Shrinkage regression for multivariate inference with missing data, and an application to portfolio balancing

TL;DR

This paper introduces a Bayesian hierarchical shrinkage regression method for multivariate inference with missing data, improving portfolio balancing by handling large asset collections and heavy-tailed errors more reliably.

Contribution

It extends existing methods by incorporating Bayesian hierarchical modeling, heavy-tailed errors, and estimation risk, enhancing robustness and applicability in financial data analysis.

Findings

Bayesian approach outperforms classical methods in synthetic data tests.

Method provides more reliable covariance estimates for portfolio optimization.

Application to real data demonstrates improved portfolio balancing.

Abstract

Portfolio balancing requires estimates of covariance between asset returns. Returns data have histories which greatly vary in length, since assets begin public trading at different times. This can lead to a huge amount of missing data--too much for the conventional imputation-based approach. Fortunately, a well-known factorization of the MVN likelihood under the prevailing historical missingness pattern leads to a simple algorithm of OLS regressions that is much more reliable. When there are more assets than returns, however, OLS becomes unstable. Gramacy, et al. (2008), showed how classical shrinkage regression may be used instead, thus extending the state of the art to much bigger asset collections, with further accuracy and interpretation advantages. In this paper, we detail a fully Bayesian hierarchical formulation that extends the framework further by allowing for heavy-tailed errors, relaxing the historical missingness assumption, and accounting for estimation risk. We illustrate how this approach compares favorably to the classical one using synthetic data and an investment exercise with real returns. An accompanying R package is on CRAN.