A Comparative Study of Intelligent Techniques for Modern Portfolio
Management
Konstantinos Metaxiotis and Konstantinos Liagkouras
Decision Support Systems Laboratory, Department of Informatics, University of Piraeus,
80, Karaoli & Dimitriou Str., 18534 Piraeus, Greece
Keywords: Portfolio Selection, Optimization Techniques, Evolutionary Algorithms.
Abstract: In this paper we present a wide range of intelligent technologies applied to the solution of the portfolio
selection problem. We also provide a classification of the available intelligent technologies, according to the
methodological framework followed. Finally, we provide a comparative study of the different intelligent
technologies applied for constructing efficient portfolios and we suggest potential paths for future work that
lie at the intersection of the presented techniques.
1 INTRODUCTION
Computer Science not only provided a fast and
reliable way of calculating computationally
demanding financial models but also revolutionized
the financial modeling research field itself by
developing innovative algorithmic approaches for
solving difficult financial problems that in many
cases cannot be solved using exact methods. The
computational approaches dealing with financial
modeling can be clustered into four different groups
depending on the applied methodology.
2 INTELLIGENT TECHNIQUES
FOR OPTIMAL PORTFOLIO
SELECTION
2.1 Evolutionary Algorithms
The first classification concerns the so called
Evolutionary algorithms (EAs). EAs are population
based stochastic optimization heuristics inspired by
Darwin’s Theory of Evolution. An EA searches
through a solution space in parallel by evaluating a
set of possible solutions. Genetic Algorithms (GAs)
which belong to the family of EAs have been proved
very effective for solving constrained portfolio
optimization problems (Shoef and Foster, 1996);
(Chang et al., 2009) that cannot be solved with exact
methods. Genetic and Evolutionary Programming
(EP) and Evolutionary Strategy (ES) belong as well
to EAs.
2.2 Swarm Intelligence
The second classification of algorithmic approaches
for the construction of efficient portfolios concerns
the Swarm Algorithms. Swarm Intelligence (SI) is
inspired from the biological examples provided by
social insects. SI is a decentralized, self-organized
system in which the agents through their collective
behavior find coherent solutions to the arisen
problems. Ant Colony Optimization (ACO) is an
optimization procedure inspired by ants’ ability to
identify optimal paths by depositing pheromone on
the ground.
Another popular SI technique is the Particle
Swarm Optimization (PSO). The particle exchanges
information with the neighboring members, in order
to adjust its trajectory towards the best attained
position. Both ACO and PSO techniques have been
applied to solve the constrained portfolio selection
problem (Deng and Lin, 2010); (Doerner et al.,
2004); (Armananzas and Lozano, 2005);
(Golmakani and Fazel, 2011); (Zhu et al., 2011).
2.3 Local Search Algorithms
The third classification of computational approaches
for the solution of the portfolio selection problem
concerns the Local Search Algorithms techniques.
268
Metaxiotis K. and Liagkouras K..
A Comparative Study of Intelligent Techniques for Modern Portfolio Management.
DOI: 10.5220/0004114102680272
In Proceedings of the 4th International Joint Conference on Computational Intelligence (ECTA-2012), pages 268-272
ISBN: 978-989-8565-33-4
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)
These algorithms try to improve an initial solution
by applying iteration in order to create the
neighborhood of the current solution. Then the best
solution of the neighborhood is selected for the next
iteration. The process continues until a solution
considered optimum is found.
Simulated Annealing (SA) is a well known local
search technique developed to deal with highly
nonlinear problems. SA techniques have been
applied extensively for the solution of the portfolio
selection problem (Chang et al., 2000); (Crama and
Schyns, 2003); (Maringer and Kellerer, 2003);
(Ehrgott et al., 2004); (Armananzas and Lozano,
2005). Hill Climbing and Tabu Search (TS) are as
well known local search techniques applied to the
portfolio optimization problem.
2.4 Multiobjective Evolutionary
Algorithms
Finally the last classification of computational
approaches for the solution of the portfolio selection
problem concerns the Multiobjective Evolutionary
Algorithms (MOEAs). Multiobjective optimization
(MO) is the problem of maximizing / minimizing a
set of conflicting objective functions subject to a set
of constraints. In MO there is not a single solution
that maximizes / minimizes each objective to its
fullest. This happens because the various objective
functions in the problem are usually in conflict with
each other. Therefore, the objective in MO is to find
the Pareto front of efficient solutions that provide a
tradeoff between the various objectives. MOEAs can
be useful in the solution of complex problems for
which no efficient deterministic algorithm exists
(Metaxiotis and Liagkouras, 2012). In finance there
are several NP-hard problems for which the use of a
heuristic is clearly justified (Schlottmann and Seese,
2004). Portfolio Selection belongs to this category of
problems, because of the simultaneous optimization
of several conflicting objectives subject to a set of
constraints imposed to the problem.
3 COMPARATIVE STUDY OF
INTELLIGENT TECHNIQUES
APPLIED FOR EFFICIENT
PORTFOLIO CONSTRUCTION
Below the table displays the most popular intelligent
techniques among the authors in the portfolio
selection research field. According to the table the
most popular artificial intelligence technique among
the authors in the field of portfolio selection is the
MOEAs with 33% of the total publications. EAs
come second with 29%. On the other hand, Local
Search Algorithms (LSAs) techniques are less
popular among the authors in the field as they count
for the 15% of all publications in the field.
Table 1: Artificial intelligence techniques for the solution
of the Portfolio Selection problem.
Multiobjective Evolutionary Algorithms 33%
Evolutionary Algorithms 29%
Local Search Algorithms 15%
Swarm Intelligence 23%
3.1 Theoretical Comparison of
Artificial Intelligence Techniques
Below we compare four well known intelligent
techniques that belong correspondently to the fields
of EAs, SI, LSAs and MOEAs.
Specifically the representatives of the four fields
are the following: GAs, PSO, SA and Non-
dominated Sorting Genetic Algorithms II (NSGA-
II). The four aforementioned techniques are
evaluated with regard to their ability to solve
efficiently portfolio selection problems. The Table
below highlights the main features of the examined
techniques.
Table 2: Comparison of artificial intelligence techniques.
Initial Population
Initial Solution
Evolve
in Genetics
Evolve in social
behavior
Evolve in
thermodynamics
GA PSO
SA
-Selection
-Evolve each
particle
-Evolve each atom
-Crossover
-Current position
-Initial temperature
-Search better
position
-Liquid metals cool
down process
-Mutation
-Velocity of
particle
As the graph above reveals the GAs and PSO
share more in common compared to SA. We notice
that GA has a population of alternative solutions
(chromosomes) while SA has only one individual
(the current solution). Additionally, there are
differences in terminology between the two
intelligent techniques that reflect the different
approaches for finding the optimal solution to the
problem. For instance in GA are used the terms:
chromosomes or individuals, fitness evaluation,
AComparativeStudyofIntelligentTechniquesforModernPortfolioManagement
269
selection, crossover and mutation. On the other hand
in SA the dominant terminology is: temperature,
costs, neighbourhood, and moves.
If we want to find common ground between the
two optimization techniques we would say that SA
can be considered a GA where the population size is
one. Since there is only one solution in the
population (the current solution) there is no
crossover but only mutation.
This is the key difference between GA and SA.
GA can create new solutions by combining existing
solutions (crossover), whereas SA creates a new
solution by modifying the current solution with a
local move. Which intelligent technique is better
able to find optimal solutions depends mainly on the
problem and representation used. Additionally, we
should highlight that both GA and SA techniques
share the assumption that good solutions are more
probable to be found near already known good
solutions rather than randomly selecting from the
whole selection space.
Table 3: Genetic algorithms vs simulated annealing.
Genetic Algorithms Simulated Annealing
chromosomes one individual - current solution
fitness evaluation calculate the energy of the system
Selection neighbourhood
Crossover modify current solution
mutation local move
Finally, it is clear that the performance of a GA
is seriously affected by the relative weights of
mutation and crossover respectively. For instance if
mutation defined to be the principal way for creating
new solutions then the GA tend to follow the way it
function a SA, as the solutions are being at large
independently improved.
Figure 1: Both GA and SA techniques share the
assumption that good solutions are more probable to be
found near already known good solutions.
3.1.1 Comparison of PSO with GAs
PSO and GAs on the other hand share many
similarities. First of all, both techniques start with a
population of random solutions and search for the
optimal solution by updating generations. However,
a striking difference between the two techniques is
that PSO does not have evolution processes such as
mutation and crossover. Instead in PSO the potential
solutions (particle) moves through the search space
by following the current best particles.
Table 4: GA vs PSO.
GA PSO
chromosomes population of solutions - particles
fitness evaluation evaluate fitness of each particle
Selection
update particle’s velocity and position
based on the best objective value found so
far by the particle and the entire population
Crossover
Mutation
Analytically, in PSO the particles are randomly
initialised and freely move through the search space.
During movement each particle updates its own
velocity and position based on the best objective
value found so far by the particle and the entire
population respectively. The updating policy drives
the particle to move towards the region of the higher
objective function. Finally, all particle gather around
the position with the highest objective function.
Figure 2: In PSO the updating policy drives the particles to
move towards the region of the higher objective function.
3.1.2 Comparison of TS with GAs
TS uses a local search procedure to move from a
current solution to a neighbor solution, until a
stopping criterion has been satisfied. The search
process starts with an initial solution and moves
from neighbor to neighbor as long as possible while
improving the objective function value.
Table 5: GA vs TS.
GA
Tabu Search
chromosomes current solution
fitness evaluation best known solution
Selection objective function value
Crossover neighbourhood of current solution
Mutation
Subset of the neighbourhood of current
solution - Allowed by the aspiration.
Tabu list
TS allows hill climbing to overcome local
optima. A key property of tabu search is to pursue
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the search whenever a local optimum is encountered
by allowing non improving moves. Additionally, the
use of memory (tabu list) prevents the cycling back
to previously visited positions.
3.1.3 Comparison of NSGA-II with GAs
NSGA-II is a popular non-domination based genetic
algorithm for MO. The algorithm creates a
population of initial solutions. After the initialization
of the population, the population is sorted based on
non domination into each front. The first front
consisted by the non-dominated set in the current
population. The second front is only dominated by
individuals of the first front, and so on.
Figure 3: NSGA-II, population is sorted based on non
domination into each front.
Each individual in each front is assigned a rank
value based on the front in which it belongs to.
Thus, individuals in the first front are assigned
fitness value of 1, and individuals in the second front
are given a value of 2 and so on.
Additionally a parameter called crowding
distance is calculated for each individual. Crowding
distance measures how close an individual is to its
neighbours. The greater the average crowding
distance the better, as indicates better population
diversity. Parents are selected from the population,
by using binary tournament selection based on the
rank and the crowding distance. The selected
population generates offsprings from crossover and
mutation operators.
Table 6: GA vs NSGA-II.
GA NSGA-II
chromosomes population of solutions
fitness
evaluation
population is sorted based on non domination
into fronts
Selection
crowding distance is calculated for each
individual
Crossover Parents are selected
Mutation
Offsprings generated from crossover and
mutation operators
Population sorted again based on non-
domination
The population including now the initial
population and the offsprings is sorted again based
on non-domination and only the N individuals are
selected. The selection is based as before on rank
and crowding distance on the last front. NSGA-II
technique has been applied extensively for the
solution of the constrained portfolio selection
problem (Deb et al., 2002); (Lin and Wang, 2002);
(Anagnostopoulos and Mamanis, 2009); (Deb et al.,
2011).
4 CONCLUSIONS
In it only since 1990s that artificial intelligence
techniques have been applied to the constrained
portfolio optimization problem. Yet in that short
space of time, they have had remarkable success in
this particular research field. Given the initial
success we can reasonably expect in the future a
growing number of powerful artificial intelligence
techniques applied to the solution of the constrained
portfolio optimization problem.
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