Managing Risk Exposures Using the Risk Budgeting Approach

33 Pages Posted: 23 Feb 2012 Last revised: 10 Apr 2012

See all articles by Benjamin Bruder

Benjamin Bruder

Lyxor Asset Management

Thierry Roncalli

Amundi Asset Management; University of Evry

Date Written: January 20, 2012


The ongoing economic crisis has profoundly changed the industry of the asset management, by putting risk management at the heart of most investment processes. This new risk-based investment style does not rely on returns forecasts and is therefore assumed to be more robust. In 2011, it has particularly encountered a great success with the achievement of minimum variance, ERC and risk parity strategies in portfolios of several large institutional investors. 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 components is equal to the budget of risk defined by the portfolio manager. Unfortunately, even if risk budgeting techniques are widely used by market practitioners, they 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 minimum variance and weight budgeting portfolios. We also discuss the existence, uniqueness and optimality of such a portfolio. In a 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.

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

JEL Classification: G11, C58, C60

Suggested Citation

Bruder, Benjamin and Roncalli, Thierry, Managing Risk Exposures Using the Risk Budgeting Approach (January 20, 2012). Available at SSRN: or

Benjamin Bruder

Lyxor Asset Management ( email )


Thierry Roncalli (Contact Author)

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015

University of Evry ( email )

Boulevard Francois Mitterrand
F-91025 Evry Cedex

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