Prospect theory–based portfolio optimization: an empirical study and analysis using intelligent algorithms

Abstract

The behaviourally based portfolio selection problem with investor's loss aversion and risk aversion biases in portfolio choice under uncertainty is studied. The main results of this work are developed heuristic approaches for the prospect theory model proposed by Kahneman and Tversky in 1979 as well as an empirical comparative analysis of this model and the index tracking model. The crucial assumption is that behavioural features of the prospect theory model provide better downside protection than traditional approaches to the portfolio selection problem.In this research the large scale computational results for the prospect theory model have been obtained for real financial market data with up to 225 assets. Previously, as far as we aware, only small laboratory tests (2-3 artificial assets) have been presented in the literature. In order to investigate empirically the performance of the behaviourally based model, a differential evolution algorithm and a genetic algorithm which are capable to deal with large universe of assets have been developed. The specific breeding and mutation as well as normalisation have been implemented in the algorithms. A tabulated comparative analysis of the algorithms' parameter choice is presented.The prospect theory model with the reference point being the index is compared to the index tracking model. A cardinality constraint has been implemented to the basic index tracking and the prospect theory models. The portfolio diversification benefit has been found. The aggressive behaviour in terms of returns of the prospect theory model with the reference point being the index leads to better performance of this model in the bullish market. However, it performed worse in a bearish market compared to the index tracking model. The tabulated comparative analysis of the performance of two studied models is provided in this paper for in-sample and out-of-sample tests. The performance of the studied models have been tested out-of-sample in different conditions using simulation of the distribution of a growing market and simulation of the t-distribution with fat tails which characterises the dynamics of a decreasing or crisis market.

Aversión al riesgo al tomar decisiones económicas, efecto certeza y estimación de probabilidades

“…La teoría de las perspectivas ha sido bien estudiada y revisada (Bendickson et al, 2017), y ha sido reconocida como la teoría descriptiva de la toma de decisiones ante el riesgo más relevante en la actualidad (Barberis, 2013;Starmer, 2000;Wakker, 2010), y a la que se le ha encontrado aplicación en muy variados ámbitos de toma de decisiones (Holmes et al, 2011), como en el análisis de las decisiones en los mercados inmobiliarios (Buisson, 2016), las apuestas (Bouchouicha y Vieiden, 2017), el sector de los seguros (Schmidt, 2016), la rentabilidad por dividendos de las acciones (Barberis et al, 2016), la toma de decisiones relativas al hecho de emigrar o permanecer viviendo en el mismo lugar (Morrison y Clark, 2016;Clark y Lisowski, 2017), decisiones acerca de si apostar o no en diferentes periodos, en un contexto dinámico (Ebert y Strack, 2015), decisiones acerca de qué cantidad de stock mantener de manera óptima, haciendo referencia al conocido "problema del vendedor de periódicos" (Long y Nasiry, 2015), los efectos de las leyes de bancarrota sobre las aspiraciones empresariales (Estrin et al, 2017), la cobertura de los seguros agrarios (Babcock, 2015), cuestiones relativas a la volatilidad de las inversiones y la baja rentabilidad (Bhootra y Hur, 2015), decisiones acerca de llevar a cabo acciones de carácter militar (Niv-Solomon, 2016), las relaciones internacionales entre los países (Feng y He, 2017;Stein, 2017), la asunción de riesgos por parte de los políticos (Linde y Vis, 2017), decisiones que se toman en el marco del deporte, en concreto en el fútbol americano (Bendickson et al, 2017), la predicción de resultados deportivos (Pérez-Martínez y Rodríguez-Fernández, 2022), la optimización de carteras (Grishina et al, 2017), entre otros.…”

Portfolio optimization model with uncertain returns based on prospect theory

“…Behavioral portfolio theory emphasizes the role of behavioral preferences in portfolio selection and investor investment [44]. Grishina et al [45] established the model of prospect theory-based portfolio optimization and designed the corresponding differential evolution algorithm and genetic algorithm. Gong et al [46] studied the portfolio selection problem under cumulative prospect theory and gave a portfolio optimization model.…”

“…In recent years, many scholars have applied prospect theory to the problem of portfolio selection [12] and have obtained fruitful research results. In fact, the S-shaped value function in prospect theory is not differentiable at the reference point, and the reference point is an inflection point; thus, the portfolio optimization model containing the S-shaped value function is nonconcave and nonsmooth, which is bound to bring great difficulties to its numerical solution [13][14][15][16]. However, the existing literature rarely mentions it.…”

Efficiency Evaluation and Selection Strategies for Green Portfolios under Different Risk Appetites

“…Because some of the parameter settings of the probabilityweighting function can lead to certain consequences might be found which would not obtain were only positive decision weights allowed, or conversely 'general' propositions might remain unverifiable. Grishina et al [28] introduced stochastic optimization algorithms to the portfolio optimization process, but ignored the prerequisite assumption of distortion of weights.…”