  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.
