
Open access
Author
Date
2016-06Type
- Journal Article
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 Conditional Value-at-Risk (CVaR) objective in the works of Rockafellar and Uryasev [43], Ogryczak and Śliwiński [41] and Espinoza and Moreno [21]. 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. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000120074Publication status
publishedExternal links
Journal / series
Statistics & Risk ModelingVolume
Pages / Article No.
Publisher
De GruyterSubject
Expectile; Linear programming; Portfolio optimization; Scenario aggregationNotes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.More
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