While responsible investors consider that the environmental and social pillars are highly interconnected when implementing ESG and climate strategies, our research shows that the green and social bond markets are not integrated. Indeed, we notice that the social bond premium is not positively...

The concept of factor investing emerged at the end of the 2000s and has completely changed the landscape of equity investing. Today, institutional investors structure their strategic asset allocation around five risk factors: size, value, low beta, momentum and quality. This approach has been...

In the last five years, the financial industry has been impacted by the emergence of digitalization and machine learning. In this article, we explore two methods that have undergone rapid development in recent years: Gaussian processes and Bayesian optimization. Gaussian processes can be seen as...

This article develops the theory of risk budgeting portfolios, when we would like to impose weight constraints. It appears that the mathematical problem is more complex than the traditional risk budgeting problem. The formulation of the optimization program is particularly critical in order to...

The mean-variance optimization (MVO) theory of Markowitz (1952) for portfolio selection is one of the most important methods used in quantitative finance. This portfolio allocation needs two input parameters, the vector of expected returns and the covariance matrix of asset returns. This process...