In plant communities, the portfolio effect, also called "statistical averaging effect", expresses the fact that stability in aggregate community properties such as biomass productivity generally rises with species diversity, simply because of the statistical averaging of the fluctuations in species' properties. This paper essentially upgrades the previous formulations of the portfolio effect, first developed by Doak and collaborators and then by Tilman. It uses a theoretical approach based on simple statistical relationships and some simplifying assumptions proposed by these authors. The new formulation presented extends and improves the previous relationships in the sense that it takes into account simultaneously a varying scaling power of the variance, the interaction effect between species, the heterogeneity in species productivity and interspecies correlated responses to the environment. It appears that the simple statistical averaging, as inferred from this formulation, does not necessarily lead to a positive correlation between species diversity and community stability.