Abstract: Apparatus and methods for automatically modifying a financial portfolio having a pre-defined universe of securities, such as, e.g., an index fund, that tracks a given capitalization weighted index, through dynamic re-weighting of a position held in each such security. Specifically, in a computer system (50, 60), a target weight is accorded to each such security, relative to others in the portfolio, in proportion to a non-constant function of current capitalization weights of the securities in the index. Once these target weights are determined, then, in response to both the target weight of each such security and an actual weight, as a proportion of the portfolio, in which that security is currently held, a trade will be generated by the system in order to conform, within a predefined band, the actual weight to the target weight so as to rebalance the holdings in the portfolio.