Risk parity refers to an asset allocation method which consists in budgeting the risk. It is today the main alternative method to the traditional mean-variance portfolio optimization. Contrary to this last one, risk parity portfolios appear robust. It is largely used by institutional investors such as pension funds, sovereign funds or insurance company to manage their equity exposure or their stock/bond asset mix.
Although portfolio management didn't change much during the 40 years after the seminal works of Markowitz and Sharpe,
the development of risk budgeting techniques marked an important milestone in the deepening of
the relationship between risk and asset management. Risk parity then became a
popular financial model of investment after the global financial crisis in 2008.
Today, pension funds and institutional investors are using this approach in the development of
smart indexing and the redefinition of long-term investment policies.
Introduction to Risk Parity and Budgeting provides an up-to-date treatment of this alternative method to Markowitz optimization.
It builds financial exposure to equities and commodities, considers credit risk in the management of
bond portfolios, and designs long-term investment policy.
The first part of the book gives a theoretical account of portfolio optimization and risk parity.
The author discusses modern portfolio theory and offers a comprehensive guide to risk budgeting.
Each chapter in the second part presents an application of risk parity to a specific asset class.
The text covers risk-based equity indexation (also called smart beta) and shows how to use risk
budgeting techniques to manage bond portfolios. It also explores alternative investments, such as
commodities and hedge funds, and applies risk parity techniques to multi-asset classes.
The book's first appendix provides technical materials on optimization problems, copula functions, and dynamic asset allocation.
The second appendix contains 30 tutorial exercises. Solutions to the exercises, slides for instructors, and Gauss computer programs
to reproduce the book's examples, tables, and figures are available on the book's website.
Go to the book's website
In this paper we extend the volatility-based risk parity approach in order to take into account the jump risk. For that, we develop a skewness-based risk measure by considering a Gaussian mixture model. We apply this portfolio construction to the traditional asset mix policy between equities and bonds when we introduce a short volatility exposure. Moreover, we show interesting results concerning some asset management problems: factor investing, alternative risk premia and CTA strategies. The working paper is available at SSRN.
In this paper we propose a cyclical coordinate descent (CCD) algorithm for solving high dimensional risk parity problems. We show that this algorithm converges and is very fast even with large covariance matrices (n > 500). Comparison with existing algorithms also shows that it is one of the most efficient algorithms. The working paper is available at SSRN.
This paper is a generalization of the risk parity approach of Bruder and Roncalli (2012) when we consider a generalized risk measure that takes into account expected returns. 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. The working paper is available at SSRN.
This paper is a generalization of the risk parity approach of Bruder and Roncalli (2012) if we consider risk factors instead of assets. It appears that the problem is trickier. For instance, we could obtain multiple solutions. We propose then to formulate the diversification problem in terms of risk factors as an optimization program. We illustrate our methodology with some real life examples and backtests, which are: budgeting the risk of Fama-French equity factors, maximizing the diversification of an hedge fund portfolio and building a strategic asset allocation based on economic factors. The working paper is available at SSRN.
This paper can be viewed as a generalization of the results obtained in the article published in the Journal of Portfolio Management. We derive theoretical properties of risk budgeting portfolios, when the risk budgets are not the same. We also study the existence, the uniqueness and the optimality of such portfolios, and compare them to weight budgeting portfolios. Applications to strategic asset allocation, bonds and equities management and multi-asset diversified funds are provided. The working paper is available at SSRN.
In this paper, we derive theoretical properties of risk parity portfolios. In particular, we show that the ERC portfolio always exists and is unique. We also show that the ERC portfolio is located between the minimum variance portfolio and the equally-weighted portfolio. An empirical application to commodities is provided. This paper has been published in the Journal of Portfolio Management (Summer 2010). The working paper is available at SSRN (with two other applications on US equities and multi-asset classes).
In this article, we consider low volatility indexing. We show that there is a trade-off between the volatility reduction and the risks of such solutions. Thus, we measure the relationships between volatility on the one hand, and diversification, tracking error, liquidity and performance on the other. This paper is available at SSRN.
Application of the risk factor parity with non-gaussian risk measures. Examples concern the Fama-French model, the yield curve, portfolios of hedge funds, strategic asset allocation and smart indexing (slides available here).
A survey on risk parity applications and some results on robustness of optimized and risk parity portfolios (slides available here).
In this research, we show how risk budgeting techniques could be useful to manage credit risk in bond portfolios and we compare risk-based indexation with debt-weighted and gdp-weighted indexations. It is certainly the first application of risk parity to bonds. This article has been published in Journal of Indexes Europe (November 2011). An extended version of this article is available at SSRN. A summary of this research appears in the French journal La Revue Banque in October 2011.
This short paper illustrates the use of the Gini coefficient to measure the risk concentration of equity indexes. A comparison between the ERC Eurostoxx index and the Eurostoxx 50 index is provided. This article has been published in the Bloomberg Risk newsletter (July 2011). A copy is available here.
Market-cap indexation presents some limits (trend-following strategy, lack of diversification and bubble bias). Alternative-weighted indexation correspond to passive indexes where the weights are not based on market capitalization. We generally distinguish two forms: fundamental indexation and risk-based indexation. Different forms of risk-based indexation exist: minimum variance, equally-weighted, mdp/msr and ERC. In this paper, we compare these four alternative indexation. This paper is available at SSRN.
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