# On Capital Allocation under Information Constraints

## TL;DR

This paper introduces the Sorted Weighted Portfolio (SWP), a novel optimization framework that uses ordinal rankings of investments instead of historical data, outperforming traditional equal-weight strategies especially for risk-neutral investors.

## Contribution

It develops a new portfolio optimization model based on ordinal rankings and a Cobb-Douglas function, extending to risk-averse investors and correlation effects.

## Key findings

- SWP outperforms Equally Weighted Portfolio for risk-neutral investors
- Model can incorporate ordinal information without historical data
- Extensions address risk aversion and correlation effects

## Abstract

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.