Scenario Aggregation Method for Portfolio Expectile Optimization

26 Pages Posted: 17 Apr 2016

See all articles by Edgars Jakobsons

Edgars Jakobsons

ETH Zürich - Department of Mathematics

Date Written: April 15, 2016

Abstract

The statistical functional expectile has recently attracted the attention of researchers in the area of risk management, because it is the only risk measure that is both coherent and elicitable. In this article, we consider the portfolio optimization problem with an expectile objective. Portfolio optimization problems corresponding to other risk measures are often solved by formulating a linear program (LP) that is based on a sample of asset returns. We derive three different LP formulations for the portfolio expectile optimization problem, which can be considered as counterparts to the LP formulations for the Condition Value-at-Risk (CVaR) objective in the works of Rockafellar and Uryasev (2000), Ogryczak and Śliwiński (2011) and Espinoza and Moreno (2014). When the LPs are based on a simulated sample of the true (assumed continuous) asset returns distribution, the portfolios obtained from the LPs are only approximately optimal. We conduct a numerical case study estimating the suboptimality of the approximate portfolios depending on the sample size, number of assets, and tail-heaviness of the asset returns distribution. Further, the computation times using the three LP formulations are analyzed, showing that the formulation that is based on a scenario aggregation approach is considerably faster than the two alternatives.

Keywords: Expectile, portfolio optimization, linear programming, scenario aggregation

JEL Classification: C61

Suggested Citation

Jakobsons, Edgars, Scenario Aggregation Method for Portfolio Expectile Optimization (April 15, 2016). Available at SSRN: https://ssrn.com/abstract=2765339 or http://dx.doi.org/10.2139/ssrn.2765339

Edgars Jakobsons (Contact Author)

ETH Zürich - Department of Mathematics ( email )

ETH Zentrum HG-F 42.1
Raemistr. 101
CH-8092 Zurich, 8092
Switzerland

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