An info‐gap approach to managing portfolios of assets with uncertain returns

The purpose of this paper is to provide a quantitative methodology based on information‐gap decision theory for dealing with (true) Knightian uncertainty in the management of portfolios of assets with uncertain returns.

Portfolio managers aim to maximize returns for given levels of risk. Since future returns on assets are uncertain the expected return on a portfolio of assets can be subject to significant uncertainty. Information‐gap decision theory is used to construct portfolios that are robust against uncertainty.

Using the added dimensions of aspirational parameters and performance requirements in information‐gap theory, the paper shows that one cannot simultaneously have two robust‐optimal portfolios that outperform a specified return and a benchmark portfolio unless one of the portfolios has arbitrarily large long and short positions.

The paper has considered only one uncertainty model and two performance requirements in an information‐gap analysis over a particular time frame. Alternative uncertainty models could be introduced and benchmarking against proxy portfolios and competitors are examples of additional performance requirements that could be incorporated in an information‐gap analysis.

An additional methodology for applying information‐gap modeling to portfolio management has been provided.

This paper provides a new and novel approach for managing portfolios in the face of uncertainties in future asset returns.