Risk allocation under shortfall constraints

Risk budgeting interpreted as efficient portfolio allocation is often based on expected outperformance, alpha or information ratio. Once these crucial parameters have been estimated, they are being treated as fixed. In this paper we develop some sense, both theoretical and practical, on the magnitude of the uncertainty and present a method to cape with uncertainty of the expected active returns. We will use examples to demonstrate the impact of the uncertainty. The developed model is widely applicable and can be used to make an optimal risk allocation on different levels of investment strategy (as set allocation, styles, managers, etc.).