The properties of alpha risk-parity

Read the latest Quantitative Investment Strategies (QIS) research paper

The QIS team at BNP Paribas Global Markets introduces its new research paper where they have used techniques from information geometry in order to extend a popular approach to portfolio construction known as risk budgeting.

Risk budgeting has become ubiquitous in modern finance, and the team’s work establishes a link between this approach and other commonly-used ways to construct risk-parity portfolios. Their contribution is twofold:

First – to the best of their knowledge – the paper is the first of its kind to apply techniques from information theory and geometry to risk parity. In this approach, investors can adjust their risk-budgeting portfolio in order to get closer to the minimum-risk portfolio or to any reference allocation. A closed-form formula determines the contribution of each asset to the risk of the portfolio. This conclusion shall be particularly relevant for all investors who use risk parity for their portfolio. The research provides numerical evidence on the benefit of using alpha risk-parity.

Second, the authors use statistical divergences in order to control the divergence between two portfolio allocations. Approaches that rely on entropy functions implicitly assume that the reference portfolio is equally weighted. Shannon’s cross entropy has been used in order to consider any reference portfolio. In the framework of divergence functions, it is easier to combine a general reference portfolio with a general entropic index.

Click below to read the full paper. Should you have any questions or requests, please reach out to Julien Turc or Jerome Gava.

Related solutions

Equity Derivatives

BNP Paribas has over 30 years of track record in developing innovative equity derivatives strategies and an established global leader in structured products. Our comprehensive range of solutions across flow and structured products is designed to meet all our clients’ needs.

Global Equities

Building on our long-established world-class Equity Derivatives business, BNP Paribas continues to diversify and scale our Equities offering. Clients can now access the combined strengths of our market-leading Prime Services and Cash Equities platforms.


Bridging the gap between academia and BNP Paribas Quantitative Investment Strategies Group, the QIS lab is dedicated to developing cutting-edge systematic strategies, such as foundations of factors investing, new strategies, research in asset allocation through systemic strategies.