قياس أمثلة المحفظة الاستثمارية باستخدام الخوارزميات الجينية حالة أسهم بورصة الجزائر

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

                        habib.zouaoui@gmail.com Nadjat_meriem@outlook.fr

Measuring of Optimal Investment Portfolio Using Genetic Algorithm

Case of Algeria Stock Exchange

Habib ZOUAOUI 1& Meriem-Nadjet NAAS 2 1. University of TAHAR Moulay SAIDA –Algeria

2. University Center of Relizane –Algeria

Received:04 Aug 2014 Accepted: 26 Dec 2014 Published: 30 June 2015

 :         ) GA (             2010/01/31 -2010/12/31        .  .           jel   G11 Abstract:

This study aims to address the problems of risk management portfolio of bank loans based on the diversification strategy sector, and seeks primarily to the application of genetic algorithms (GA) to improve the Markowitz model (return - risk), The problem of portfolio optimization is a multi-objective problem that aims at simultaneously maximizing the expected return of the portfolio and minimizing portfolio risk. Present study is a heuristic approach to portfolio optimization problem using genetic algorithms technique.

The present study data on a sample of stocks price between 31/01/2010 -31/12/2010 in the Algerian stock Exchange. Further more in an attempt to evaluate the effectiveness of genetic algorithms to improve the level of risk optimization.

Keywords : Optimal portfolio, Diversification, Artificial intelligence, Genetic Algorithm, Return & Risk . (JEL) Classification : G11

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                          

Modern Portfolio Theory

     1990                          1952                         1      (Métaheuristic)                          2  1          2             

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                          3                Efficient portfolio                 4                    2010/01/31 -2010/12/31             1990      Diversification                    H. Markowitz,1952  .                                                          .                                     Static Model    Dynamic Model  .  

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1    1.1       1952                   3                           Covariance)        4   2.1   Static Model                                 5  (2.1)…. ....   





 

         1 : / : e w R R w c s Vw w Min P        1 : / ; : ' ' ' e w k Vw w c s R w Max

(5)

           1               (2.2)  (2.3) 3.1   Dynamic Model    Continuous-time       

Regime Switching Models

 6                  ,1969  P.A.Samuelson     N.H.Hakansson ,1971      ,1997  S.R.Pliska         Optimal Dynamic Strategies      H.Richardson, 1991 &  D.Duffie     M.Schweizer ,1996      2000  ,  Zhou & Li    

Stochastic Linear Quadratic

  7     1999 

J.Yong & X.Y.Chou

            Stochastic Differential Equations                *   Markov Chain   Brownian Motion  8    ,1995 

R. Korn & S. Trautmann

  9  

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_ij _n n n n V e R R R R R R w w w        1 1 1 1 ) 1 ,...., 1 ( ) ,...., ( ) ,...., ( ) ,...., ( 

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RP

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

(6)

 

  

 

Engle & Ferstenberg , 2007



 

Garleanu & Pedersen, 2009

             Transaction Costs         10   (2.4)  (2.5) (2.6)       (2.7)    (2.8)      :     t :  t     Xt :     t     ft :    t     :     G :     pt :   t .                     Artificial Intelligence                                

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                                 –                   1970                Michigan  University of        Johon Holland

                                                 Optimization Problem                           11              1993      Franklin    Risto Karijalainen                   1998    Herbert Dawid   Michael Kope            Sylvie Geisendorf  2000                 Alfons Balmann   Katrin Happe    2003   Pmar Keskinocak  Feryal Erhun    2012    12   146    M. Garkaz    2011    

S.Sefiane & M. Benbouziane

    2012   

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1.2                                             13       Start                    Fitness Function   .         New Population                      Selection   Parents Chromosomes     (2.9)   fi       i    n             r   ] 0 ، 1 [    r<p1                   : r<pi < pi-1       Crossover    Offspring          Mutation                           Replacement                

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   Test          Stopping Creteria                                      :                                 R+



   wi   

Monthly closing prices

                 31 / 01 / 2010   31 / 12 / 2010   w1 :   SONELGAZ/14



w2 :   Air Algérie  w3 :   Alg Telecom  w4 :   EGH EL AURASSI  w5 :    SAIDAL 1                      

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RP

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                      2   Fitness function                                      (2.10)                  3   Population  The                    50     50      4          .   5     Stopping Creteria                                 100                            Current portfolio 

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                 Inputs    R+     Arithmetic Crossover     13    4       Chromosome   

Objective function value

   Variance of Portfolio  Mean Return of Portfolio      Computing time 1 0,90612% 2,984% 0,3610% 3,5840 2 0,146695% 3,238% 0,4750% 3,2580 3 0,153187% 3,734% 0,5720% 3,1950 5 0,157452% 4,522% 0,7120% 2,7560 11 0,176732% 4,934% 0,872 % 2,5480   R+  5    W5 W4 W3 W2 W1 0,1699% 0,1182% 0,1788% 0,4102% 0,1229%    R+            GA     fitness function                Maximization       0 10     4  5                         W1 = 12,29% :   SONELGAZ/14    W2 = 41,02% :   Air-Algérie      W3 = 17,88% :   Alg-Telecom     W4 = 11,82% :    EGH EL AURASSI    W5 = 16,99% :  SAIDAL    4,934%  0,872 %   

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    Markowitz                                         

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      1        01 / 2010 -12 / 2010       http://www.sgbv.dz      2    Portfolio weights           Excel   R+    01   2010   SAIDAL EGH EL AURASSI Alg Telecom Air Algérie SONELGAZ/14 0,00067 0,0224 0,00016 0,00025 -0,00197  Mean 2,706 0,00068 0,000315 5,2 1,1454  Variance   http://www.sgbv.dz     02                    Var-Cov Matrix SAIDAL EGH EL AURASSI Alg Telecom Air Algérie SONELGAZ/14 1,146 1,036 -2,145 8,983 1,1454 SONELGAZ/14 1,146 1,036 -3,938 5,2 8,982 Air Alegrie -1,0489 0,00016 0,000315 -3,94 -2,145 Alg Telecom -1,852 0,00068 0,00016 1,097 0,00068 EGH EL AURASSI 2,7062 -1,852 -1,0489 -2,51 1,1464 SAIDAL

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      http://www.sgbv.dz     03        http://www.sgbv.dz            1 .      »    «      2008    

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12 .                         21  2012      304 -315 .    .       (Stochastic Process)   .       

13. Slimane Sefiane,Mohamed Benbouziane, “Portfolio Selection Using Genetic Algorithm”,Journal of Applied Finance & Banking, 2012, vol.2,

no.4.

14. Luca Scrucca, "GA: A Package for Genetic Algorithms in R", Journal of Statistical Software, 2013 ,Volume 53, Issue 4. http://www.jstatsoft.org/ . Correlation.Matrix SAIDAL EGH EL AURASSI Alg Telecom Air Algérie SONELGAZ/14 0,20591 0,11683 -0,35691 0,36805 1 SONELGAZ/14 -0,21122 0,58071 -0,00308 1 0,36805 Air Alegrie -0,00359 0,34610 1 -0,00308 -0,35691 Alg Telecom -0,04297 1 0,34610 0,58071 0,11683 EGH EL AURASSI 1 -0,04297 -0,00359 -0,21122 0,20591 SAIDAL