A bell-shaped normal distribution curve representing the density of timing t-statistics. The x-axis represents the t-statistic values ranging from negative twenty to twenty, and the y-axis represents the density values ranging from zero to zero point one six. The curve peaks around zero, indicating the highest density of t-statistics near this value. Two vertical dashed lines mark the t-statistic values of negative one point nine six and one point nine six, with corresponding percentages of twelve point six two percentage and twenty one point six eight percentage, respectively. The shaded area under the curve highlights the central region of the distribution. The sample size is three hundred nine.Kernel density of t-statistics of stock-selection timing coefficients. Note: The kernel density of the cross-sectional distribution of the Newey-West t-statistics of the stock-selection timing coefficients is plotted in the figure above. The stock-selection timing coefficients gi are estimated using the following cross-sectional equation: ACTi,t = ci + giSSOt+1 + εi,t+1, where ACTi,t denotes the active share in monthly period t and SSOt+1 represents the stock-selection opportunity in period t+1. Active share is defined according to Cremers and Petajisto (2009). To measure stock-selection opportunity, we calculate the average positive alpha value estimated from daily returns during period t+1 using the model described in Eq. (4). The t-statistics are corrected for heteroskedasticity and autocorrelation using the Newey and West (1987) method. The sample period spans from January 1, 2012, to December 31, 2024