Optimal ETF Selection for Passive Investing

This paper considers the problem of isolating a small number of exchange traded funds (ETFs) that suffice to capture the fundamental dimensions of variation in U.S. financial markets. First, the data is fit to a vector-valued Bayesian regression model, which is a matrix-variate generalization of the well known stochastic search variable selection (SSVS) of George and McCulloch (1993). ETF selection is then performed using the decoupled shrinkage and selection (DSS) procedure described in Hahn and Carvalho (2015), adapted in two ways: to the vector-response setting and to incorporate stochastic covariates. The selected set of ETFs is obtained under a number of different penalty and modeling choices. Optimal portfolios are constructed from selected ETFs by maximizing the Sharpe ratio posterior mean, and they are compared to the (unknown) optimal portfolio based on the full Bayesian model. We compare our selection results to popular ETF advisor Wealthfront.com. Additionally, we consider selecting ETFs by modeling a large set of mutual funds.