In this short note, we consider mean-variance optimized portfolios with transaction costs. We show that introducing quadratic transaction costs makes the optimization problem more difficult than using linear transaction costs. The reason lies in the specification of the budget constraint, which...

This article explores the use of machine learning models to build a market generator. The underlying idea is to simulate artificial multi-dimensional financial time series, whose statistical properties are the same as those observed in the financial markets. In particular, these synthetic data...

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...

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...

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...

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 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...

ESG investing has gained considerable traction over the past few years and, alongside smart beta, factor investing and alternative risk premia, is one of the current hot topics for the asset management industry. Nevertheless, even though large institutions such as insurance companies, pension...