Academic journal article IUP Journal of Applied Economics

Allocation of Stocks in a Portfolio Using Antlion Algorithm: Investor's Perspective

Academic journal article IUP Journal of Applied Economics

Allocation of Stocks in a Portfolio Using Antlion Algorithm: Investor's Perspective

Article excerpt

(ProQuest: ... denotes formulae omitted.)

Introduction

A portfolio consists of clubbing of different stocks together to ensure diversification. The design of a best portfolio that meets the requirements of the investors can be modelled as an optimization problem (Fabozzi et al., 2007). In case of portfolio optimization, the optimal weights of the stocks have to be found in order to meet the satisfaction of the investor, which lies in maximizing return and minimizing risk. Various traditional methods to construct portfolio have been used previously (Markowitz, 1959; Lee and Lerro, 1973; Elton and Gruber, 2001; and Gupta and Aggarwal, 2009). In recent years, various nature inspired optimization techniques are being used to find solution of portfolio optimization problem (Anagnostopoulas and Mamanis, 2011). The nature inspired techniques derive their inspiration from nature and there are various such algorithms in literature, like Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Bacterial Foraging Algorithm (BFO), Ant Colony Optimization (ACO), Firefly Algorithm (FA), Cuckoo Optimization (CO), and Antlion Algorithm (ALO).

Many studies in finance have used GA for predicting the forecasting performance of financial models (Leinweber and Arnott, 1995; and Kabundi and Mwamba, 2012), in developing trading strategy patterns (Colin, 1996; Nelly et al., 1997; and Allen and Karjalainen, 1999). Soleimani et al. (2009) have used GA for portfolio optimization taking different sets of parameters. Kendall and Su (2005) applied PSO for the construction of optimal risky portfolios. A particle swarm solver was developed and various restricted and unrestricted risky investment portfolios were tested. The particle swarm solver showed high computational efficiency in constructing optimal risky portfolios of less than 15 assets. Zhang and Li (2010) used PSO for solving construction time-cost trade-off problem. Zu et al. (2011) focused on solving the portfolio optimization problem with PSO method, where the objective functions and constraints were based on both the Markowitz model and the Sharpe ratio model. PSO has become a popular optimization method as one finds the best optimum as compared to other common optimization algorithms. Niu et al. (2012) proposed a new model using 'variance' measuring both market and liquidity risk and then employed a new swarm intelligence-based method-Bacterial Foraging Optimization (BFO) to solve this model. The recently developed FA, ACO and CO have also been used for portfolio optimization (Haqiqi and Kazemi, 2012; Sawaya, 2012; and Bacanin and Tuba, 2014).

The ALO is a relatively recent nature inspired heuristic algorithm that is computationally less expensive than other techniques (Mirjalili, 2015). ALO has been used for design of optimal portfolio in this study. Several operators were proposed and mathematically modeled for equipping the ALO with high exploration and exploitation. Five main steps of hunting a prey such as the random walk of ants, building traps, entrapment of ants in traps, catching preys, and re-building traps are implemented in this algorithm.

The rest of the paper is organized as follows: it presents the formulation of fitness function for ALO, followed by a brief overview of ALO and its application in the context of portfolio optimization. Subsequently, the results and discussion are presented, and finally, the conclusion is offered.

Formulation of Fitness Function for ALO

The fitness function specifies which quantities are to be optimized. The decision makers prefer portfolios with high returns and low risk. In this problem, it is required to maximize return for a particular level of risk to be tolerated by the investor. The constraint is that total sum of money insured is taken as one unit and all investments are positive. Thus, an optimization problem that constructs efficient portfolios of stocks can be modeled on this basis.

Consider a portfolio with a vector of portfolio returns r, and a covariance matrix K, and the fitness function can be formulated as follows:

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