🤖 AI Summary
This study addresses the limitation of existing portfolio theory, which is constrained by Simaan’s (1993) three-fund separation assumption and thus struggles to characterize more general weighted selection elliptical distributions. To overcome this, the work proposes stochastically representing weighted selection elliptical distributions as the sum of an affine combination and an independent directional elliptical component, while employing first-order stochastic dominance analysis techniques to construct a unified framework. The primary contribution lies in transcending the traditional three-fund restriction by rigorously deriving the first-order stochastic dominance separation conditions for q+2 funds. This result substantially broadens the applicability of fund separation theory, providing a more generalized theoretical foundation for portfolio optimization under complex distributional assumptions.
📝 Abstract
We represent (weighted-)selection-elliptical distributions as an affine combination of the $q$ selection variables plus an elliptical term whose direction alone is independent. This form suffices for $q+2$ fund separation via first-order stochastic dominance, inter alia relaxing Simaan's (1993) three-fund assumptions.