Abstract
Entropy, a term used in Physics to quantify the degree of randomness in a complex system, is shown to be relevant for portfolio diversification. The link between entropy and diversification lies in the notion of uncertainty. We introduce the concept of available diversification in an investment universe and of diversification curves. We build a framework for assembling a fully diversified risk parity-like portfolio with a fundamental-based high-conviction strategy, through a constrained entropy-maximisation process by which a portion of potential portfolio return is swapped for extra diversification. The main results of this study are:• mean-variance optimised portfolios are highly concentrated and scarcely related to the asset return assumptions;• few basis points of expected returns can be converted into a huge amount of extra diversification that making the portfolio allocation more robust to parameter uncertainty;• on a more conceptual ground, we investigate the relationship between portfolio risk and diversification concluding that they should be managed distinctly.The empirical analysis presented in this work shows that entropy is a useful means to alleviate the lack of diversification of portfolios on the efficient frontier.
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Acknowledgements
The article is based on a series of lectures on quantitative finance, which the author gave at the Milan Polytechnic (MIP School of Management) since 2011, and hence he would like to thank all the students for their feedback, which helped him to further refine the subject. Moreover, he would like to thank Simone Facchinato, Sylvie de Laguiche and Ali Zerrad for very useful discussions.
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1PhD is Senior Portfolio Manager at ANIMA SGR in the Multiasset & Multimanager Division and Lecturer on Quantitative Finance at the MIP School of Management (Milan Polytechnic). Previously he worked in AMUNDI Group as Senior Quantitative Analyst (until July 2015) in Milan and Paris working on the diversified business line and advisory to international clients including Central Banks & Sovereign Wealth Funds. He holds a PhD in Computational Neuroscience from the University of Newcastle (UK) and a first class honours degree in Theoretical Physics from the University of L’Aquila (Italy).
Appendix
Appendix
Time-series details and risk-return parameters
The investment universe is composed of 12 assets: 4 bonds, 4 equities and 4 alternatives as detailed in Table A1. Risk-return parameters are given in tables A2 and A3.
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Pola, G. On entropy and portfolio diversification. J Asset Manag 17, 218–228 (2016). https://doi.org/10.1057/jam.2016.10
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DOI: https://doi.org/10.1057/jam.2016.10