## Bayesian Analysis

### Shrinkage regression for multivariate inference with missing data, and an application to 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.

#### Article information

Source
Bayesian Anal. Volume 5, Number 2 (2010), 237-262.

Dates
First available in Project Euclid: 20 June 2012

https://projecteuclid.org/euclid.ba/1340218338

Digital Object Identifier
doi:10.1214/10-BA602

Mathematical Reviews number (MathSciNet)
MR2719652

Zentralblatt MATH identifier
1330.91185

#### Citation

Gramacy, Robert B.; Pantaleo, Ester. Shrinkage regression for multivariate inference with missing data, and an application to portfolio balancing. Bayesian Anal. 5 (2010), no. 2, 237--262. doi:10.1214/10-BA602. https://projecteuclid.org/euclid.ba/1340218338.

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