  Attempts to allocate capital across a selection of different investments are
often hampered by the fact that investors' decisions are made under limited
information (no historical return data) and during an extremely limited
timeframe. Nevertheless, in some cases, rational investors with a certain level
of experience are able to ordinally rank investment alternatives through
relative assessments of the probabilities that investments will be successful.
However, 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 to calculate an optimal capital
allocation based on a Cobb-Douglas function, which we call the Sorted Weighted
Portfolio (SWP). Considering risk-neutral investors, we show that the results
of this portfolio optimization model usually outperform the output generated by
the (intuitive) Equally Weighted Portfolio (EWP) of different investment
alternatives, which is the result of optimization when one is unable to
incorporate additional data (the ordinal ranking of the alternatives). To
further extend this work, we show that our model can also address risk-averse
investors to capture correlation effects.
