PORTFOLIO OPTIMIZATION USING NATURE INSPIRED COMPUTING TECHNIQUES: A REVIEW

A portfolio of is a collection of different types of stocks. This diversification is necessary to reduce investment risk. This paper presents a state of art review of various nature inspired techniques used for portfolio optimization. There are various nature inspired techniques like Genetic Algorithm etc., which are successfully used in many areas of science, engineering and management. This paper looks for applications of these for portfolio optimization. This also presents the gaps, which are present in this research area, and can be surveyed further

A fundamental principle of investments is diversification, where investors diversify their investments into different types of assets. The different stocks can be clubbed in one portfolio. Portfolio diversification minimizes investors' exposure to risks, and maximizes returns on portfolios. Since it is rarely desirable to invest the entire funds of an individual or an institution in a single security, it is essential that every security be viewed in a portfolio context. Thus it seems logical that the expected return of a portfolio should depend on the expected return of each of the security contained in the portfolio. The aggregate characteristics of the constituent securities may or may not be accommodated in a portfolio (Bhalla, 2008).

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The most important investment decision which the owner of a portfolio must make is the portfolio's asset allocation. Asset allocation refers to the percentage invested in various security classes. Designing of a best portfolio that meets the needs of the investors can be modeled as an optimization problem (Fabozzi et al., 2007). In case of portfolio optimization, the optimal weights of the securities have to be found in order to meet the satisfaction of the investor. The satisfaction of the investors lies in maximizing return and minimizing risk. Constructing an optimal risky profile is a high dimensional constrained optimization problem where financial investors look for an optimal combination of their investments among different financial assets with the aim of achieving maximum reward to variability ratio. In these days, various nature inspired optimization techniques are being applied in this area (Anagnostopoulas and Mamanis, 2011).
Optimization is a term used to refer to a branch of computational science concerned with finding the "best" solution to a problem. Here, "best" refers to an acceptable (or satisfactory) solution, which may be absolute best over a set of candidate solutions. Optimization algorithms are search methods, where the goal is to find a solution to an optimization problem, such that a given quantity is optimized, possibly subject to a set of constraints. Optimization provides an elegant blend of theory and applications. The theory uses elements beginning with elementary calculus and basic linear algebra and continues with functional and convex analysis. The applications of optimization involve science, many areas in engineering, economics, and industry (Goldberg, 1997).
An optimization algorithm searches for an optimum solution by iteratively transforming a current candidate solution into a new, hopefully better solution. An optimization problem can be single or multi-objective depending upon the number of objectives to be fulfilled. Further, optimization methods can be classified as deterministic or stochastic. Stochastic method make use of random values and probability theory, whereas deterministic do not. The nature inspired optimization methods belong to the category of stochastic methods. The nature inspired optimization algorithms are optimization algorithms which are inspired from natural processes (Engelbrecht, 2005).

Application of various nature inspired techniques for portfolio optimization:-
Byrne and Lee (1994) have used modern portfolio theory (MPI) as a more rational approach in the construction of a real estate portfolio. This is a process which can be achieved using powerful facilities found in spreadsheets. The use of relatively sophisticated analytical methods such as Solver is too easy to use on the problem. Leinweber and Arnott (1995) have used Genetic Algorithm for predicting the forecasting performance of financial models. Many studies in finance (Colin, 1996; Nelly et al., 1997; Allen and Karjalainen, 1999) use GA particularly in developing trading strategy patterns. Ostermark (2001) has applied Genetic Hybrid Algorithm (GHA) for complex nonlinear programming problems. The algorithm combines features from parallel programming, classical non linear optimization and techniques of numerical calculus. The test results add significant evidence in solving complicated optimization problems successfully. Kendall and Su (2005) have applied Particle Swarm Optimization for the construction of optimal risky portfolios. A particle swarm solver is developed and various restricted and unrestricted risky investment portfolios are tested. The particle swarm solver has shown high computational efficiency in constructing optimal risky portfolios of less than fifteen assets. Marinakis et al. (2009) have proposed ant colony optimization and the particle swarm optimization algorithm to solve the feature subset selection problem. The proposed algorithm was tested in two financial classification tasks, involving credit risk assessment and audit qualifications. This algorithm was found to provide the best results in terms of accuracy rates.  2010) have used a greedy randomized adaptive search procedure (GRASP) to solve the mixed integer portfolio optimization problem. GRASP is a powerful metaheuristic approach to solve many hard optimization problems. Uryasev et al. (2010) have analyzed that risk aggregation in Internal Capital Adequacy Assessment Process (ICAAP) is based on risk adjusted aggregation approaches. It is possible to obtain optimal portfolios with similar properties by using different values of confidence level α and variances. Gazioglu and Hayfavi (2010) have used stochastic optimization technique to optimize the consumer-investor function subject to a self-financing constraint. Bequest is included in the model. The main contribution of this article is that the assumption of constant-consumption-wealth ratio, which was assumed in the literature, was dropped. The Stochastic optimization model with a self-financing portfolio has been simulated which distinguishes risk neutral investors (Y-low) from high risk averse investors (Y-high), both with and with no bequest. Lin (2012) introduces a PONSGA model by applying the non-dominated sorting genetic algorithm (NSGA-2) on portfolio optimization problems. NSGA is the well known non-linear optimization method. A PONSGA model has introduced for portfolio optimization to get the maximum return at minimum risk under different risk measures such as mean-variance, semi-variance, mean-variance skewness, mean-absolute-deviation and lower-partial moment. The experimental results indicated that the PONSGA is superior to GA in all performances, as it had a lower coefficient of variation, a higher sharp index, sortino index and PPI index and relatively higher return with low risk.
Vazhayil and Balasubramanian (2012) have formulated Hierarchical multi-objective policy optimization for the planning and design of energy strategy framework and applied to the energy sector planning for India's 12 th five year plan for which the objectives of faster growth, better inclusion, energy security and sustainability have been identified. Niu et al. (2012) have proposed a new model using VAR measuring both market and liquidity risk and then employed a new swarm intelligence based method, Bacterial foraging optimization (BFO) to solve this model. Kabundi and Mwamlia (2012) have used genetic algorithm (GA) approach for a South African investor who wants to maximize his return but facing exchange rate risk. The performance of GA is compared with the non-linear models, namely the quadratic mean-variance (QMV) and the quadratic variance minimization.

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Ha (2013) has conducted a numerical experiment to see the performance of two well established optimization methods-steepest ascent and genetic algorithm , in the solution of an optimal risk-allocation problem in primaryinsurance portfolio management. The steepest-ascent method was found to be functionally dependent on the initial starting policy that is chosen. The genetic algorithm produced superior results as compared to steepest ascent method. Stchedroff (2013) have examined the effects of evaluating large numbers of proposed solutions in parallel for use with direct search optimization. This leads to a method that has considerable performance increase. Zheng and Liang (2013) have presented a robust mean-variance portfolio selection model of tracking error with transaction cost that only risky assets exist and expected returns of assets are uncertain and belong to a convex polyhedron. Portfolio optimization can yield substantial benefits in terms of risk reduction. The recent interest in asset allocation methods, including international diversification, has also spurred interest in portfolio optimization. Another factor is the increased use of sophisticated nature inspired computing methods in the investment industry, together with increased computing power. There is an increased emphasis on risk control in the investment management industry. Thus there is a strong requirement of application of a recent nature inspired technique on the portfolio optimization problem.