Downside Performance Measures and the Sharpe Ratio

20 Pages Posted: 3 Oct 2019

See all articles by Benedikt Hoechner

Benedikt Hoechner

Otto-von-Guericke-Universität Magdeburg

Peter Reichling

Otto-von-Guericke University Magdeburg

Gordon Schulze

Otto-von-Guericke-Universität Magdeburg

Date Written: September 25, 2019

Abstract

In a mean-downside risk framework, portfolio lines that combine the market portfolio and the risk-free asset (i.e., passive benchmark strategies) are non-linear if the target differs from the risk-free rate. Here, downside risk-based performance measures assign different performance levels to passive strategies depending on the composition of the passive portfolio. The same applies for the evaluation of mutual funds. Therefore, we analyze the shape of portfolio lines for arbitrary targets above the risk-free rate in detail. We show that these portfolio lines can be characterized by the Kappa ratio with a target equal to the risk-free rate and, surprisingly, the Sharpe ratio. In addition, we show that minimum downside risk portfolios with varying target can be positioned on a straight line. This allows us to apply target-independent performance measures, even if portfolio lines depend on the target set by the investor. We substantiate our analytical results with an empirical study.

Keywords: Downside risk, Kappa ratio, performance measurement, Sharpe ratio

JEL Classification: D81, G11

Suggested Citation

Hoechner, Benedikt and Reichling, Peter and Schulze, Gordon, Downside Performance Measures and the Sharpe Ratio (September 25, 2019). Available at SSRN: https://ssrn.com/abstract=3459524 or http://dx.doi.org/10.2139/ssrn.3459524

Benedikt Hoechner

Otto-von-Guericke-Universität Magdeburg ( email )

Universitätspl. 2
PSF 4120
Magdeburg, D-39106
Germany

Peter Reichling (Contact Author)

Otto-von-Guericke University Magdeburg ( email )

Universitätspl. 2
PSF 4120
Magdeburg, D-39106
Germany
+49 391 6758412 (Phone)
+49 391 6741242 (Fax)

HOME PAGE: http://www.finance.ovgu.de

Gordon Schulze

Otto-von-Guericke-Universität Magdeburg ( email )

Universitätspl. 2
PSF 4120
Magdeburg, D-39106
Germany

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