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


  • Thierry Roncalli

    (Lyxor Asset Management, University of Evry)


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 compare risk budgeting portfolios and optimized portfolios and illustrate that the new approach defines a defensive model of active management. Then, we consider long-term investment policy and the determination of strategic asset allocation.

Suggested Citation

  • Thierry Roncalli, 2015. "Introducing Expected Returns into Risk Parity Portfolios: A New Framework for Asset Allocation," Bankers, Markets & Investors, ESKA Publishing, issue 138, pages 18-28, September.
  • Handle: RePEc:rbq:journl:i:138:p:18-28

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    Cited by:

    1. Jean-Charles Richard & Thierry Roncalli, 2019. "Constrained Risk Budgeting Portfolios: Theory, Algorithms, Applications & Puzzles," Papers 1902.05710,

    More about this item


    Risk parity; Risk budgeting; Expected returns; ERC portfolio; Value-at-risk; Expected shortfall; Active management; Tactical asset allocation; Strategic asset allocation;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions


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