Proceedings of 10th Global Business and Social Science Research Conference
23 -24 June 2014, Radisson Blu Hotel, Beijing, China, ISBN: 978-1-922069-55-9
Investment Portfolio Management: A Review from 2009 to 2014
Amitava Ghosh1 and Ambuj Mahanti2
This paper reviews the literature on portfolio management from 2009 to 2014
with a focus on the algorithms used, contribution by various nationalities,
performance attributes used, etc. and brings out the current state of research
in this field. The paper proposes a methodology to conduct a systematic
review of the literature and considers seventy-three peer-reviewed journal
articles for this. Sharpe Ratio is the most common performance measure.
Authors have mostly performed mathematical modeling of the portfolio
1
selection problem and genetic algorithm and fuzzy logic have been used to
address the problem. A combination of empirical, theoretical and modeling
have been used by most the authors. This review sheds light on how the
practical constraints like transaction costs, cardinality constraints, etc. have
been modeled in the literature. The review is done on the basis of some peer
review journals only. Conference papers and book chapters also have not
been considered.
Field of Research: Finance
Keywords: Review, Portfolio Management, Algorithms, Performance Attributes, Investment
1. Introduction
Portfolio selection was originally proposed by Markowitz (1952, 1959). Markowitz formulated the
portfolio selection problem as a tradeoff between mean and variance of a portfolio of assets.
Keeping constant variance and maximizing expected return or keeping return as constant and
minimizing variance led to the efficient frontier of the portfolio from where the investor could
choose his portfolio mix depending upon his risk attitude. This has led to the Modern Portfolio
Theory. An important implication is that an asset should not be chosen only on the basis of its
individual return and risk characteristics but when it is selected along with other assets, its comovement with respect to other assets can lead to same return but can reduce the risk of the
entire portfolio. The mean-variance (MV) model has been modified in the literature in many ways.
One such work is the market model or the single index model which ignores the covariance
between returns of the securities (Sharpe, 1964; Lintner, 1965). The single index model
considers the returns of securities to be dependent only on a market index and the co-variance
between each pair of assets are not needed. This further led to the development of the Capital
Asset Pricing Model (CAPM). Markowitz's single period MV model was later extended to multiple
periods (Hakansson, 1971; Elton & Gruber, 1974; Mossin, 1968; Li & Ng, 2000) . Several studies
have been done on the Modern Portfolio Theory and the associated risk measures. In addition to
variance; Mean Absolute Deviation (Konno et.al., 1993; Zenios & Kang,1993), Gini mean
difference (Bey & Howe, 1984; Shalit & Yitzhaki, 1984), entropy (Philippatos & Wilson, 1972),
lower partial moments (Price et.al.,1982), Value-at-Risk (VaR) (Gaivoronski & Pflug, 2005),
Conditional VaR (CVaR) (Rockafeller & Uryasev, 2002) , Conditional Drawdown-at-Risk (CDaR)
(Chekhlov et.al., 2000) have been considered as risk measures. Several papers have considered
1
2
Amitava Ghosh, Doctoral Student, Indian Institute of Management Calcutta, India
Ambuj Mahanti, Professor, Indian Institute of Management Calcutta, India
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Proceedings of 10th Global Business and Social Science Research Conference
23 -24 June 2014, Radisson Blu Hotel, Beijing, China, ISBN: 978-1-922069-55-9
a combination of two or more risk measures (Alexander et.al., 2006; Bryne & Lee, 2004). A
central problem in portfolio management is evaluating the performance of risky portfolios. Several
performance attributes have been proposed. (Sharpe, 1966) measured the systematic risk and
non-systematic risk of the mutual funds and proposed a ratio to measure the excess return of the
portfolio. (Treynor, 1965) measured the performance of a portfolio as the ratio of the excess
returns to the systematic risk of the portfolio over the evaluation period rather than considering
the total market risk. (Jensen, 1968) proposed the Jensen index or alpha as an absolute measure
of the performance of the portfolio manager. If the manager can forecast the future returns better
and can achieve better diversification to insure against the risk, then his portfolio will earn more
than the normal risk premium at that level of risk. Several other measures have also been used in
performance measurement. In order to solve the MV problem, several attempts have been made
to solve the single objective and multi objective portfolio selection problem which include linear
goal programming models (Sharpe, 1967), genetic algorithms (Xia et.al., 2000; Loraschi et.al.,
1995) and support vector machines (Fan & Palaniswami, 2001), fuzzy modeling (Tanaka et.al.,
2000), particle swarm optimization (Kendall & Su, 2005), stochastic programming (Samuelson,
1969), etc.
All these attempts can be classified into three extensions: (i) developing criteria and models to
capture the investor's preferences, (ii) capturing practical constraints of the market into the
portfolio planning models, (iii) using features of several disciplines to solve the practical portfolio
selection problem.
The objective of this paper is three-fold. The first objective is to present the current state of
research in portfolio management from 2009 to 2014. The second objective is to develop a
framework to perform the literature review of the various papers to find the trend of current
research in the portfolio selection field. The third objective is to identify the potential areas of
concern based on the review of the papers.
This article is organized as follows: The second section discusses the literature reviews in
portfolio selection area. The third section deals with the research methodology. The fourth
section provides a discussion on the results and the fifth section provides the conclusion and
presents the future scope of research.
2. Literature Review
(Webster & Watson, 2002) consider literature review as more than just an analysis of collection of
summaries of research papers. A literature review can be defined as "the use of ideas in the
literature to justify the particular approach to the topic, the selection of methods, and
demonstration that this research contributes something new" (Hart, 1998). An effective literature
review should create a firm foundation of advancements in the field (Webster & Watson, 2002)
and how one piece of research builds another (Shaw, 1995). Very few reviews on various
methodologies for solving the portfolio selection problem are available in the literature. But we
could not find any single paper which reviews the current trend of research in the portfolio domain
considering all the algorithms. This missing link motivated us to carry this study. Table-1 shows a
sample of review papers retrieved through cursory search of Google Scholar.
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Proceedings of 10th Global Business and Social Science Research Conference
23 -24 June 2014, Radisson Blu Hotel, Beijing, China, ISBN: 978-1-922069-55-9
Sl.
No.
1.
Author(s)
Table 1: Review papers in portfolio management
Year
Remarks
Metaxiotis &
Liagkouras
2012
2.
Huang
2009
3.
Inuiguchi &
Ramik
2000
4.
Elton &
Gruber
1997
Reviewed the current state of research in portfolio selection
problems with respect to multi objective evolutionary algorithms
(MOEA).
Reviewed several definitions of risk in for fuzzy portfolio
investment and discussed several credibilistic portfolio selection
models along with mean risk model, mean variance model,
mean semi-variance model, credibility maximization model,
entropy optimization model, game models, etc.
Presented a comparison of stochastic programming and fuzzy
programming models through their application in portfolio
selection problems.
Discussed issued related to modern portfolio theory and outlined
some important topics for future research.
3. Modern Portfolio Theory: Review of the current literature from 2009-2014
(Chiam et. al., 2009) use the compensatory property of evolutionary algorithm (EA) and particle
swarm optimization (PSO) to show its application in computational finance areas which include
real world problems like portfolio optimization. It uses PSO as a local optimizer for fine tuning in
evolutionary search which improved the convergence ability of the evolutionary search. (Huang
and Jane, 2009) integrate the moving average autoregressive exogenous (ARX) prediction model
along with grey systems theory and rough set (RS) theory to create an automated stock market
forecasting method and portfolio selection technique. (Huang, 2009) integrates fuzzy C-means
(FCM) classification theory, variable precision rough set (VPRS), average autoregressive
exogenous (ARX) prediction model and grey systems theory for stock market forecasting and
portfolio selection. (Lin and Ko, 2009) introduce the genetic algorithm (GA) based portfolio valueat-risk (PVaR) forecasting mechanism using the extreme value theory (EVT). The experiments on
the seventy eight companied listed and traded on the Taiwan Stock Exchange show the stability
and robustness of this algorithm with success rates higher than the exponential weighted moving
average (EWMA) and historical simulation (HS) methods both with 95% and 99% confidence
levels. (Soleimani et. al., 2009) present a genetic algorithm (GA) based approach for the
Markowitz MV model taking minimum transaction lots, cardinality constraints and market sector
capitalization as constraints into account. (Xidonas et. al., 2009) develop an expert system (ES)
methodology for equity selection by analyzing the various financial ratios and understanding the
strengths and weakness of firms. A significantly large number of firms across multiple business
sectors can be evaluated parallely. (Chang et. al., 2009) introduce a genetic algorithm (GA) to
solve the portfolio optimization model with different risk measures based upon the MV model by
Markowitz: semi-variance, mean absolute deviation and variance with skewness. (Chen &
Huang, 2009) cluster equity mutual funds on the basis of four evaluation techniques and groups
them on the basis of their performance. The authors use a two stage method of cluster analysis.
It uses Ward's method to compute the distance between clusters in the first stage. It then applies
the non-hierarchical method, k-means to minimize the variance of objects in one cluster and to
maximize variance amongst other clusters. The rate of return and variance are represented as
fuzzy numbers to reflect the uncertainty at the evaluation stage. (Chen & Lin, 2009) developed a
partitioned portfolio insurance (PPI) strategy by partitioning the portfolio into several similar subportfolios and then insuring the sub-portfolios individually. A new relation-based genetic algorithm
is designed to solve this portfolio partitioning problem. (Chen et. al., 2009) propose a portfolio
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Proceedings of 10th Global Business and Social Science Research Conference
23 -24 June 2014, Radisson Blu Hotel, Beijing, China, ISBN: 978-1-922069-55-9
optimization algorithm using genetic network programming with control nodes. This method
makes stock trading strategies considering the information of technical indices and candlestick
charts for efficient trading decision making. (Chen et. al., 2009) distribute the wealth to a set of
investment strategies or security rule pairs. The investment strategy problem is formulated as a
combination optimization problem and a new combination genetic algorithm is proposed to solve
it. (Zhang et. al., 2009) consider a possibilitistic mean-variance utility function and discusses the
portfolio selection problem for bounded assets. It proposes a parametric quadratic programming
model for portfolio selection for 'n' assets and then presents a sequential minimal optimization
(SMO) algorithm to obtain the optimal portfolio. (Branke et. al., 2009) propose an envelope-based
MOEA which is combined with an embedded critical line algorithm to solve the portfolio selection
problems with non-convex constraints. The EA takes care of the non-convex constraints. The
problem is divided into convex constraints which can be solved by the critical line algorithm. The
overall solution is a combination of the solutions to the individual sub-problems. (Zakamouline &
Koekebakker, 2009) consider performance measure as not just a reward to risk ratio; but as a
score attached to each financial asset, which is related to the level of expected utility provided by
the asset. The paper presents two methods of practical estimation of Generalized Sharpe Ratio
(GSR) and shows how GSR can be used for portfolio performance evaluation by removing the
shortcomings of the standard SR. (Diaz et. al., 2009) develop a portfolio selection model to
conduct out-of-sample contingent and pure immunization strategies that allow for different
degrees of risk and expectations about interest rate movements. (Tiryaki & Ahlatcioglu, 2009)
combine fuzzy analytic hierarchy process (AHP) with the portfolio selection problem. The basic
approach in a AHP is to set up a model that incorporates the firm's risk behavior (high, medium or
low risk), the risk class of the investor (high, medium or low), the investor's objectives and
extrinsic and intrinsic factors. (Chang et. al., 2010) evaluate the performance of mutual funds
under the broad framework of multi-attribute decision analysis (MADA) where all criteria is
considered to provide a final ranking to the mutual funds. (Estahinapour & Aghamiri, 2010) focus
mainly on the prediction of future stock price in their study. This paper uses a neuro-fuzzy
inference system adopted on a Takagi-Sugeno-Kang (TSK) type fuzzy rule based system for
stock price prediction. (Fasanghari & Montazer, 2010) describe a new method for the design of a
fuzzy expert system for portfolio recommendation at the Tehran Stock Exchange. It ranks the
stock on the basis of fundamental analysis ratios and qualitative criteria from the exchange. The
qualitative factors used to evaluate stocks in the paper are arrived at by distributing a
questionnaire among experts. (Nanda et. al., 2010) integrate clustering techniques like k-means,
self organizing maps and Fuzzy C-means into portfolio management and builds a hybrid system
for generating efficient portfolios. (Rodder et. al., 2010) describe a model that does not calculate
the classical risk measures like variance and standard deviation. It simply takes the return
distributions of the securities as input and suggests an unbiased portfolio by a rule-based
inference mechanism under maximum entropy and minimum relative entropy. (Wang & Huang,
2010) construct a responsive mutual fund performance evaluation system using fast adaptive
neural network classifier (FANNC) which combines features of back propagation network (BPN),
adaptive resonance theory (ART) and field theory. (Alexander & Baptista, 2010) characterize the
alpha-tracking error variance (TEV) which consists of portfolios that minimize TEV for various
levels of alpha. The paper shows that the portfolios on the alpha-TEV frontier exhibit three fund
separation with funds being the two portfolios on the MV frontier and the benchmark.
(Anangnostopoulos & Mamanis, 2010) formulate the portfolio optimization problem as a triobjective optimization problem to find tradeoffs between risk, return and number of securities in
the portfolio. Restrictions are imposed on the proportion of the investments in assets in order to
avoid small holdings or investments in assets with common characteristics. This mixed-integer
multi-objective optimization is solved using three evolutionary multi-objective techniques. (Chen
et. al., 2010) provide a decision making model for dynamic portfolio optimization and uses the
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Proceedings of 10th Global Business and Social Science Research Conference
23 -24 June 2014, Radisson Blu Hotel, Beijing, China, ISBN: 978-1-922069-55-9
time adapting genetic network programming (TA-GNP) which considers the time related
fluctuation of stock prices. The paper uses technical indices and candlestick chart as judgment
functions for the TA-GNP. (Aluja et. al., 2011) present a framework for portfolio management
based on the use of some fuzzy topological axioms and grouping. It uses a fuzzy algorithm that
reduces the number of elements of the power sets of related sets by connecting them to the sets
that form the topology. (Golmakani & Fazel, 2011) propose a particle swarm optimization (PSO)
approach called CBIPSO to solve the extended Markowitz portfolio selection problem. The
algorithm is a combination of binary PSO and the improved PSO. The search space in binary
PSO is considered as all possible combinations of a two state (0/1) bit string whereas in the
improved PSO, a mutation operator is used to search in isolated regions to prevent particles from
being stuck in local optimums. The algorithm uses four sets of constraints: bounds on holdings,
cardinality, minimum transaction lots and sector capitalization constraints. (Liu, 2011) utilizes
concepts of mean-absolute deviation and Zadeh's extension principle to develop a solution
method for the fuzzy portfolio optimization problem where the forecasted rate of return and risk
are expressed as fuzzy numbers. It then constructs a pair of two-level mathematical programs to
derive the upper bound and lower bound of the returns from the portfolio at a specific confidence
level. The programs are then converted into a pair of ordinary one-level linear programs using
duality theorem and variable transformation techniques. (Adachi & Takemura, 2011) use a
bounded forecasting game formulated by Shafer and Vovk and neural network models to
propose an investment strategy. (Chen et. al., 2011) shows the efficiency of the genetic relation
algorithm with guided mutation to solve large scale portfolio problems. It adapts a genetic
network programming based strategy for stock trading. (Dastkhan et. al., 2011) use a fuzzy
weighted max-min mathematical model in a mean-absolute deviation portfolio selection problem
with real features like minimum transaction lots, fixed and variable transaction costs, cardinality
and bounds on holdings as constraints. To solve this problem, a hybrid genetic algorithm is
proposed. (Pinto et. al., 2011) propose an autoregressive exogenous (ARX) predictor model to
provide the risks and returns of securities in the Brazilian stock market. (Zhao et. al., 2011)
propose a two-quadratic constrained data envelopment analysis (DEA) model for evaluation of
mutual funds and considers risk and return as the two vital factors affecting mutual fund
performance. (Zhu et. al., 2011) employ a PSO algorithm for portfolio selection and optimization.
The model is tested on various unrestricted portfolios with no constraints on short selling and on
restricted portfolios and then compared with a genetic algorithm (GA) to establish the superiority
of the proposed PSO. (Zymlere et. al., 2011) combine robust portfolio optimization and classical
portfolio insurance to hedge against events which are rare and not captured by an uncertainty
set. The model enriches the portfolio with certain products in order to obtain a deterministic lower
bound on the worst case return of the portfolio. (Asgharian, 2011) applies a conditional version of
the optimal orthogonal portfolio (OOP) proposed by Mackinlay and Pastor by allowing for a timevarying risk premium. It captures the latent factors important for pricing a group of assets and
constructs a portfolio representation of the OOP. The paper uses both a cross-sectional and a
time series regression approach to evaluate the estimated OOP's out of sample pricing ability.
(Daskalaki & Skiadopoulos, 2011) study the impact of including commodities in a portfolio with
stocks, bonds and cash as asset classes. The paper finds that only when higher order moments
are taken into account, commodities can offer in-sample diversification benefits in the portfolio.
(Fortin & Hlouskova, 2011) examine the portfolio selection problem from an investor's point of
view and not as a general equilibrium problem. The paper investigates how the maximization of a
certain form of loss-averse (LA) utility relates to the optimization of CVaR. It formulates
assumptions under which LA, MV and CVaR problems are equivalent. (Moon & Yao, 2011)
propose a simple robust mean absolute deviation (MAD) model with reduced computational
complexity and transforms the portfolio optimization problem into a linear programming problem.
The proposed model considers parameter uncertainty by controlling the impact of estimation
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Proceedings of 10th Global Business and Social Science Research Conference
23 -24 June 2014, Radisson Blu Hotel, Beijing, China, ISBN: 978-1-922069-55-9
errors on portfolio strategy performance. The study considers several factors like market
condition, financial elasticity, standard deviation, parameter estimation period to specify
conditions of superiority of the proposed robust optimization method over a nominal optimization
method. (Garcia et. al., 2012) propose a re-sampling method based on time stamping
mechanism, along with risk and return to address the uncertainty in these parameters during the
optimization process. This approach is then tested with four popular MOEA for eight indices
representing different asset classes with considerable reliability. (Huang, 2012) discusses a
portfolio selection model in which Markowitz's MV problem is combined with uncertainty theory to
select portfolios where returns are mainly given by estimations from experts. A method for
calculating expected value, variance and semivariance is proposed which is integrated with GA to
produce an intelligent algorithm. (Liu et. al., 2012) present two types of chance-variance (C-V)
models where returns are characterized by fuzzy random variables with known possibility and
probability distributions. The C-V models are formulated into equivalent stochastic programming
which are solved by using a Monte-Carlo (MC) simulation based PSO algorithm. The MC
simulated the probability distribution functions of the objective and constraints, while the PSO
performs the search for optimal solutions. (Chen et. al., 2012) consider the long term asset class
allocation problem and proposes a belief-rule-based (BRB) system which combines high
dimensional return distributions of assets and portfolios to get the return distribution of a new
portfolio. The BRB system solves non-linear portfolio optimization problem in the presence of
non-linear cash flows and constraints. It then constructs the efficient frontier by using portfolios
generated by BRB inference and then searches along the frontier to get the optimal portfolio.
(Meskarian et. al., 2012) study the penalization scheme for stochastic programming models with
SSD constraints. It applies this penalization scheme to some portfolio problems where the return
functions of the assets are not always linear. (Li et. al., 2012) use credibility theory to
characterize fuzziness and proposes a regret minimization model for fuzzy portfolio selection.
The credibilistic model used in the paper leads to diversified investments unlike other credibilistic
models which lead to concentrated investments. (Ballestero et. al., 2012) consider the case of
environmentally responsible investments and deals with the problem of portfolio selection from
the perspective of socially responsible investments. It classifies the assets as ethical and nonethical depending on the type of business the company is in and the transparency and credibility
rating of the company. The investors are classified into three types based on the strength of their
preference for ethical assets. (Patari et. al., 2012) discuss a portfolio-forming criteria based on
the DEA efficiency scores for forming equity portfolios in which input and output factors are
derived from stock valuation and price momentum indicators. (Nguyen & Lo, 2012) use a robust
ranking model which is a minimax mixed integer programming problem for generating weights to
maximize an objective function for the worst realization of the ranking. Constraints are generated
using a network flow model. Ranking stocks itself gives a discrete uncertainty set. The authors
then apply this method to portfolio optimization. (Zhang et. al., 2012) present the possibilistic
mean-semivariance-entropy model for multi-period fuzzy portfolio selection. The authors consider
four criteria: return, risk, transaction cost and diversification degree of the portfolio. The paper
then proposes a hybrid intelligent algorithm which combines genetic algorithm (GA) and
simulated annealing (SA) based techniques to solve the problem. (Tsaur, 2012) include a
behavioral analysis of the investor's risk attitude to formulate a fuzzy portfolio model to solve the
portfolio selection problem when return of assets are uncertain. (Fernandes et. al., 2012) propose
the use of a portfolio optimization methodology which combines features of both Black Litterman
(BL) methodology and re-sampling methodologies. It then generates a robust and diversified
optimal allocation which are desirable to long term investors. (Hjalmarsson & Manchev, 2012)
show how the weights in a MV optimization problem can be directly estimated as functions of the
underlying stock characteristics, such as volume and momentum. It also studies the long-short
portfolio choice in international MSCI indices for eighteen developed markets using three different
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Proceedings of 10th Global Business and Social Science Research Conference
23 -24 June 2014, Radisson Blu Hotel, Beijing, China, ISBN: 978-1-922069-55-9
characteristics: book-to-market, dividend-price ratio and momentum. The paper brings forth the
robust performance achieved by parameterizing portfolio weights directly as functions of
underlying characteristics, unlike methods where the returns are modeled and estimated in an
intermediate step. (Lebeault & Kharoubi, 2012) use an empirical copula analysis of the nonGaussian dependence structure on the equity market to study the diversification effect in portfolio
optimization. It studies the impact of portfolio size on various risk measures over the period
including the 2008 market crash. (Kourtis et. al., 2012) focus on the estimation of the inverse
covariance matrix in the context of optimal portfolio choice using a 'shrinkage approach' to the
maximum likelihood estimator of the inverse covariance matrix in order to replace portfolio risk
and increase risk-adjusted returns. (Chen & Kwon, 2012) propose a robust selection problem for
tracking a market index. The model is a 0-1 integer problem which avoids the computational
difficulties of using quadratic tracking error by maximizing pair wise similarities between assets of
the tracking portfolio and its target index. (Aranha et. al., 2012) extend the memetic tree-based
genetic algorithm with the concept of terrain-based memetic algorithms for solving the portfolio
optimization problem. (Huang & Qiao, 2012) introduce risk index as an alternate risk measure
and employs uncertainty theory to solve a multi-period portfolio selection problem where the
expected and standard deviation values of the uncertain security returns are given by expert's
evaluations. (Yunusoglu & Selim, 2013) discuss the design of a fuzzy rule based expert system
(ES) for portfolio managers. The ES considers the investor's risk profile and specific preferences
by changing some parameters only. The ES outperforms all risk profiles when compared with a
particular benchmark. (Tamiz et. al., 2013) incorporate macroeconomic, regional and country
based factors in addition to factors specific to mutual funds into three variants of goal
programming models for selection a portfolio of mutual funds across ten countries. (Cumning et.
al., 2013) propose a modified appraisal value-based private equity (PE) benchmark. It shows that
this method has statistically lower levels of risk than when listed PE indices are used as proxy.
The listed PE indices are considered insufficient for portfolio optimization as they do not include
the entire PE universe and their expected valuations often do not match the actually PE
valuation, especially during crisis. (Miguel et. al., 2013) propose a new calibration criteria for
shrinkage estimators of moments of asset returns and for shrinkage portfolios. It then studies a
multivariate non-parametric approach to compute the optimal shrinkage intensity for independent
and identically distributed returns. It also carried out a comprehensive empirical investigation of
shrinkage estimators for portfolio selection on six empirical datasets. (Traglia & Gerlach, 2013)
use a bivariate extreme value theory (EVT) model to study the extreme dependence of individual
stocks and portfolios with the market index. It shows that lower tail dependence contains
important information for risk averse investors and is relatively more stable over time than other
risk measures like variance, semi-variance, skewness, beta, etc. (Behr et. al., 2013) devise a
constrained minimum variance portfolio strategy to achieve portfolios with statistically significant
higher Sharpe Ratio (SR). This strategy is built on the shrinkage estimation theory and imposes a
data dependent structure on the empirical variance-covariance matrix estimate by trading off the
reduction of sampling error and loss of sample information. This strategy achieves sizeable
reductions in out-of-sample variances w.r.t. the other minimum variance portfolio strategies like
constrained short selling, factor model, etc. (Li & Xu, 2013) propose a constrained multi-objective
portfolio selection model with fuzzy random returns for investors. A compromise approach-based
genetic algorithm is designed. The model has the capability to introduce judgment and expert
opinion in accordance with the attitudes of the investors. (Gupta et. al., 2013) propose a multicriteria credibilistic portfolio selection fuzzy model integrated with a real-coded genetic algorithm
(RCGA) which maximizes credibility such that the short-term return, long-term return and liquidity
of the portfolio are greater than some given threshold levels. Several constraints, namely, capital
budget constraint, cardinality constraint and diversification constraints are applied for investments
in individual assets. (Lim et. al., 2013) develop a MV framework of portfolio selection based on
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Proceedings of 10th Global Business and Social Science Research Conference
23 -24 June 2014, Radisson Blu Hotel, Beijing, China, ISBN: 978-1-922069-55-9
DEA cross-efficiency evaluation. The efficiency score and variance of the cross efficiencies of the
decision making units (DMU) are used to represent the DMU's return and risk characteristics.
Markowitz's MV formulation is then used to determine the inclusion of the DMU in a portfolio.
(Takano & Gotoh, 2014) develop an efficient solution algorithm for kernel-based non-linear
control policy based on dimensionality reduction technique. It then uses the technique for
attaining high out-of-sample investment performance. (Utz et. al., 2014) discusses how inverse
portfolio optimization can be used in a tri-criterion model. The third criteria causes the traditional
non-dominated frontier to become a surface. Another empirical contribution is the application of
the tri-criterion framework to socially responsible mutual funds. (Smimou, 2014) examines the
impact of political instability on the composition of international portfolio under the discrete time
version of Markowitz's MV portfolio selection problem. It studies to what extent can international
diversification outperform domestic stock portfolios in presence of instability risk. (Levy & Levy,
2014) compare the performance of main optimization methods in literature when parameter
estimation errors are accounted for. It then proposes two novel methods: variance-based
constrained optimization (VBC) and global variance-based constrained optimization (GVBC)
which take consider that estimation errors are larger for stocks with larger sample variance.
(Castellano & Cerqueti, 2014) propose an extension of the MV Markowitz model by considering
the presence of infrequently traded stocks and their effect on long-run optimal portfolio and shortterm trading strategies. (Bernand & Vanduffel, 2014) derive optimal portfolio with state dependent
constraints by considering the dependence between the portfolio and the benchmark. The paper
also derives tighter bounds on the Sharpe Ratio (SR) which is useful for fraud detection. (Fu et.
al., 2014) study optimal asset allocation in a regime switching market comprising of an option, an
underlying stock and a risk-free bond. The paper considers power and logarithmic utility functions
and provides a solution to the portfolio optimization problem in incomplete markets.
3. Research Methodology
In this section, we present a methodological framework for analyzing the issues and solutions
regarding to portfolio selection. Initially a significant amount of literature was collected by
searching through general databases such as 'Google Scholar' and 'EBSCO' using a combination
of keywords like 'portfolio planning', 'financial portfolio selection', 'heuristic for portfolio
optimization', etc from 2009 to 2014. It was assumed that most authors will definitely include the
keyword 'portfolio' in the related articles. More than fifty-eight thousand results were available in
Google Scholar which needed to be filtered. It included literature reviews, articles on project
portfolio optimization, articles related to project portfolio management, book reviews, conference
papers, articles in journals, etc. A cursory glance at few related abstracts revealed a large
amount of repetition in the research materials when working papers and conference papers were
later converted to journal papers, PhD and MS theses or reports led to publications in
conferences and journals. So, in the first stage of the study, we had to decide which articles to
consider and establish boundaries. To filter out irrelevant articles from the search results, it was
decided to establish boundaries. This was done by considering to:
(i) include only papers published in peer-reviewed journals.
(ii) Papers were collected from five well-known journals to study the current trend of research in
this field.
(iii) The timeline was set from 2009 to 2014. Only papers which had theoretical, mathematical or
empirical modeling were considered. Review papers were ignored.
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Sl. No.
1.
2.
3.
4.
5.
Table 2: Contribution of papers by journals for this review.
Journal Title
Papers
Expert Systems with Applications
European Journal of Operational Research
Journal of Banking and Finance
Computers & Operations Research
Information Sciences
31
19
5
4
14
Percentage
42.47
26.03
6.85
5.48
19.18
Each paper was then selectively screened and finally seventy-three papers were considered for
review. As the purpose of the study is to understand the current state of research and identify
potential areas of concern in the portfolio management field, we try to find which author, country,
year of publication, journal has the maximum contribution in this field and what are the
performance measures and algorithms used to address this portfolio selection problem. We start
by presenting the contribution of the selected journals to the field of portfolio management. This is
listed in table-2. Next, we attempt to find out that as first authors only, which authors have
contributed most to the recent literature. This is summarized in table-3.
Sl. No.
1.
2.
3.
Table 3: Number of papers as first author.
First Author
Number of papers as first
author
Yan Chen
3
Xiaoxia Huang
2
Kuang Yu Huang
2
Rest authors have contributed only once as first author. However, they may have contributed as
second co-authors or above in other research papers which have been considered here, but that
has not been analyzed. We now try to consider the number of authors in each of the publication
and cluster them. This is shown in table-4.
Table 4: Number of authors in each publication.
Number of
Number of
Percentage
authors
publications
1
6
8.22
2
28
38.36
3
27
36.99
4
7
9.59
5
3
4.11
6
1
1.37
7
1
1.37
An important issue is the year of publication. Table-5 shows the number of publications in
respective years.
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Table 5: Number of publications in each year.
Year of
Number of papers
Percentage
Publication
2009
16
21.92%
2010
9
12.33%
2011
14
19.18%
2012
18
24.66%
2013
8
10.96%
2014
8
10.96%
Another important issue is the nationality of the institutions that contributed to the literature. In
order to obtain the relevant results, we kept a track of the nationality of the first authors. The coauthors (other than the first author) may have different nationality that the first author. This has
not been considered during the calculation for the contribution of papers by various nations. The
results are presented in table-6. Across these five journals, China and Taiwan dominate the
contribution to the literature of 15.07% and 13.7% respectively.
Table 6: Contribution of various countries in the current research.
Country of First
Number of
Percentage
Author
papers
Austria
1
1.37%
Brazil
3
4.11%
Canada
5
6.85%
China
11
15.07%
Finland
1
1.37%
France
1
1.37%
Germany
3
4.11%
Greece
3
4.11%
India
2
2.74%
Iran
5
6.85%
Israel
1
1.37%
Italy
1
1.37%
Japan
4
5.48%
Korea
2
2.74%
Kuwait
1
1.37%
Norway
2
2.74%
Singapore
1
1.37%
Spain
4
5.48%
Sweden
1
1.37%
Taiwan
10
13.70%
Turkey
2
2.74%
UK
7
9.59%
US
2
2.74%
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Next, we study the use of performance attributes in the review papers. The table-7 shows the
popular performance attributes and their frequency of occurrence in the publications. The
analysis of table-7 clearly shows that Sharpe Ratio is the most commonly used performance
attribute in portfolio management.
Table 7: Performance measures and their occurrence in various papers
Performance Measure
Number of
Percentage
papers
Alpha
3
4.48%
Beta
1
1.49%
Coefficient of Variation
1
1.49%
CVaR
2
2.99%
Entropy
1
1.49%
Farinelli-Tibiletti Herfindahl
1
1.49%
Index
Financial Ratios
1
1.49%
Hypervolume
1
1.49%
Information Ratio
3
4.48%
Intraclass Inertia
1
1.49%
M-2
2
2.99%
MAPE
1
1.49%
Market Ratio
1
1.49%
Mean Runtime
3
4.48%
Moments
1
1.49%
Omega
1
1.49%
Portfolio Turnover
3
4.48%
Profitability
3
4.48%
Return on Investment
1
1.49%
Sharpe Ratio
25
37.31%
Skewness
1
1.49%
Sortino Ratio
1
1.49%
Spearman's Rank
1
1.49%
Correlation Coefficient
Tracking Error
1
1.49%
Training Error
1
1.49%
Treynor Ratio
3
4.48%
Turnover Rate
1
1.49%
VaR
2
2.99%
Next, we can check how many performance measures have been used together in a single
publication. The table-8 shows this.
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Table 8: Number of performance measures in each paper.
Number of performance
Number of
Percentage
measures
publications
0
24
33.80
1
33
46.48
2
9
12.68
3
2
2.82
4
2
2.82
6
1
1.41
Clearly, most papers use one performance measure and generally it is Sharpe Ratio (Wang &
Huang, 2011; Zhu et.al., 2011; Smimou, 2014; Levy & Levy, 2014; Castellano & Cerqueti, 2014;
Bernard & Vanduffel, 2014; Lim et.al., 2013; Asgharian, 2011; Zakamouline & Koekebakkar,
2009; Alexander & Baptista, 2010; Hjalmarsson & Manchev, 2012; Cumming et.al., 2013;
DeMiguel et.al., 2013; Behr et.al., 2013; Aranha et.al., 2012; Patari et.al. 2012; Barros et.al.,
2012; Diaz et.al., 2009; Daskalaki & Skiadoupoulos, 2011; Kourtis et.al., 2012; Zymler et.al.,
2011; Fortim & Hlouskova, 2011; Yunusoglu & Selim, 2013; Zhao et.al., 2011). In spite of the
drawbacks of the Sharpe Ratio, its frequent usage may be because of the ease of calculation.
Another important area of concern is the study of the various algorithms used in the field of
portfolio management. The table-9 shows the area of focus of the algorithms used to address the
portfolio selection problem.
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Table 9: Various algorithms used in the field of portfolio management.
Algorithm
Number of papers
Analytic Hierarchy Process
1
Adaptive Resonance Theory
1
Autoregressive Exogenous
3
Prediction
Back propagation Neural
1
Network
Belief Rule based System
1
Cluster Analysis
1
Constrained Optimization
1
models
Data Envelopment Analysis
3
Evolutionary Algorithm
2
Entropy
2
Expert Systems methodology
3
Extreme Value Theory
1
Field Theory
1
Fuzzy Logic
13
Genetic Algorithm variants
11
Game Theory
1
Genetic Network Programming
3
Goal Programming
2
Grey System
2
K-means Clustering
1
Mathematical Modeling
17
Memetic Algorithm
1
Mixed Integer Programming
1
Model
Multiobjective Evolutionary
2
Algorithm
Multi Attribute Decision
1
Analysis
Neural Network
2
Possibilistic Theory
1
Particle Swarm Optimization
4
Quadratic Programming Model
3
Resampling Methodology
1
Robust Portfolio Optimization
2
Rough Set
2
Self Organizing Maps
1
Simulated Annealing
1
Stochastic Programming
1
Models
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A final issue that we will address is the classification of the papers according to the
methodological approach followed by the authors. For carrying this, we went through the titles
and abstracts and when that was inconclusive, we read through the main body of the paper.
Reviewing the papers, we find that these are the main methods followed in the papers which are
listed in table-10.
Table 10: Methodology followed by the authors
Methodological
Description
Number of
Category
papers
Empirical Experiment Papers focusing on qualitative
4
or quantitative analysis of
data.
Theoretical
Papers
proposing
a
2
framework without any testing
with real data.
Model Design
Papers developing a new
3
algorithm or model to explain
the problem.
Combined
Papers using a combination
64
of either of the above.
Percentage
5.48
2.74
4.11
87.67
We can see that most papers use a combination of two or more methods which is pretty natural
considering that the authors would like to validate their proposed framework or model with stock
market data.
5. Conclusion
The purpose of this article is to provide an insight into the current state of research in the area of
portfolio management. In order to understand this, we have analyzed seventy-three shortlisted
papers from five major journals from 2009-2014 by classifying them on various headers. Our
analysis revealed that only 8.22 percent of the papers are single authored (Huang, 2009; Liu,
2011; Huang, 2012; Tsaur, 2012; Smimou, 2014; Asgharian, 2011). Rest all papers are coauthored. We have analyzed the contribution of the various nationalities in the research in
portfolio management. Sharpe Ratio is the most prominently used performance measure with
37.31 percent of the papers using it. In spite of the shortcomings of Sharpe Ratio, this may be
because of the ease of calculation of this ratio compared to other performance attributes. Most
papers use a single performance measure which is the Sharpe Ratio. On analyzing the broader
area of the algorithms used to address the problem of problem management, it was found that
fuzzy logic, genetic algorithm and its variants like genetic network programming, combined
genetic algorithm, etc. have been used in many papers in addition to mathematical modeling. A
final issue concerns the methodological choice of the authors in their papers. About 87.67
percent authors use a combination of any two of empirical-experiment, theoretical and model
designing approach.
6. Future Research
The decision making process in portfolio optimization is a very complex problem and should
consider practical constraints like cardinality constraints, transaction costs, sector capitalization
constraints. Research can be done to check how the models have evolved incorporating these
constraints. Also, we have not checked the number of objective functions and risk measures
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used by the authors in their papers. This can shed light on the multi-objective algorithms being
designed to solve complex problems like the portfolio optimization problem. We find maximum
use of Sharpe Ratio as a performance attribute in spite of its limitations. Better performance
indicators should be used to assess the performance of the models. We have tried to identify
some of the possible directions of future research in the portfolio management field. It is evident
that this field presents intense challenges and significant research opportunities for interested
academicians and practitioners.
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