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Orderings and risk probability functionals in portfolio theory

Ortobelli S., Rachev S., Shalit H., Fabozzi F. J.

Probability and Mathematical Statistics

2008

Vol. 28, Fasc. 2

203--234

This paper studies and describes stochastic orderings of risk/reward positions in order to define in a natural way risk/reward measures consistent/isotonic to investors’ preferences. We begin by discussing the connection between the theory of probability metrics, risk measures, distributional moments, and stochastic orderings. Then we examine several classes of orderings which are generated by risk probability functionals. Finally, we demonstrate how further orderings could better specify the investor’s attitude toward risk.

Distributional analysis of the stocks comprising the DAX 30

Hoechstoetter M., Rachev S., Fabozzi F.

Probability and Mathematical Statistics

2005

Vol. 25, Fasc. 2

363--383

In this paper, we analyze the returns of stocks comprising the German stock index DAX with respect to the α-stable distribution. We apply nonparametric estimation methods such as the Hill estimator as well as parametric estimation methods conditional on the α-stable distribution. We find for both the nonparametric and parametric estimation methods that the α-stable hypothesis cannot be rejected for the return distribution. We then employ the GARCH model; the fit of innovations modeled with an underlying α-stable distribution is compared to the fit obtained from modelling the innovations with the skew-t distribution. The α-stable distribution is found to out-perform the skew-t distribution.