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Two risk dimensions are captured: asset covariance risk along risk in left-hand tail similarity and volatility. The key ingredient is an informative set on the left-hand tail distributions of asset returns obtained by an adaptive clustering procedure. This set allows a left tail similarity and left tail volatility to be defined, thereby providing a definition for the left-tail-covariance-like matrix. The convex combination of the two covariance matrices generates a \u201ctwo-dimensional\u201d risk that, when applied to portfolio selection, provides a measure of its systemic vulnerability due to the asset centrality. This is done by simply associating a suitable node-weighted network with the portfolio. Higher values of this risk indicate an asset allocation suffering from too much exposure to volatile assets whose return dynamics behave too similarly in left-hand tail distributions and\/or co-movements, as well as being too connected to each other. Minimizing these combined risks reduces losses and increases profits, with a low variability in the profit and loss distribution. The portfolio selection compares favorably with some competing approaches. An empirical analysis is made using exchange traded fund prices over the period January 2006\u2013February 2018.<\/jats:p>","DOI":"10.1007\/s10287-022-00422-2","type":"journal-article","created":{"date-parts":[[2022,1,20]],"date-time":"2022-01-20T13:04:05Z","timestamp":1642683845000},"page":"425-455","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A tail-revisited Markowitz mean-variance approach and a portfolio network centrality"],"prefix":"10.1007","volume":"19","author":[{"given":"Francesca","family":"Mariani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gloria","family":"Polinesi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maria Cristina","family":"Recchioni","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,1,20]]},"reference":[{"key":"422_CR1","doi-asserted-by":"crossref","unstructured":"Abbasi A, Hossain L (2013) Hybrid centrality measures for binary and weighted networks. 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