Abstract

The Integration of Rare Events into "Classical" Diversification Considerations

Bernhard Nietert

Universität Passau

Stock price movements are characterized by occasional extreme vibrations, resulting in dramatic losses during stock market crises. This can be demonstrated by the October crises in 1987 and 1989 as well as the Southeast Asia, Russia and Brazil crises in 1998/99. Despite its obvious importance, literature has neglected jumps in the context of optimum portfolio strategies. For that reason, the objective of our paper is the integration of price jumps into portfolio selection. To that end, we are looking to find in a first step a well-founded model of the jump/diffusion process: Reasonable representations of jumps distinguish between firm-specific and market jumps (scope of jumps) as well as crashes and explosions (direction of jumps). Only now, with this economically founded jump model can we be ready to establish portfolio selection in a next step: Optimum portfolio weights are a linear combination of the mu-sigma-efficient portfolio of the diffusion component and jump-induced correction terms. Moreover, both parts of the optimum portfolio can be combined to an extended Tobin separation.