Statistically (optimal) estimators of semivariance: A correction of Josephy-Aczel’s proof

• Authors: Karlheinz Fleischer , Bernhard Nietert
• Languages of publication: PL EN

Abstracts

EN

Semivariance is an intuitive risk measure because it concentrates on the shortfall below a target and not on total variation. To successfully use semivariance in practice, however, a statistical estimator of semivariance is needed; Josephy and Aczel provide such an estimator. Unfortunately, they have not correctly proven asymptotic unbiasedness and mean squared error consistency of their estimator since their proof contains a mistake. This paper corrects the computational mistake in Josephy-Aczel’s original proof and, that way, allows researchers and practitioners in the field of downside portfolio selection, hedging, downside asset pricing, risk measurement in a regulatory context, and performance measurement to work with a meaningfully specified downside measure.

Keywords

EN

risk analysis; semivariance; statistical estimation

• Publisher: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
• Journal: Śląski Przegląd Statystyczny
• Year: 2019
• Issue: 17 (23)
• Pages: 9-30

Contributors

author

Karlheinz Fleischer

author

Bernhard Nietert