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Portfolio optimisation in an uncertain world


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.

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  1. By rabbi Isaac bar Aha and brought to the attention by Shefrin and Statman, see Benartzi and Thaler (2001). The advice was to hold a third in the family dwellings, a third in business activity and a third in liquid assets.

  2. Selling an asset short is an active position based on conviction.

  3. We refer to Clarke et al. (2013) for further analysis, who make comparisons between optimisation outcomes adopting Sharpe’s (1964) capital asset pricing model.


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

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Correspondence to Marielle de Jong.

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de Jong, M. Portfolio optimisation in an uncertain world. J Asset Manag 19, 216–221 (2018).

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  • Modern portfolio theory
  • Risk parity
  • Diversification
  • Entropy

JEL Classification

  • G11