We derive the decomposition of the ranked continuous semimartingales i.e. order- statistics processes. We apply it to portfolios generated by functions of the ranked market weights. Thus we generalize recent results of Fernholz.

Dynamic equity portfolios can be generated by positive twice continuously differentiable functions of the ranked capitalization weights of an equity market. The return on such a portfolio relative to the market follows a stochastic differential equation that decomposes the relative return into...