Portfolio Choice and Estimation Risk. A Comparison of Bayesian to Heuristic Approaches

Herold, Ulf 
Maurer, Raimond 

ASTIN Bulletin International Actuarial Association - Brussels, Belgium
2006: Vol. 36, No. 1
135-160
http://www.casact.org/library/astin/vol36no1/135.pdf 

Abstract
Estimation risk is known to have a huge impact on mean/variance optimized portfolios, which is one of the primary reasons to make standard Markowitz optimization unfeasible in practice. This issue has attracted new interest in the last years, and several approaches to incorporate estimation risk into portfolio selection have been developed only recently. In this article, we review these approaches as well as some older ones and compare them in an empirical out-of-sample study. The approaches can be classified along two criteria. First, we can differentiate heuristic approaches (restricting portfolio weights and employing simulation techniques) and those based on Bayesian statistics (shrinking the portfolios towards a pre-determined target). Second, the assumptions about the return-generating process differ, either assuming returns to the IID distributed or to be partly predictable. The central result of our empirical study is that all of the IID approaches, whether they account for estimation risk or not, are not superior to simple investment strategies like holding the market portfolio. A risk-adjusted outperformance is possible only if sample means are substituted with conditional expected return estimates. Furthermore, the Bayesian approaches reduce turnover and stabilize portfolio weights. 

KEYWORDS: Portfolio selection, estimation risk, predictive regressions. 