Equal Risk Contribution Portfolios using MAD

After the work by Markowitz (1952), portfolio selection has gained a great relevance in financial literature. Many risk measures, besides the variance proposed by Markowitz, have been used since 1952. However, there are two main issues in portfolio optimization models: the first one is that the resulting optimal portfolios tend to be very sensitive to changes in input parameters required by the models (Kondor et al, 2007; Cesarone et al, 2018a); while the second one is the possible lack of diversi fication in terms of risk. As for the second problem, indeed, the portfolio optimization models based on Gain-Risk analysis tend to select few assets and, consequently, the portfolios obtained are not balanced in terms of risk attributed to each asset. One way to deal with this issue could be to choose an equally weighted portfolio; however, this approach does not try to yield an optimal solution and, besides, there is no guarantee of risk diversifi cation. For this latter purpose, Maillard et al (2010) propose a more re ned approach to risk diversi fication, called equally weighted risk contribution or risk parity. The authors aim at fi nding a portfolio where each asset has the same risk contribution to total risk, where the risk is measured by the variance. However alternative risk measures can also be considered (Roncalli, 2014; Cesarone and Colucci, 2018) as well as alternative strategies based on the requirement that the risk contributions of all assets do not exceed a given threshold which can then be minimized (Cesarone and Tardella, 2017), or approaches based both on optimization and diversi fication (Cesarone et al, 2018b). In this preliminary work, we investigate the features and the performance of the risk parity portfolio using the Mean-Absolute Deviation (MAD) as risk measure. Furthermore, we propose several strategies to practically find the MAD Risk Parity portfolios, and we compare them in terms of accuracy and efficiency.