Upload
others
View
3
Download
0
Embed Size (px)
Citation preview
[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
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
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.
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
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
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
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
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
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
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
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 %
مجلة رؤى اقتصاديةجامعة الشهيد حمه خلضر، الوادي، اجلزائر،132 2015، جوان 8دد الع
DOI: 10.12816/0011892
Markowitz
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
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