Symmetry and order in the portfolio allocation problem
In a single period model of a securities market with a finite number of assets, the classical portfolio allocation problem can be described as the problem of choosing the best portfolio for maximizing the expected utility of terminal wealth. If the asset returns are independently distributed and ordered (either in the likelihood ratio order or the reversed hazard order) then the optimum portfolio choices are also ordered for some classes of decision makers (for instance, those with non-decreasing and continuously differentiable utility functions). The present article extends these findings to the case of multivariate asset returns distributions that present certain kinds of symmetry structure. First they work with multivariate arrangement increasing density functions that allow strictly controlled asymmetries into the distribution of the rates of returns. Then, by considering permutation symmetric random returns, they place the asymmetry in the mappings of random draws on the rates of return that enter the terminal payoff in the utility function. Theses symmetries and asymmetries in the distribution structure are critical to understand optimum portfolio allocations even in the presence of a risk-free asset.
multivariate distribution of asset returns
scientific article; zbMATH DE number 1748973