We introduce a model for stock prices consisting of a fundamental price process and a news impact curve, which allows for either overreaction, underreaction, or correct response to changes of the fundamental value. We further develop statistics based on OHLC data, which separately measure upside and downside overreaction. The distribution of these statistics under the hypothesis of correct response and fundamental prices following Brownian motions is used to derive tests for upside and downside overreaction. We show that more realistic and frequently used fundamental price processes with correct response leave the distribution of the test statistics widely unaffected or lead to conservative tests. Empirical application to different stock markets provides strong evidence for intraday overreaction, particularly to bad news. The economic significance of the discrimination induced by the proposed statistics is further illustrated by analyzing the performance of a simple buy on bad news strategy.