This paper examines the price effects after one-day abnormal returns in stock markets indices of both developed and emerging while differentiating between Environmental, social, and governance (ESG) and conventional indices. Using daily data of MSCI family indices over the period 2007-2020. Using various methods to avoid methodological bias, the following hypotheses are tested: after one-day abnormal returns specific price effects (momentum/contrarian) do appear (H1) for the case of positive (H1.1) and negative (H1.2) returns; price effects after one-day abnormal returns are stronger for the case of traditional indices compared to ESG indices (H2); price effects after one-day abnormal returns are stronger during the crisis period (H3); dynamic trigger approach is more appropriate to define abnormal returns than static (H4); price effects after one-day abnormal returns are stronger for emerging markets compared to developed ones (H5). The results are mixed for the case of H1 and provide no evidence in favor of H2-H5. They do not exhibit significant differences between ESG and conventional indices. Types of detected effects are the same; in some cases, the power of the effects is different, but not significantly, and no patterns in these differences are detected. Overall, there is a strong contrarian effect in the US stock market after one-day abnormal returns. A trading strategy constructed based on this effect can generate profits from trading. The main results give additional evidence against the Efficient Market Hypothesis and provide implications that can help practitioners in beating the market.