Martin Larsson: Large-scale dynamics of equity markets of variable size

Stochastic portfolio theory (SPT) is concerned with the dynamic properties of large equity markets, especially over long time horizons. While the theoretical literature is well developed, the empirical literature is much less so (with some notable exceptions). In this work we perform an empirical analysis of the large-scale behavior of the U.S. public equity universe, with a focus on the role of listing and delisting events. Such events have a profound impact on the distribution of capital. They can also produce severe biases in various statistical procedures that do not take these events into account. This phenomenon explains certain counterintuitive results that can arise when standard SPT models are calibrated to observed volatilities, collision rates, and long-term capital distributions. We develop procedures that correct for these biases, and find that our corrected estimates are remarkably consistent with the relationship between volatilities, local correlations, collision rates, and particle densities predicted by very simple diffusion models. Finally, we identify a mechanism by which listings and delistings can stabilize an otherwise unstable particle system. This is joint work with David Itkin and Licheng Zhang.