In this paper, a new method is proposed for the direct calculation of the size component of equity returns. The method is based on the analysis of changes in the distribution of capital in the market, and since the method does not involve statistical estimation, instability and nonlinearity do not interfere with it. Application of the proposed method indicates that the exposure of some managers' returns to the size factor may be significantly greater than is implied by conventional estimates. 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 portfolios is related to the return on the market as a whole by a stochastic differential equation involving semimartingale local times based on the ranked market weights.
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. This report proposes an estimate of leakage that is independent of stocks outside the index. Antitrust and the No-Arbitrage Hypothesis by Robert Fernholz. Then the hypothesis that the market be arbitrage-free imposes certain conditions on the dividend rates of the stocks in the market. Analysis of the U.S. equity market indicates that historically these conditions have not been satisfied.