Risk Parity, Maximum Diversification,and Minimum Variance: An Analytic Perspective
推导了风险平价、最大分散化和最小方差组合的解析解，揭示了系统性风险和特质风险如何影响资产权重，并指出风险平价组合包含所有可投资资产，而其他组合可能排除部分资产。
Analytic solutions to risk parity, maximum diversification, and minimum variance portfolios provide useful perspectives about their construction and composition. Individual asset weights depend on both systematic and idiosyncratic risk in all three risk-based portfolios, but systematic risk eliminates many investable assets in long-only, constrained, maximum-diversification, and minimum-variance portfolios. On the other hand, risk-parity portfolios include all investable assets, and idiosyncratic risk has little effect on weight magnitude. The algebraic forms for optimal asset weights derived in this article yield generalizable properties of risk-based portfolios, in contrast to empirical simulations that employ a specific set of historical returns, proprietary risk models, and multiple constraints. These analytic solutions reveal precisely how various kinds of predicted risk affect the relative magnitude of security weights in each type of risk-based portfolio construction. <b>TOPICS:</b>Portfolio construction, portfolio theory, volatility measures