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Managing Risk Exposures using the Risk Budgeting Approach

by Benjamin Bruder of Lyxor Asset Management, and
Thierry Roncalli of Lyxor Asset Management

March 2012

Abstract: The ongoing economic crisis has profoundly changed the industry of asset management by putting risk management at the heart of most investment processes. This new risk-based investment style does not rely on return forecasts and is therefore assumed to be more robust. 2011 was marked by several great successes in transforming the practice of asset management with several large institutional investors moving their portfolios to minimum variance, ERC or risk parity strategies. These portfolio constructions are special cases of a more general class of allocation models, known as the risk budgeting approach. In a risk budgeting portfolio, the risk contribution from each component is equal to the budget of risk defined by the portfolio manager. Unfortunately, even if risk budgeting techniques are widely used by market practitioners, there are few results about the behavior of such portfolios in the academic literature. In this paper, we derive the theoretical properties of the risk budgeting portfolio and show that its volatility is located between those of the minimum variance and weight budgeting portfolios. We also discuss the existence, uniqueness and optimality of such a portfolio. In the second part of the paper, we propose several applications of risk budgeting techniques for risk-based allocation, like risk parity funds and strategic asset allocation, and equity and bond alternative indexations.

JEL Classification: G11, C58, C60.

Keywords: risk budgeting, risk management, risk-based allocation, equal risk contribution, diversification, concentration, risk parity, alternative indexation, strategic asset allocation.

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