RT Journal Article SR Electronic T1 Risk Parity, Maximum Diversification,
and Minimum Variance: An Analytic Perspective JF The Journal of Portfolio Management FD Institutional Investor Journals SP 39 OP 53 DO 10.3905/jpm.2013.39.3.039 VO 39 IS 3 A1 Roger Clarke A1 Harindra de Silva A1 Steven Thorley YR 2013 UL https://pm-research.com/content/39/3/39.abstract AB 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.TOPICS: Portfolio construction, portfolio theory, volatility measures