We carry out a comprehensive investigation of shrinkage estimators for asset allocation, and we find that size matters—the shrinkage intensity plays a significant role in the performance of the resulting estimated optimal portfolios. We study both portfolios computed from shrinkage estimators of the moments of asset returns (shrinkage moments), as well as shrinkage portfolios obtained by shrinking the portfolio weights directly. We make several contributions in this field. First, we propose two novel calibration criteria for the vector of means and the inverse covariance matrix. Second, for the covariance matrix we propose a novel calibration criterion that takes the condition number optimally into account. Third, for shrinkage portfolios we study two novel calibration criteria. Fourth, we propose a simple multivariate smoothed bootstrap approach to construct the optimal shrinkage intensity. Finally, we carry out an extensive out-of-sample analysis with simulated and empirical datasets, and we characterize the performance of the different shrinkage estimators for portfolio selection.

ABSTRACT Moreira and Muir question the existence of a strong risk‐return trade‐off by showing that investors can improve performance by reducing exposure to risk factors when their volatility is high. However, Cederburg et al. show that these strategies fail out‐of‐sample, and Barroso and Detzel show they do not survive transaction costs. We propose a conditional multifactor portfolio that outperforms its unconditional counterpart even out‐of‐sample and net of costs. Moreover, we show that factor risk prices generally decrease with market volatility. Our results demonstrate that the breakdown of the risk‐return trade‐off is more puzzling than previously thought.

We propose a formal statistical test to compare asset-pricing models in the presence of price impact. In contrast to the case without trading costs, we show that in the presence of price-impact costs different models may be best at spanning the investment opportunities of different investors depending on their absolute risk aversion. Empirically, we find that the five-factor model of Hou et al. (2021), the six-factor model of Fama and French (2018) with cash-based operating profitability, and a high-dimensional model are best at spanning the investment opportunities of investors with high, medium, and low absolute risk aversion, respectively.

Abstract We study the impact of parameter uncertainty on the expected utility of a multiperiod investor subject to quadratic transaction costs. We characterize the utility loss associated with ignoring parameter uncertainty, and show that it is equal to the product between the single-period utility loss and another term that captures the effects of the multiperiod mean-variance utility and transaction cost losses. To mitigate the impact of parameter uncertainty, we propose two multiperiod shrinkage portfolios and demonstrate with simulated and empirical data sets that they substantially outperform portfolios that ignore parameter uncertainty, transaction costs, or both.

Abstract We investigate how transaction costs change the number of characteristics that are jointly significant for an investor’s optimal portfolio and, hence, how they change the dimension of the cross-section of stock returns. We find that transaction costs increase the number of significant characteristics from 6 to 15. The explanation is that, as we show theoretically and empirically, combining characteristics reduces transaction costs because the trades in the underlying stocks required to rebalance different characteristics often cancel out. Thus, transaction costs provide an economic rationale for considering a larger number of characteristics than that in prominent asset-pricing models. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.