Journal of Asset Management

, Volume 19, Issue 4, pp 216–221 | Cite as

Portfolio optimisation in an uncertain world

  • Marielle de JongEmail author
Original Article


Mean–variance efficient portfolios are optimal as modern portfolio theory alleges, only if risk were foreseeable, which is under the hypothesis that price (co)variance is known with certainty. Admitting uncertainty changes the perception. If portfolios are presumed vulnerable to unforeseen price shocks as well, risk optimality is no longer obtained by minimising variance but also pertains to the diversification in the portfolio, for that provides protection against unforeseen events. Generalising MPT in this respect leads to the double risk objective to minimise variance and maximise diversification. We demonstrate that a series of portfolio construction techniques developed as an alternative to MPT, in fact, address this double objective, under which Bayesian optimisation, entropy-based optimisation, risk parity and covariance shrinkage. We give an analytical demonstration and provide by that new theoretical backing for these techniques.


Modern portfolio theory Risk parity Diversification Entropy 

JEL Classification




The author would like to thank Bruce Phelps for his unconditional support and Thierry Roncalli for his useful suggestions.


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Copyright information

© Macmillan Publishers Ltd., part of Springer Nature 2017

Authors and Affiliations

  1. 1.ParisFrance

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