A Shrinkage Theory of Asset Allocation Using Asset-pricing Models

Abstract

This paper develops a shrinkage theory of asset allocation using asset-pricing models and provides insights into the recently developed Bayesian framework that uses informative prior distributions of Jensen's alpha. Each informative prior distribution of Jensen's alpha is shown to imply a shrinkage factor, which indicates the relative weight between the model and the data and thus measures the model's impact on asset allocation. The shrinkage factor is a function of four variables: the prior variance of Jensen's alpha, the sample size, the highest Sharpe ratio of the factor portfolios and the average variance of the residual terms in the regression of asset returns on the factors. The shrinkage theory explains why a asset-pricing model's impact on asset allocation is often weak unless the prior variance of Jensen's alpha is small. The empirical Bayes approach, in which the prior variance of Jensen's alpha is estimated from the observed data, is shown to assign equal weights to the model and the data so that they have equal impact on asset allocation. The shrinkage theory also provides a unified understanding of the different approaches in studies of international diversification. Inference about the magnitude of diversification benefits is found to be heavily influenced by economists' prior belief in the world version of the capital asset-pricing model.