Pitfalls of downside performance measures with arbitrary targets

Benedikt Hoechner (), Peter Reichling () and Gordon Schulze ()
Additional contact information
Benedikt Hoechner: Faculty of Economics and Management, Otto-von-Guericke University Magdeburg
Peter Reichling: Faculty of Economics and Management, Otto-von-Guericke University Magdeburg
Gordon Schulze: Faculty of Economics and Management, Otto-von-Guericke University Magdeburg

No 150018, FEMM Working Papers from Otto-von-Guericke University Magdeburg, Faculty of Economics and Management

Abstract: The Sharpe ratio has been criticized with regard to the assumptions of mean-volatility portfolio selection. Downside performance measures were developed to resolve this critique; they are consistent with expected utility under less restrictive assumptions. The most prominent family of downside performance measures is known as Kappa ratios and puts above target returns into relation to lower partial moments. While the Sharpe ratio of a mutual fund examines whether portfolios of mutual fund and risk-free asset dominate risk-adjusted passive portfolios of benchmark and risk-free asset, this characteristic cannot be transferred to downside performance measures with arbitrary targets. We show that Kappa ratios assign different values to passive strategies with varying fractions of benchmark and risk-free asset if the target differs from the risk-free rate. This effect can lead to reverse rankings of inferior and superior performing mutual funds. In addition, even the ratio of excess return and excess downside risk of passive portfolios is not constant in general. Therefore, downside performance measures turn out to be only applicable in asset management if the target is set equal to the risk-free rate.

Keywords: Downside risk; Kappa ratios; lower partial moment; performance measurement; Sharpe ratio (search for similar items in EconPapers)
JEL-codes: D81 G11 (search for similar items in EconPapers)
Pages: 18 pages
Date: 2015-11
New Economics Papers: this item is included in nep-rmg and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.fww.ovgu.de/fww_media/femm/femm_2015/2015_18.pdf First version, 2011 (application/pdf)

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:mag:wpaper:150018

Access Statistics for this paper

More papers in FEMM Working Papers from Otto-von-Guericke University Magdeburg, Faculty of Economics and Management Contact information at EDIRC.
Bibliographic data for series maintained by Guido Henkel ().