Solving portfolio optimization problem through differential evolution

Zaheer, Hira; Pant, Millie

doi:10.1109/iceeot.2016.7755462

Cited by 10 publications

(5 citation statements)

References 21 publications

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“…Some studies [29]- [33] used particle swarm optimization (PSO) to identify the best portfolio. One study [34] used the artificial bee colony algorithm (ABC) to search for the best portfolio using different indicators, another study [35] used the differential evolution method (DE) and considered Markovitz's mean-variance model to find an efficient solution, another study [36] utilized the multi-objective genetic algorithm and Fuzzy theory to optimize the portfolio, while another [37] utilized the bat algorithm to search for the best portfolio and compared it with a different algorithm.…”

Section: Related Studiesmentioning

confidence: 99%

Using Trend Ratio and GNQTS to Assess Portfolio Performance in the U.S. Stock Market

et al. 2021

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Stock selection is an important issue in the stock market, and when assessing portfolio performance, return and risk are important conditions. The Sharpe ratio is a well-known assessment strategy that simultaneously considers portfolio return and risk. However, as the Sharpe ratio uses the average line to assess portfolio risk, it can easily assess a portfolio with stable uptrend as high risk, thus, this paper uses the trend ratio to address this problem. The trend ratio can assess a stable uptrend portfolio with low risk and identify a portfolio that has a higher daily expected return per unit daily risk. As the solution space in stock solution is huge, it is hard to use brute-force method to exhaust selections within a limited time. Thus, this paper uses the Global-best guided Quantum-inspired Tabu Search algorithm with Not-gate (GNQTS) to effectively optimize a portfolio given limited time. In addition, this paper uses 13 different kinds of sliding windows to train and test data, and identify a suitable period with a high trend ratio. The experimental results show that the proposed method can identify a portfolio with stable uptrend in the U.S. stock market. This paper does not exclude any stocks in the solution space; therefore, our method can comprehensively consider all the possible combinations of a portfolio. Moreover, we find some interesting phenomenon: the best single stock may not be contained in a portfolio and the stock with negative return cannot be excluded in the solution space. In addition, this study compares our portfolio performance with the portfolio guided by the Sharpe ratio; according to the experimental results, a portfolio guided by the trend ratio has more stable uptrend and lower risk than the Sharpe ratio. Thus, our method can outperform other assessment strategies.INDEX TERMS Stock selection, portfolio optimization, metaheuristic algorithm, trend ratio, quantuminspired tabu Search algorithm (QTS), the U.S. Stock Market.

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Section: Related Studiesmentioning

confidence: 99%

Using Trend Ratio and GNQTS to Assess Portfolio Performance in the U.S. Stock Market

et al. 2021

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“…Equation (19) can now be used to relate the drift and volatility to the average value and sample variance of monthly returns from the market data (see table 1 in (Zaheer and Pant 2016)…”

Section: The Decoupled Return Function In Portfolio Optimizationmentioning

confidence: 99%

“…1.5521 1.6268 1.5447 1.0347 0.8814 1.9151 1.0856 0.8129 1.4232 0.7285 Table 2. Sample covariance matrix from the data in (Zaheer and Pant 2016).…”

Section: The Decoupled Return Function In Portfolio Optimizationmentioning

confidence: 99%

“…Equation ( 19) can now be used to relate the drift and volatility to the average value and sample variance of monthly returns from the market data (see table 1 in (Zaheer and Pant 2016)). Taking the expected value and variance of ( 19) yields two formulas for the drift and volatility of the 𝑖 th stock over a single month.…”

Section: The Decoupled Return Function In Portfolio Optimizationmentioning

confidence: 99%

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Kelly's Criterion in Portfolio Optimization: A Decoupled Problem

Peterson¹

2017

Preprint

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Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe over long periods of betting or investing. These ideas are conspicuously absent from portfolio optimization problems in the financial and automation literature. This paper will show how Kelly's Criterion can be incorporated into standard portfolio optimization models. The model developed here combines risk and return into a single objective function by incorporating a risk parameter. This model is then solved for a portfolio of 10 stocks from a major stock exchange using a differential evolution algorithm. Monte Carlo calculations are used to verify the accuracy of the results obtained from differential evolution. The results show that evolutionary algorithms can be successfully applied to solve a portfolio optimization problem where returns are calculated by applying Kelly's Criterion to each of the assets in the portfolio.

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“…Pekar et al, used differential evolution (DE) to solve the portfolio selection problem [14]; where they employed the Omega function and Sortino ratio to measure the portfolio's risk based on the Sharpe Ratio. Presently, DE algorithms have been applied in several portfolio applications: Dow Jones [14], S&P, BOFA, Frank Russell, MSCI [15], and National Stock Exchange [16]. The use of DE combined with other methods has increased the quality of results [15,17].…”

Section: Introductionmentioning

confidence: 99%

SAIPO-TAIPO and Genetic Algorithms for Investment Portfolios

Frausto–Solís

Aldaz

Angel

et al. 2022

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The classic model of Markowitz for designing investment portfolios is an optimization problem with two objectives: maximize returns and minimize risk. Various alternatives and improvements have been proposed by different authors, who have contributed to the theory of portfolio selection. One of the most important contributions is the Sharpe Ratio, which allows comparison of the expected return of portfolios. Another important concept for investors is diversification, measured through the average correlation. In this measure, a high correlation indicates a low level of diversification, while a low correlation represents a high degree of diversification. In this work, three algorithms developed to solve the portfolio problem are presented. These algorithms used the Sharpe Ratio as the main metric to solve the problem of the aforementioned two objectives into only one objective: maximization of the Sharpe Ratio. The first, GENPO, used a Genetic Algorithm (GA). In contrast, the second and third algorithms, SAIPO and TAIPO used Simulated Annealing and Threshold Accepting algorithms, respectively. We tested these algorithms using datasets taken from the Mexican Stock Exchange. The findings were compared with other mathematical models of related works, and obtained the best results with the proposed algorithms.

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Solving portfolio optimization problem through differential evolution

Cited by 10 publications

References 21 publications

Using Trend Ratio and GNQTS to Assess Portfolio Performance in the U.S. Stock Market

Using Trend Ratio and GNQTS to Assess Portfolio Performance in the U.S. Stock Market

Kelly's Criterion in Portfolio Optimization: A Decoupled Problem

SAIPO-TAIPO and Genetic Algorithms for Investment Portfolios

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