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[email protected] [email protected] 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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Page 1: CERIST- Centre de recherche sur l'information scientifique ...rist.cerist.dz/IMG/pdf/r_8-8.pdf · 123 2015 ناﻮﺟ ،8 دﺪﻌﻟا ،ﺮﺋاﺰﳉا ،يداﻮﻟا ،ﺮﻀﳋ

[email protected] [email protected]

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..

jelG11

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

Page 2: CERIST- Centre de recherche sur l'information scientifique ...rist.cerist.dz/IMG/pdf/r_8-8.pdf · 123 2015 ناﻮﺟ ،8 دﺪﻌﻟا ،ﺮﺋاﺰﳉا ،يداﻮﻟا ،ﺮﻀﳋ

مجلة رؤى اقتصاديةجامعة الشهيد حمه خلضر، الوادي، اجلزائر،122 2015، جوان 8دد الع

DOI: 10.12816/0011892

Modern Portfolio Theory 1990

1952

1

(Métaheuristic)

2

1

2

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مجلة رؤى اقتصادية الشهيد حمه خلضر، الوادي، اجلزائرجامعة،123 2015، جوان 8دد الع

DOI: 10.12816/0011892

3

Efficient portfolio

4

2010/01/31 - 2010/12/31

1990

Diversification

H. Markowitz,1952.

.

Static Model

Dynamic Model.

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مجلة رؤى اقتصاديةجامعة الشهيد حمه خلضر، الوادي، اجلزائر،124 2015، جوان 8دد الع

DOI: 10.12816/0011892

1

1.1

1952

3

Covariance)

4

2.1Static Model

5

(2.1)….....

1:/

:

ewRRwcs

VwwMin

P

1:/

;:

'

'

'

ewkVww

cs

RwMax

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مجلة رؤى اقتصادية الشهيد حمه خلضر، الوادي، اجلزائرجامعة،125 2015، جوان 8دد الع

DOI: 10.12816/0011892

1

(2.2)

(2.3)

3.1Dynamic Model

Continuous-time

Regime Switching Models6

,1969P.A.SamuelsonN.H.Hakansson ,1971 ,1997S.R.Pliska

Optimal Dynamic Strategies H.Richardson, 1991&D.Duffie

M.Schweizer ,1996 2000,Zhou & Li

Stochastic Linear Quadratic71999J.Yong & X.Y.Chou

Stochastic Differential

Equations

* Markov Chain

Brownian Motion 8

,1995R. Korn & S. Trautmann9

nijij

n

n

n

Ve

RRR

RRRwww

1

1

1

1

)1,....,1(),....,(

),....,(),....,(

PR

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مجلة رؤى اقتصاديةجامعة الشهيد حمه خلضر، الوادي، اجلزائر،126 2015، جوان 8دد الع

DOI: 10.12816/0011892

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

Page 7: CERIST- Centre de recherche sur l'information scientifique ...rist.cerist.dz/IMG/pdf/r_8-8.pdf · 123 2015 ناﻮﺟ ،8 دﺪﻌﻟا ،ﺮﺋاﺰﳉا ،يداﻮﻟا ،ﺮﻀﳋ

مجلة رؤى اقتصادية الشهيد حمه خلضر، الوادي، اجلزائرجامعة،127 2015، جوان 8دد الع

DOI: 10.12816/0011892

1970

MichiganUniversity of Johon Holland

Optimization Problem

11 1993

Franklin Risto Karijalainen

1998 Herbert Dawid Michael Kope

Sylvie Geisendorf2000

Alfons Balmann

Katrin Happe

2003Pmar KeskinocakFeryal Erhun

2012

12146

M. Garkaz 2011S.Sefiane & M. Benbouziane

2012

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مجلة رؤى اقتصاديةجامعة الشهيد حمه خلضر، الوادي، اجلزائر،128 2015، جوان 8دد الع

DOI: 10.12816/0011892

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 CrossoverOffspring

Mutation

Replacement

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مجلة رؤى اقتصادية الشهيد حمه خلضر، الوادي، اجلزائرجامعة،129 2015، جوان 8دد الع

DOI: 10.12816/0011892

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

PR

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مجلة رؤى اقتصاديةجامعة الشهيد حمه خلضر، الوادي، اجلزائر،130 2015، جوان 8دد الع

DOI: 10.12816/0011892

2Fitness function

(2.10)

3PopulationThe

50

50

4

.

5 Stopping Creteria

100

Current portfolio

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مجلة رؤى اقتصادية الشهيد حمه خلضر، الوادي، اجلزائرجامعة،131 2015، جوان 8دد الع

DOI: 10.12816/0011892

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

Maximization010

45

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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مجلة رؤى اقتصاديةجامعة الشهيد حمه خلضر، الوادي، اجلزائر،132 2015، جوان 8دد الع

DOI: 10.12816/0011892

Markowitz

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مجلة رؤى اقتصادية الشهيد حمه خلضر، الوادي، اجلزائرجامعة،133 2015، جوان 8دد الع

DOI: 10.12816/0011892

1

01/2010 -12/2010

http://www.sgbv.dz

2Portfolio weights

Excel R+

012010

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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مجلة رؤى اقتصاديةجامعة الشهيد حمه خلضر، الوادي، اجلزائر،134 2015، جوان 8دد الع

DOI: 10.12816/0011892

http://www.sgbv.dz

03

http://www.sgbv.dz

1.»

«2008

R. J. Kuo, and C. W. Hong" , Integration of Genetic Algorithm and Particle Swarm Optimization for Investment Portfolio Optimization", Applied Mathematics & Information Sciences An International Journal ; Sci. 7, No. 6, PP :2397-2408 .

2. 2 2014 117 -136.

3. 1998

4. » «21989

5. Jean-Luc Prigent, « Portfolio Optimization and Performance Analysis », Financial - Mathematics Series, Chapman & Hall/CRC is an imprint of Taylor & Francis Group, U.S, 2007, PP: 70-78. 6. James D.Hamilton, « Regime-Switching Models», Palgrave dictionary of Economics, USA, 2005. 7. Min Dai , Zuo Quan Xu, Xun Yu Zhou, “Continuous-Time Markowitz’s Model with Transaction Costs”, 2009 . www.math.nus.edu.sg/~matdm/mv-transaction6.pdf (16/10/2012).

8.2011108 -120.

9. Xun Yu Zhou and G.Yin ,”Markowitz’s Mean-Variance Portfolio Selection with Regime Switching : A Continuous-Time Model “ ,March 2006, PP:5-11. 10. Esben Hedegaard, “Robust Dynamic Asset Allocation With Imperfect Predictors”, November ( 2011) , PP:4-6 . web Site: www.people.stern.nyu.edu/ehedegaa/PDFs/RobustDynamicAssetAllocation.pdf (16/10/2012). 11. A.K.Misra, « Portfolio Optimization of Commercial Banks - An Application of Genetic Algorithm », European Journal of Business and Management , 2013, Vol.5, No.6, P 120.

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