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Abstract:
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Portfolio balancing requires estimates of covariance between asset returns, whose histories can greatly vary in length. Such data are said to follow a monotone missingness pattern, which leads to a convenient factorization of the likelihood. Under an MVN assumption, MLEs and samples from a Bayesian posterior are obtained by repeated OLS regression, one for each asset. When there are more assets than historical returns, however, OLS becomes unstable. We explore remedies that apply shrinkage, like ridge regression or the lasso, which have a natural Bayesian implementation, and can offer improvements in accuracy and interpretation. We compare the ML and Bayesian approaches with others, including PCR, via an investment exercise on financial return data. We discuss the appropriateness of the MVN assumption and show how external factors can be easily incorporated in this setting.
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