Optimal ETF Selection for Passive Investing

TL;DR

This paper develops a Bayesian approach to select a small set of ETFs that effectively capture market variation, optimizing portfolios based on the Sharpe ratio and comparing results to popular advisory services.

Contribution

It introduces a novel Bayesian ETF selection method using matrix-variate regression and decoupled shrinkage, tailored for vector responses and stochastic covariates.

Findings

Selected ETFs outperform benchmarks in capturing market variation.

Optimized portfolios achieve higher Sharpe ratios than alternatives.

Method compares favorably to Wealthfront's ETF choices.

Abstract

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.