Arbitrage in Equity Markets by Robert Fernholz. If the average relative variance of each of the stocks with respect to the market is bounded away from zero, then there exist well-behaved portfolios which dominate the market portfolio. Diversity-Weighted Indexing by Robert Fernholz, Robert Garvy, and John Hannon. Diversity-weighted indexing is a new type of passive index strategy. It is based on a mathematical measure of the diversity of the distribution of capital in an equity market.
Leakage is caused by stocks leaving an index because their capitalization has declined.
An adjustment must be made to account for leakage in diversity-weighted index portfolios. Portfolio Generating Functions by Robert Fernholz. A general method is presented for constructing equity portfolios through the use of mathematical generating functions. The return on these functionally generated portfolios is related to the return on the market portfolio by a stochastic differential equation. Under appropriate conditions, this equation can be used to establish a dominance relationship between a functionally generated portfolio and the market portfolio.