2009/07/13 by Robert B. Gramacy, Ester Pantaleo, Gramacy, Robert B. +1
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Applications (stat.AP) #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Statistical Methods and Inference #Stock Market Forecasting Methods
paper · pdf · doi:10.48550/arxiv.0907.2135
openalex publication_date 2009/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Portfolio balancing requires estimates of covariance between asset returns.\nReturns data have histories which greatly vary in length, since assets begin\npublic trading at different times. This can lead to a huge amount of missing\ndata--too much for the conventional imputation-based approach. Fortunately, a\nwell-known factorization of the MVN likelihood under the prevailing historical\nmissingness pattern leads to a simple algorithm of OLS regressions that is much\nmore reliable. When there are more assets than returns, however, OLS becomes\nunstable. Gramacy, et al. (2008), showed how classical shrinkage regression may\nbe used instead, thus extending the state of the art to much bigger asset\ncollections, with further accuracy and interpretation advantages. In this\npaper, we detail a fully Bayesian hierarchical formulation that extends the\nframework further by allowing for heavy-tailed errors, relaxing the historical\nmissingness assumption, and accounting for estimation risk. We illustrate how\nthis approach compares favorably to the classical one using synthetic data and\nan investment exercise with real returns. An accompanying R package is on CRAN.\n