In this article, we analyze the impact of weights constraints in portfolio theory using the seminal work of Jagannathan and Ma (2003). They show that solving the global minimum variance portfolio problem with some constraints on weights is equivalent to use a shrinkage estimate of the covariance...

The influence of the CAPM theory on the financial theory of investment has increased with the development of passive management. Today, equity or fixed-income market portfolios can easily be defined using equity and fixed-income indexes. These indexes also play an important role in active...

To implement strategic asset allocation, we must determine risk and return expectations for the various asset classes. Starting from the paradigm that long-run asset returns are determined by the long-run fundamentals of the economy, a fair value approach to building expectations is crucial....

In the last few years, the financial advisory industry has been impacted by the emergence of digitalization and robo-advisors. This phenomenon affects major financial services, including wealth management, employee savings plans, asset managers, private banks, pension funds, banking services,...

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...