Stochastic portfolio theory (SPT) is concerned with the dynamic properties of large equity markets, especially over long time horizons, and often with a focus on the distribution of capital. While the theoretical literature is well developed, the empirical literature is much less so (with some notable exceptions). In this work we perform a comprehensive empirical analysis of the large-scale behavior of the U.S. public equity universe, with a focus on the role of listing and de-listing events. Such events have a profound impact on the distribution of capital. They also produce severe biases in various established statistical procedures that do not take these events into account. This phenomenon explains various counterintuitive results that arise when one tries to fit standard models, such as so-called rank-based models, to observed volatilities, collision rates, and long-term capital distributions. We develop procedures that correct for these biases, and find that the corrected estimates are remarkably consistent with the relationship between volatilities, local correlations, collision rates, and particle densities predicted by simple diffusion models.

Bio: Martin Larsson is a professor in the Department of Mathematical Sciences at Carnegie Mellon University working in mathematical finance, probability theory, stochastic analysis, and statistics. Before joining CMU in 2019, he was an Assistant Professor of Mathematical Finance at the Department of Mathematics at ETH Zurich. He holds a PhD in Operations Research and Information Engineering from Cornell University, and was a postdoctoral fellow at the Swiss Finance Institute at EPFL in Lausanne. He is the mathematics representative on the Steering Committee of the Master of Science in Computational Finance (MSCF) program at CMU.