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Positive Weights on the Efficient Frontier

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  • Phelim Boyle

Abstract

One of the fundamental insights of the Capital Asset Pricing Model is that the market portfolio is mean variance efficient. Since the market portfolio has positive weights on all assets, the conditions under which frontier portfolios have this property are of interest. This article derives a simple explicit solution for an efficient portfolio with positive weights. Assuming the covariance matrix is given, we obtain an expected return vector such that there is a compatible frontier portfolio. This portfolio is derived from the dominant eigenvector of the correlation matrix and provides a proxy for the market portfolio. Examples are provided to illustrate the basic idea.

Suggested Citation

  • Phelim Boyle, 2014. "Positive Weights on the Efficient Frontier," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(4), pages 462-477, October.
    • Handle: RePEc:taf:uaajxx:v:18:y:2014:i:4:p:462-477
    DOI: 10.1080/10920277.2014.922032
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    Cited by:

    1. Marco Avellaneda & Brian Healy & Andrew Papanicolaou & George Papanicolaou, 2020. "PCA for Implied Volatility Surfaces," Papers 2002.00085, arXiv.org.
    2. Andrew Papanicolaou & Hao Fu & Prashanth Krishnamurthy & Farshad Khorrami, 2023. "A Deep Neural Network Algorithm for Linear-Quadratic Portfolio Optimization with MGARCH and Small Transaction Costs," Papers 2301.10869, arXiv.org, revised Feb 2023.
    3. Elisabeth Leoff & Leonie Ruderer & Jörn Sass, 2022. "Signal-to-noise matrix and model reduction in continuous-time hidden Markov models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 327-359, April.
    4. Marco Avellaneda & Juan Andr'es Serur, 2020. "Hierarchical PCA and Modeling Asset Correlations," Papers 2010.04140, arXiv.org.

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