The dirichlet portfolio model: Uncovering the hidden composition of hedge fund portfolios.

摘要

This dissertation is a compilation of three papers developing a class of compositional state space models for modeling a latent set of time-varying portfolio compositions on the simplex as well as net leverage values given a time series of portfolio return observations. Estimation techniques incorporating particle filtering and particle learning concepts are exhibited. These estimation techniques are motivated by the estimation of asset class weights and net leverage values on the aggregate hedge fund industry from 1995 to 2012.;In the first paper, I present a compositional state space model for estimation of an investment portfolio's unobserved asset allocation weightings on a set of candidate assets when the only observed information is the time series of portfolio returns and the candidate asset returns. I exhibit both sequential Monte Carlo numerical and conditionally Normal analytical approaches to solve for estimates of the unobserved asset weight time series. Furthermore, I show how to implement the results as predictive investment weightings in order to construct hedge fund replicating portfolios.;In the second paper, I demonstrate how to implement joint estimation of net portfolio leverage dynamics into the previous paper's setup. By incorporating recent work in parameter learning in state space models, I also show how to not only sequentially estimate the time-varying latent values, but also the parametrization of their generative distributions. Using this technique, I estimate net portfolio leverage on a set of hedge fund indices representing the returns on different broad classifications of funds. Finally, I exhibit the accuracy of these techniques by estimating asset class level regressions on the asset class return values against the same-period changes in the portfolio investment weights in order to demonstrate investment effects on same-period prices.;In the third paper, I identify that since the complete picture of hedge fund holdings is not observable, this presents a significant analytical hurdle for more detailed analysis because while the average hedge fund does not outperform benchmarks on the whole, it is possible that they exhibit skill in certain asset classes. Using the previously developed decomposition techniques, I discover that net leverage levels in the hedge fund industry are smaller than popular belief due to netting both internally and across different funds. As well, using these estimates, we confirm previous findings that hedge funds do not contribute to herding behavior in most asset classes, and in fact exhibit negative-feedback trading behavior in oil and municipal bonds. As well, the accuracy of these techniques is demonstrated on a set of actively managed diversified equity mutual funds where true industry allocation compositions are readily observable.