Computational analysis of expectile and deviation expectile portfolio optimization models

Abstract

Expectile has recently gained an admiration in the area of portfolio optimization (PO) mainly because of its unique property of being both coherent and elicitable function. Additionally, a PO model minimizing Expectile function as risk measure is a linear program under discrete time setting. With these favorable features, we aim to study and analyze the Expectile and its deviation counterpart, deviation Expectile (DExpectile) based PO models in comparison to much more popular PO models comprising Conditional Value-at-Risk (CVaR) and deviation CVaR (DCVaR). We first conduct sensitivity analysis of Expectile and DExpectile PO models with respect to their two model parameters, risk-return trade-off parameter and tail-risk trade-off parameter. Thereafter, we conduct a computational analysis among Expectile, DExpectile, CVaR, and DCVaR PO models on the basis of several performance indices. Empirical study of this paper is carried out over the sample data of S &P 500 (USA) with a sample period from 06 January 2015 to 07 June 2022. Numerical results show the favorable outcomes of Expectile PO model in comparison to the models DExpectile and DCVaR, whereas it performs better than CVaR model for many likely scenarios of model parameters. On many occasions, the model DExpectile dominates DCVaR in terms of mean return, risk measures, and financial ratios while it able to outperform model CVaR under some special cases of parameters. Therefore, our numerical findings hint that the Expectile based PO models can become potential competitors to CVaR based PO models in practice.