The Dirichlet Portfolio Model: Uncovering the Hidden Composition of Hedge Fund Investments

Abstract: Hedge funds have long been viewed as a veritable "black box" of investing since outsiders may never view the exact composition of portfolio holdings. Therefore, the ability to estimate an informative set of asset weights is highly desirable for analysis. We 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. In this paper, we exhibit both sequential Monte Carlo numerical and conditionally Normal analytical approaches to solve for estimates of the unobserved asset weight time series. This methodology is motivated by the estimation of monthly asset class weights on the aggregate hedge fund industry from 1996 to 2012. Furthermore, we show how to implement the results as predictive investment weightings in order to construct hedge fund replicating portfolios.