We show that a linear pure strategy equilibrium may not exist in the model of Madrigal (1996), contrary to the claim of the original paper. This is because Madrigal's characterization of a pure strategy equilibrium omits a second‐order condition. If the nonfundamental speculator's information about noise trading is sufficiently precise, a linear pure strategy equilibrium fails to exist. In parameter regions where a pure strategy equilibrium does exist, we identify a few calculation errors in Madrigal (1996) that result in misleading implications.