ´ µ  c { ´ µ ~ ð – F 1  ‰ ä ³  *Ô í  6 › µ š ì Æ g  8P  6 › µ  — ò  Ø 8{  6 › µ 7 .  s Œ uí ¦ {  c 9 : .  q J6  Ø *7 8à x 6 ½¾ )  Ì  } š g 1   *! M Shi and EberhartŸ1998¢"  6 ½¾ › µ ~ ó   4Ã Ñ Ò  6 ½¾ ëÔ Ó › µ Ý Þ – · 1 å # ò X wmax —0.9wmin—0.4Vc1=c2=2.0*

Kennedy and SpearsŸ1998¢Ä • 5 à $ 1 ´ µ ¶ œ  ž ë Æ 5 „ 1 " › œ  ž ~ ó ê –  & —5 Ú ç Í s £5 Ú ç Ã É VÚ ç Ë Ì £Í s £Ã É  Œ3`  • ² Y + ´ µ 1 ´ µ ¶ ] · ¸  ` ‹ ½ ( " › œ  ž \ U ´ µ ¶ œ  ž 1 TB – š  ô * Yoshida et al. (1999)8 Ø ” • ´ µ ¶ œ  ž xB Ý º Ì Ä • +% Ð ­ ® ë% & ' × Ì  & á • à $ ëß ‚ 1 ' × s ò ~ ó Œi ´ µ ¶ œ  ž Q +àì ' × s ò î„ . ~ ó ] · ¸ Ä  *AbidoŸ2002¢å æ b c 1 ´ µ ¶ œ  ž xº g t Ð ­ ® ( g 6 ] · 1 Ù ò ò X +àŒL ) Ù ò 1  c

* + × +g 1 ò X h , +t © ² - L 5 ‹ j 1 + × ^ _ *Ujjin and Bentley Ÿ2003¢” • ´ µ ¶ œ  ž xª « . / ­ ® Ý Þ 3` AB ´ µ ¶ œ  ž Š – " › œ  ž š – I„ € ç  c 4à ´ µ ¶ œ  ž Q ¬   1 R t ] 0 X * Baumgartner, Maggele and RenhartŸ2004¢Ä • ´ µ ¶ œ  ž x6 Á ã ] · ¸ ^ _ ŒŒ3` \ U PSO+Pareto-optimal front. àÆ 6 Á ã ] · ¸ ^ _ š Š Ç  1 1 ` *Nenortaite and SimutisŸ2004¢Ä • ´ µ ¶ œ  ž %  § ¨ © ª « x; j Ã è ­ ®  & x2 • ô ï ð ëÏ ~ ó ŒÝ H 3` \ U  5 Ú ç 2 • ô à2 » ¼ 2 T U @ xS&P5002 T U 3 M 4 5  2 • ô @ x 0.2%l 2 x S&P500 ¦ – ¼ ¥ *Œ_ —´ µ ¶ œ  ž Ç š  ” • x ; j < k 0 î ] · ¸ ^ _ *

4.
 













Ü ŒP Ý Þ  ì 6  6 " " #1   â ã ~ ó " #$CC S   Â7 3 Û ; j " #4P “ 2 ; ê 8 ] I1 Â3 @ ; j S é ~ ó ; j $ C] uCS “ T U s Œ ê ô – I1 ; j å æ ; j 2 » ¼ ‡ ó6 l ' ( " › œ  ž V´ µ ¶ œ  ž ~ ó ; j 2 » ¼ L Ø & ; j 2 ½¾ 1 É  *

4.1.
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Œþ æ é1  6  82 Y 1  ú £Ý Þ -  1 ) g £" #ã 1 CS £   â ã Ù ò ã ç ¸ 1 ( ² V; j ã 1 CS *Œþ æ éŽ ~ xé4-1*

@ A " # T U ô— 40.70%à  6 7  8 Ü Œ  Z å æ 1; j  2 » ¼ “T U ô ` ] ·*‹ ¼ Ì Z L +  , ; 1Î † / 0  Ý õ ö ÷ ‘ 3 1T U ô5 ¦ 8 " › œ  ž Ö 8 ´µ ¶ œ  ž Z å æ 1; j  2 » ¼ “T U ôæ ê ï ½ ; ñ â òÖ 8  - ; j " # ] ·T U ô t F   Ý j ¼ Ü Ý Þ 1„ -Á ã * l -  1T U ô3 `  d ´µ ¶ œ  ž Z å æ 1; j  2 » ¼    ¬ 8 –  x " › œ  ž Z å æ 1; j  2 » ¼ * Ý Þ  ëÝ Þ ó 1Œ  3 ` A B Ä • ´µ ¶ œ  ž Z å æ 1; j  2 » ¼ T U ô   TB ¿ À  x " › œ  ž Z å æ 1; j  2 » ¼ *, ’ “ Ž ´ µ ¶ œ  ž +Ü Œ  1Ý Þ L  Ý A s  œ  ] ·¸ 1À 6 “Û š 1– · 2 # É  Q Ð  ” å æ ÷ I T U ô1; j  2 » ¼ ' M Ü ú 1Œ  Á 1*“é +  , ; / 0 — 1Ý Þ ) * ' ( Ý Þ •ëÝ Þ ó 1Ý H 3 `  •– — È H Ý Q  x  2 š  2 » ¼ ) * *



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1. Abido, M. A. (2002). Optimal power flow using particle swarm optimization. Int. J. Electr. Power Energy System, Vol. 24(7), 563-571.

2. Baumgartner, U., Magele, Ch. and Renhart, W. (2004). Pareto Optimality and Particle Swarm Optimization. IEEE Transactions on Magnetics, Vol. 40(2), 1172-1175.

3. Brianton, G.. (1997). Risk Management and Financial Derivatives. 431-469. 4. Chang, J. F., S. C. Chu, J. F. Roddick and J. S. Pan (2005). A Parallel Particle

Swarm Optimization Algorithm with Communication Strategies. Journal of Information Science and Engineering, 21, 809-818.

5. Clark, R. G., and Harindra de S. (1998). State-Dependent Asset Allocation. Journal of Portfolio Management, Winter.

6. Evans,J.L. and S.H.Archer, (1968). Diversification and the reduction of dispersion: an empirical analysis. Journal of finance, December.

7. Eun C., Kolodny R. and Resnick B. (1991). U.S-based International Mutual Funds: A Performance Evaluation. Journal of Portfolio Management, 88-94. 8. Eberhart, R. C. and Shi, Y. (2001). Particle swarm optimization: developments,

applications and resources. Congress Evolutionary Computation 2001 IEEE service center, Piscataway, NJ., Seoul, Korea.

9. Grubel, H. (1968). Internationally Diversified Portfolios: Welfare Gains and Capital Flows. American Economic Review, Vol. 58, 1299-1314.

10. Holland, J. H. (1975). Adaptation in natural and artifical systems. Ann Arbor: The University of Michigan Press.

11. Jensen, M. J. (1968). The performance of mutual fund in the period 1945-1964. Journal of Finance, 23, 389-416.

12. J. Korczak and P. Roger. (2002). Stock timing using genetic algorithm. Applied Stochastic Models in Business and Industry.18:121-134, 2002.

13. Kyoung-jae Kim and Ingoo Han, (2000). Genetic Algorithms Approach to Feature Discretization in Artificial Neural Networks for the Prediction of Stock Price Index, Expert Systems with Applications 19, pp.125-132.

14. Kennedy, J. and Spears, W. (1998). Matching algorithms to problems: an experimental test of the particle swarm and some genetic algorithms on the multimodal problem generator. IEEE World Congress on Computational Intelligence, 74–77.

15. Levy, H. and Sarant, M. (1970). International Diversification of Investment Portfolios. American Economic Review, Vol. 17(4), 668-675.

16. Levy, H. and Lerman, Z. (1988). The Benefits of International Diversification in Bonds. Financial Analysis Journal, Vol. 44(5), 56-64.

17. Markowitz, H. (1952). Portfolio Selection. Journal of Finance, Vol. 7(1), 77-91. 18. Nenortaite, J. and Simutis, R. (2004). Stock’s Trading System Based on the

Particle Swarm Optimization Algorithm. ICCS 2004, LNCS 3039, 843-850. 19. Orito, Y., Yamamoto, H., & Yamazaki, G. (2001). Index fund selections with

genetic algorithms and heuristic classifications. Computers and Industrial Engineering, 45, 97-109.

20. Sharpe, W. F. (1966). Mutual fund performance. Journal of Business, 39, 119-138.

21. Siegel, J. (1991). Does it pay stock investors to forecast the business cycle?, Journal of Portfolio Management, Vol. 18, 27-31.

22. Shi, Y. and Eberhart, R. C. (1998). Parameter selection in particle swarm optimization. the 7th Annual Conference on Evolutionary programming, 591-600.

23. Treynor, J. L. (1965). How to rate management investment funds. Harvard Business Review, 43, 69-75.

24. R.J.Kuo,C.H.Chen & Y.C.Hwang, (2001). An intelligent stock trading decision support system through integration of genetic algorithm based fuzzy neural network and artificial neural network. Fuzzy sets and systems,118,pp.21-45. 25. Rui Jiang and K. Y. Szeto. (2002). Discovering investment strategies in portfolio

management: a genetic algorithm approach. Proceedings of the 9th International Conference on Neural Information Processing. Vol. 3, 1206-1210, 2002.

26. Ujjin, S. and Bentley, P. J. (2003). Particle Swarm Optimization Recommender System. the IEEE Swarm Intelligence Symposium, Indiana, USA, 124-131.

27. Xia, Y., Liu, B., Wang, S., & Lai, K. K. (2000). A model for portfolio selection with order of expected returns. Computers and Operations Research, 27, 409-422.

28. Yoshida, H., Kawata, K., Fukuyama, Y., and Nakanishi, Y. (1999). A particle swarm optimization for reactive power and voltage control considering voltage stability. In G. L. Torres and A. P. Alves da Silva, Eds., Proc. Intl. Conf. on Intelligent System Application to Power Systems, Rio de Janeiro, Brazil, 117–121.