Abstract: A probabilistic threshold index or fund method of determining membership of financial instruments in an index or fund comprises determining measurement values for a list of companies, determining constraints based on these measurement values, specifying a probability model, and reconstituting the index or fund based on the model probability that the measurement values of these financial instruments will satisfy the constraints at a time in the future. The method can be used with fixed probability thresholds, deleting financial instruments with probabilities lower than the lower threshold, and adding non-member financial instruments with probabilities higher than the upper threshold. The method may be adapted to maintain an index or fund with a fixed number of financial instruments. A fund or index may be constituted according to the index or fund, and a marketplace may comprise one or more funds or indices.

Abstract: A method for creating or maintaining a family of size based indices or funds includes selecting a list of M companies, assigning a raw share quantity to each company, and determining a rank i for each company based on size of the company. The method includes determining rank thresholds and creating or maintaining a family of indices or funds.