We investigate odd‐lot trades in equity markets. Odd lots are increasingly used in algorithmic and high‐frequency trading, but are not reported to the consolidated tape or in databases such as TAQ. In our sample, the median number of odd‐lot trades is 24% but in some stocks odd lots are 60% or more of trading. Odd‐lot trades contribute 35% of price discovery, consistent with informed traders using odd lots to avoid detection. Omitting odd‐lot trades leads to inaccuracies in order imbalance measures and makes sentiment measures unreliable. Excluding odd lots from the consolidated tape raises important regulatory issues.

We study how firms allocate cash flow by estimating the cash-flow sensitivities of various uses of cash flow. We decompose cash flow into a transitory and a permanent component and focus on the allocation of the transitory component, which by construction contains little information about future growth opportunities. We find that more financially constrained firms allocate more transitory cash flow to cash savings and direct less toward investment than do less constrained firms, consistent with constrained firms accumulating liquidity to buffer against future financial constraints. We also illustrate several methodological advantages of our approach over alternative methods in previous studies.

There is a long-standing debate on whether sell-side analysts learn from their experience to improve earnings forecast skills. This study shows that incentive is an important factor for understanding the “learning by doing” effect by analysts. We examine analysts’ response to a complex type of information – corporate pension underfunding. Pension underfunding negatively impacts future earnings and analysts on average underreact to such information in their earnings forecasts. More importantly, when there is a strong incentive for analysts to deliver accurate forecasts, analyst learning effectively reduces their underreaction to pension underfunding information. On the other hand, when such an incentive is absent, the analyst learning effect is not discernible in the data. Further evidence suggests that analyst learning and incentive jointly reduce stock market mispricing associated with corporate pension underfunding.