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Article

Risk Parity, Maximum Diversification,
and Minimum Variance: An Analytic Perspective

Roger Clarke, Harindra de Silva and Steven Thorley
The Journal of Portfolio Management Spring 2013, 39 (3) 39-53; DOI: https://doi.org/10.3905/jpm.2013.39.3.039
Roger Clarke
is chairman of Analytic Investors, LLC, in Los Angeles, CA.
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  • For correspondence: rclarke@aninvestor.com
Harindra de Silva
is president of Analytic Investors, LLC, in Los Angeles, CA.
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  • For correspondence: hdesilva@aninvestor.com
Steven Thorley
is the H. Taylor Peery Professor of Finance at Brigham Young University in Provo, UT.
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  • For correspondence: steven.thorley@byu.edu
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Abstract

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.

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The Journal of Portfolio Management: 39 (3)
The Journal of Portfolio Management
Vol. 39, Issue 3
Spring 2013
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Risk Parity, Maximum Diversification,
and Minimum Variance: An Analytic Perspective
Roger Clarke, Harindra de Silva, Steven Thorley
The Journal of Portfolio Management Apr 2013, 39 (3) 39-53; DOI: 10.3905/jpm.2013.39.3.039

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Risk Parity, Maximum Diversification,
and Minimum Variance: An Analytic Perspective
Roger Clarke, Harindra de Silva, Steven Thorley
The Journal of Portfolio Management Apr 2013, 39 (3) 39-53; DOI: 10.3905/jpm.2013.39.3.039
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  • Article
    • Abstract
    • ANALYTIC SOLUTIONS TO RISK-BASED PORTFOLIOS
    • ONE THOUSAND STOCK EMPIRICAL EXAMPLE
    • WEIGHT DISTRIBUTIONS AS A FUNCTION OF RISK
    • SUMMARY AND CONCLUSIONS
    • APPENDIX
    • ENDNOTES
    • REFERENCES
  • Info & Metrics
  • PDF

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