Striving for maximum diversification we follow Meucci (2009) in measuring and managing a multi-asset class portfolio. Under this paradigm the maximum diversification portfolio is equivalent to a risk parity strategy with respect to the uncorrelated risk sources embedded in the underlying...

We investigate portfolio diversification strategies based on hierarchical clustering. These hierarchical risk parity strategies use graph theory and unsupervised machine learning to build diversified portfolios by acknowledging the hierarchical structure of the investment universe. In this...

The concept of second-order risk operationalizes the estimation risk in portfolio construction induced by model uncertainty. We study its contribution to the realized volatility of recently developed risk parity strategies. For each strategy, we derive closed-form solutions for the second-order...

Multi-asset multi-factor portfolio allocation is typically centred around a risk-based allocation paradigm, often striving for maintaining equal volatility risk budgets. Given that the common factor ingredients can be highly skewed, we specifically incorporate the notion of tail risk management...

We forecast portfolio risk for managing dynamic tail risk protection strategies, based on extreme value theory, expectile regression, Copula-GARCH and dynamic GAS models. Utilizing a loss function that overcomes the lack of elicitability for Expected Shortfall, we propose a novel Expected...

The 2015 Paris Agreement is a landmark in limiting emissions and targeting global warming well below 2, preferably 1.5, degrees Celsius compared to pre-industrial levels. In this light, we investigate how to efficiently construct equity portfolios that help mitigating climate change risk but at...