This study provides an explanation for the emergence of power laws in asset trading volume and returns. We consider a two-state model with binary actions, where traders infer other traders' private signals regarding the value of an asset from their actions and adjust their own behavior accordingly. We prove that this leads to power laws for equilibrium volume and returns whenever the number of traders is large and the signals for asset value are sufficiently noisy. We also provide numerical results showing that the model reproduces observed distributions of daily stock volume and returns.