Introducing Expected Returns into Risk Parity Portfolios: A New Framework for Asset Allocation

19 Pages Posted: 6 Sep 2013 Last revised: 14 Jun 2014

Thierry Roncalli

Amundi Asset Management; University of Evry

Date Written: April 2014


Risk parity is an allocation method used to build diversified portfolios that does not rely on any assumptions of expected returns, thus placing risk management at the heart of the strategy. This explains why risk parity became a popular investment model after the global financial crisis in 2008. However, risk parity has also been criticized because it focuses on managing risk concentration rather than portfolio performance, and is therefore seen as being closer to passive management than active management. In this article, we show how to introduce assumptions of expected returns into risk parity portfolios. To do this, we consider a generalized risk measure that takes into account both the portfolio return and volatility. However, the trade-off between performance and volatility contributions creates some difficulty, while the risk budgeting problem must be clearly defined. After deriving the theoretical properties of such risk budgeting portfolios, we apply this new model to asset allocation. First, we consider long-term investment policy and the determination of strategic asset allocation. We then consider dynamic allocation and show how to build risk parity funds that depend on expected returns.

Keywords: risk parity, risk budgeting, expected returns, ERC portfolio, value-at-risk, expected shortfall, tactical asset allocation, strategic asset allocation

JEL Classification: G11

Suggested Citation

Roncalli, Thierry, Introducing Expected Returns into Risk Parity Portfolios: A New Framework for Asset Allocation (April 2014). Available at SSRN: or

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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