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.

We analyze the optimal portfolio policy for a multiperiod mean–variance investor facing multiple risky assets in the presence of general transaction costs. For proportional transaction costs, we give a closed-form expression for a no-trade region, shaped as a multi-dimensional parallelogram, and show how the optimal portfolio policy can be efficiently computed for many risky assets by solving a single quadratic program. For market impact costs, we show that at each period it is optimal to trade to the boundary of a state-dependent rebalancing region. Finally, we show empirically that the losses associated with ignoring transaction costs and behaving myopically may be large.

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.

Machine-learning methods exploit fund characteristics to select tradable long-only portfolios of mutual funds that earn significant out-of-sample annual alphas of 2.4% net of all costs. The methods unveil interactions in the relation between fund characteristics and future performance. For instance, past performance is a particularly strong predictor of future performance for more active funds. Machine learning identifies managers whose skill is not sufficiently offset by diseconomies of scale, consistent with informational frictions preventing investors from identifying the outperforming funds. Our findings demonstrate that investors can benefit from active management, but only if they have access to sophisticated prediction methods.