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...

A capitalization-weighted index is the most common way to gain access to broad equity market performance. These portfolios are generally concentrated in a few stocks and present some lack of diversification. In order to avoid this drawback or to simply diversify market exposure, alternative...

With the recent development of the European debt crisis, traditional index bond management has been severely called into question. We focus here on the risk issues raised by the classical market-capitalization weighting scheme. We propose an approach to properly measure sovereign credit risk in...

Portfolio construction and risk budgeting are the focus of many studies by academics and practitioners. In particular, diversification has spawn much interest and has been defined very differently. In this paper, we analyze a method to achieve portfolio diversification based on the decomposition...

In this paper we propose a coordinate descent algorithm for solving high dimensional risk parity problems. We show that this algorithm converges and is very fast even with large covariance matrices (n500). Comparison with existing algorithms also shows that it is one of the most efficient...

In this article, we show how to take into account skewness risk in portfolio allocation. Until recently, this issue has been seen as a purely statistical problem, since skewness corresponds to the third statistical moment of a probability distribution. However, in finance, the concept of...

The concept of alternative risk premia can be viewed as an extension of the factor investing approach. Factor investing is a term that is generally dedicated to long-only equity risk factors. A typical example is the value equity strategy. Alternative risk premia designate non-traditional risk...

This article develops a model that takes into account skewness risk in risk parity portfolios. In this framework, asset returns are viewed as stochastic processes with jumps or random variables generated by a Gaussian mixture distribution. This dual representation allows us to show that skewness...

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...

The capital asset pricing model (CAPM) developed by Sharpe (1964) is the starting point for the arbitrage pricing theory (APT). It uses a single risk factor to model the risk premium of an asset class. However, the CAPM has been the subject of important research, which has highlighted numerous...