# Comparative issues between linear and non-linear risk measures for non-convex portfolio optimization: evidence from the S&P 500

*Panos Xidonas* and
*George Mavrotas*

*Quantitative Finance*, 2014, vol. 14, issue 7, 1229-1242

**Abstract:**
This article focuses on inferring critical comparative conclusions as far as the application of both linear and non-linear risk measures in non-convex portfolio optimization problems. We seek to co-assess a set of sophisticated real-world non-convex investment policy limitations, such as cardinality constraints, buy-in thresholds, transaction costs, particular normative rules, etc. within the frame of four popular portfolio selection cases: (a) the mean-variance model, (b) the mean-semi variance model, (c) the mean-MAD (mean-absolute deviation) model and (d) the mean-semi MAD model. In such circumstances, the portfolio selection process reflects to a mixed-integer bi-objective (or in general multiobjective) mathematical programme. We precisely develop all corresponding modelling procedures and then solve the underlying problem by use of a novel generalized algorithm, which was exclusively introduced to cope with the above-mentioned singularities. The validity of the attempt is verified through empirical testing on the S&P 500 universe of securities. The technical conclusions obtained not only confirm certain findings of the particular limited existing theory but also shed light on computational issues and running times. Moreover, the results derived are characterized as encouraging enough, since a sufficient number of efficient or Pareto optimal portfolios produced by the models appear to possess superior out-of-sample returns with respect to the benchmark.

**Date:** 2014

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** Track citations by RSS feed

**Downloads:** (external link)

http://hdl.handle.net/10.1080/14697688.2013.868027 (text/html)

Access to full text is restricted to subscribers.

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:taf:quantf:v:14:y:2014:i:7:p:1229-1242

**Ordering information:** This journal article can be ordered from

http://www.tandfonline.com/pricing/journal/RQUF20

Access Statistics for this article

Quantitative Finance is currently edited by *Michael Dempster* and *Jim Gatheral*

More articles in Quantitative Finance from Taylor & Francis Journals

Bibliographic data for series maintained by Chris Longhurst ().