Mean-variance efficient portfolios are risk optimal only if risk were foreseeable, that is, under the hypothesis that asset price (co)variance is known with certainty. Admitting uncertainty changes the perception. When unforeseen price shocks are deemed possible, risk optimality is no longer synonymous to minimum price variance, but pertains to the diversification in the portfolio as well, for that provides protection against unforeseen shocks.
Generalising Modern Portfolio Theory (Markowitz 1952) in this respect leads to a double risk objective: minimise variance and maximise diversification. The optimum is attained when the portfolio is in parity, meaning that all assets contribute equally to the overall price variance. In that configuration the probability of incurring an unfavourable price shock, foreseen or not, is minimised.
Amundi Working Paper - December 2016
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