“…Our findings about the upward bias of the low-frequency measures raise questions about their suitability for optimal portfolio choice problems with transaction costs, where the so-called no-trade region is a function of the level of transaction costs (Constantinides, 1986), and for evaluation of trading strategies and asset pricing anomalies, where small changes in transaction costs have a large impact on performance (Novy-Marx and Velikov, 2015, Chen and Velikov, 2018, and Patton and Weller, 2018. The dependence of the lowfrequency measures on volatility limits their use in studies of the commonality in liquidity, where liquidity proxies are used to measure co-movements in liquidity across assets and markets (Chordia, Roll, and Subrahmanyam, 2000, Hasbrouck and Seppi, 2001, Korajczyk and Sadka, 2008, Karolyi, Lee, and Van Dijk, 2012, Mancini, Ranaldo, and Wrampelmeyer, 2013. In all of these applications, using imperfect proxies for transaction costs can lead to suboptimal financial decisions.…”