Note(s): We adopted an overlapping method with a 12-month estimation period and a rolling frequency of 1 month to obtain monthly loadings. Specifically, during the initial 12-month sample period, we perform time-series monthly regressions following the model outlined in equation (1) to derive the cross-section of $βTMBO$⁠. This process was repeated for the subsequent 12-month period until the end of the sample period. Consequently, we obtained monthly $βTMBO$ values for each stock. These estimated $βTMBO$ values are then employed to classify stocks into quintile portfolios, and the value-weighted averages of these $βTMBO$ values are presented in the column labeled pre-ranking $βTMBO$⁠. The portfolios are reclassified on a monthly basis. Once the portfolios are formed, we calculate the value-weighted average excess and abnormal returns for each quintile portfolio one month after the formation date. We computed the time-series averages for each portfolio. Additionally, we estimate the loadings on the left-tail factor during the same period to calculate the average excess returns, aiming to explore any contemporaneous patterns between them. The post-ranking $βTMBO$ for the entire sample was estimated by conducting time-series monthly regressions of the post-ranking portfolio returns on the left-tail factor. The t-statistics are shown in parentheses. ***, ** and * indicate the 1%, 5% and 10% statistical significance, respectively

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