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  1. 1 Śląski Przegląd Statystyczny

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  1. 1 Fleischer K.

  2. 1 Nietert B.

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  1. 1 2019

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

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Fleischer K., Nietert B.
Śląski Przegląd Statystyczny
|
2019
|
issue 17 (23)
9-30
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.
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