This study investigates the liquidation of a portfolio when there is delayed information such as prices and trading signals. Its motivation stems from the calendar-time effect of information or the momentum effect on market prediction. When the stock price series is modeled by high-order vector autoregressive models, it converges to a system of stochastic delay differential equations in a continuous-time economy. The optimal solution indicates that the agent should trade gradually toward a path-dependent target portfolio to minimize execution costs. We numerically show a surprising novel pattern in which the agent with a liquidation mission sometimes purchases assets first to take advantage of the price predictability stemming from the delay effect. Moreover, optimally utilizing the delay effect has impacts on the time synchronization of trading in different assets and leads to significant cost reduction when the initial market trend is informative. Copyright © 2023 Elsevier B.V. All rights reserved.