Analytic solutions to Risk Parity, Maximum Diversification, and Minimum Variance portfolios provide useful perspectives … Diversification and Minimum Variance portfolios. On the other hand, all investable assets are included in Risk Parity portfolios, and …

This paper analyses and develops insights to systematic risk and diversification when random, imperfectly dependent …, losses are aggregated. Systematic risk and diversification are shown to vary across layers of component losses according to … local dependence and volatility structures. Systematic risk is high and diversification is weak overall if high risk layers …