Considering the three first moments and allowing short sales, the efficient portfolios set for n risky assets and a riskless one is found, supposing that agents like odd moments and dislike even ones. Analytical formulas for the solution surface are obtained and important geometric properties provide insights on its shape in the three dimensional space defined by the moments. A special duality result is needed and proved. The methodology is general, comprising situations in which, for instance, the investor trades a negative skewness for a higher expected return. Computation of the optimum portfolio weights is feasible in most cases.

The Queen Elisabeth Musical Competition is the best-known international competition for violin and piano organised in Belgium, and is considered among the best and most demanding in the world. Each competition, organized in principle every four years, attracts some 40 violinists or 85 pianists, from many countries around the world.There is little doubt that winning this contest may have a significant impact on the future course of an artist. Therefore it may be relevant to study whether the final ranking is fair, or whether it may depend on some exogenous factors, related to the organisation of the competition. In the paper, we examine whether one of these objectively observable factors, the order of appearance of a candidate, has an influence on his final ranking.The tests show that the final rank is (unfortunately) not independent of the day in which the candidate appears; there is a statistically significant effect, especially for piano contests: those who appear first have a lower chance to be ranked among the first, while those who perform during the fifth day have a higher chance.We believe that the result is partly due to the way the competition is organized, and suggest some changes to avoid the bias.

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This paper investigates the impact of foreign direct investment (FDI) on the productivity of Portuguese manufacturing sectors. It improves on previous studies by considering the choice of the most appropriate interval of the technological gap for spillovers diffusion. Sectoral variation in the coefficients of the spillover effect is also allowed for. Idiosyncratic factors are identified by means of a fixed effects panel model and positive inter-sectoral spillovers are also examined. Significant spillovers require a proper technological differential between foreign and domestic producers and favourable sectoral characteristics. They may occur in modern industries in which the foreign firms have a clear, but not too sharp, edge on the domestic ones. Agglomeration effects are also a pertinent specific influence. Ce texte examine les r�percussions des investissements directs �trangers (IDE) sur la productivit� des secteurs manufacturiers au Portugal. La sp�cification du mod�le est am�lior�e par le choix de l'intervalle le plus appropri� de l'�cart technologique pour la diffusion des spillovers. Nous tenons �galement compte des variations sectorielles dans les coefficients de spillovers; des facteurs sectoriels idiosyncrasiques sont identifi�s au moyen d'un mod�le � effets fixes. Les spillovers intersectoriels positifs sont examin�s. Des spillovers importants requi�rent un v�ritable �cart technologique entre producteurs �trangers et domestiques ainsi que des caract�ristiques sectorielles favorables. Ils peuvent se produire dans les industries modernes o� les entreprises �trang�res jouissent d'une sup�riorit� nette, mais pas trop marqu�e. Les effets d'agglom�ration exercent aussi une influence sp�cifique pertinente.