In an equity market with stable capital distribution, a capitalization-weighted index of small stocks tends to outperform a capitalization-weighted index of large stocks.} This is a somewhat careful statement of the so-called "size effect", which has been documented empirically and for which several explanations have been advanced over the years. We review the analysis of this phenomenon by Fernholz (2001) who showed that, in the presence of (a suitably defined) stability for the capital structure, this phenomenon can be attributed entirely to portfolio rebalancing effects, and will occur regardless of whether or not small stocks are riskier than their larger brethren. Collision local times play a critical role in this analysis, as they capture the turnover at the various ranks on the capitalization ladder.
We shall provide a rather complete study of this phenomenon in the context of a simple model with stable capital distribution, the so-called ``Atlas model" studied in Banner et al.(2005).
This is a Joint work with Adrian Banner, Robert Fernholz, Vasileios Papathanakos and Phillip Whitman.