This article extends the parametric portfolio policy approach to optimizing portfolios with a large numbers of assets (Brandt et al. 2009). The proposed approach incorporates unobserved effects into the portfolio policy function. These effects measure the importance of unobserved heterogeneity for exploiting the difference between groups of assets. The source of the heterogeneity is local priced factors, such as industry or country. The statistical model allows testing the importance of such local factors in portfolio optimization. The results suggest that local effects or return heterogeneity associated with economic sectors or geographic factors is not as straightforward to exploit financially or as relevant as suggested by the extensive multivariate factor literature on the subject. Furthermore, trying to exploit industry effects rarely provides a gain over simple benchmarks, neither in-sample nor more importantly, out-of-sample. On the other hand, exploiting country effects does provide gains over the benchmark. However, these gains may be offset by the increasing cost of and risk inherent in such strategies. Finally, exploiting size, momentum, and liquidity anomalies in the cross-section of stocks provides strictly greater returns than the industry and country effects.
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