This paper provides new evidence concerning the probability of informed trading (PIN) and the PIN-return relationship. We take measures to overcome known estimation biases and improve the quality of quarterly PIN estimates. We use the average of a firm’s PIN estimates in four consecutive quarters to smooth out the effect of seasonal variation in trading activities. We find that when high-quality PIN estimates are used, the Fama–MacBeth cross-sectional regressions show stronger evidence for the positive PIN-return relationship than documented in the prior literature. This finding is robust to controls for the January, liquidity, and momentum effects.

We report evidence that boundary solutions can cause a bias in the estimate of the probability of informed trading (PIN). We develop an algorithm to overcome this bias and use it to estimate PIN for nearly 80,000 stock-quarters between 1993 and 2004. We obtain two sets of PIN estimates by using the factorized likelihood functions in both Easley et al., 2010, Lin and Ke, 2011, respectively. We find that the estimate based on the EHO factorization is systematically smaller than the estimate based on the LK factorization, meaning that there is a downward bias associated with the EHO factorization. In addition, we find that boundary solutions appear with a very high frequency when the LK factorization is used. Thus it is necessary to use the LK factorization together with the algorithm in this paper. At last, we document several interesting empirical properties of PIN.

We examine stock trading activities in days before Chinese listed firms made public announcement to start share-structure reform. There is significant evidence that, relative to a benchmark period, institutional investors bought more event firms’ shares in the last two trading days prior to announcement. Randomization tests show significant differences in institutional trading activities between event firms and matched control firms, which suggests that some institutions had inside information. Moreover, large trades account for a significant proportion of daily stock price changes in the last 2days. The evidence is consistent with the prediction by Holden and Subrahmanyam (1992) that, when multiple informed investors acquire the same piece of information, they will trade aggressively. We also find that over the reform period, the median share value change of event firms is 6% higher than that of control firms. Our findings have important implications for enforcement of insider trading regulations in China.