On capital allocation under information constraints

Christoph J. Börner, Ingo Hoffmann, Fabian Poetter and Tim Schmitz

Abstract

Attempts by investors to allocate capital across a selection of different investments are often hampered by the fact that their decisions are made with limited information (eg, no historical return data) and within an extremely limited time frame. In some cases, however, rational investors with enough experience are able to ordinally rank investment alternatives through relative assessments of the probabilities that such investments will be successful. However, in order to apply traditional portfolio optimization models, analysts must use historical (or simulated/expected) return data as the basis for their calculations. This paper develops an alternative portfolio optimization framework that is able to handle this kind of information (given by an ordinal ranking of investment alternatives) and calculate an optimal capital allocation based on a Cobb–Douglas utility function (which we call the sorted weighted portfolio). With risk-neutral investors in mind, we show that the results of this portfolio optimization model usually outperform the output generated by the (intuitive) equally weighted portfolio of investment alternatives, which is the result of optimization when it is not possible to incorporate additional data (the ordinal ranking of the alternatives). We show that our model can further contribute to this area by helping risk-averse investors capture correlation effects.