A. A Simple Model

We develop our testable hypotheses by relying on a simple model of insider trading with an insider who possesses short-term information (i.e., information stemming from mispricing, arising after misinterpretation of a public announcement by the market) and long-term information (i.e., foreknowledge of material private information). The insider trades along with arbitrageurs who possess only the short-term information. We assume that the long-term information is truly private: it is undisclosed, price-sensitive, and in possession exclusively by the insider. The insider could be prosecuted if trading on this long-term information. The short-term information is also available to arbitrageurs because they have a superior ability to process public news releases relative to the rest of the market. Anybody who can do this would be classified as an arbitrageur in our model. Trading on the short-term information is not illegal because it is based on public information.

In order to test our research question of whether insiders (illegally) trade on foreknowledge of long-term material information, we derive two benchmarks and formulate testable predictions corresponding to each benchmark. In the first benchmark, we assume that the insider manager abstains from trading based on the long-term information to avoid legal prosecution, and denote it the “No-Long-term-Information” ( $ NLI $ ) benchmark. In the second benchmark, denoted as the “All-Information” ( $ AI $ ) benchmark, we assume that the insider trades optimally by taking into account both the short-term and long-term information. This benchmark shows insider trading patterns in the limiting case when the insider does not care about prosecution.

The market is populated by four types of market participants: a competitive market maker, a single insider trader, $ n $ identical arbitrageurs, and a group of liquidity traders. The model has three periods, which we index as $ t\in \left\{\mathrm{1,2,3}\right\} $ . Consider a firm with an initial fundamental value of $ {v}_0 $ , which is publicly known. We assume that the firm has one share of stock outstanding and its price is $ {p}_0={v}_0 $ . The insider initially holds $ \eta $ shares. In period 1, the insider and arbitrageurs learn that the fundamental value of the firm changes from the initial $ {v}_0 $ to $ {v}_0+{v}_1 $ , where $ {v}_1\sim N\left(0,{\sigma}^2\right) $ . Here, $ {v}_1 $ innovation represents the short-term information. The market maker knows only the distribution of $ {v}_1 $ . Moreover, in period 1, the insider also learns that the fundamental firm value will change from $ {v}_0+{v}_1 $ to $ {v}_0+{v}_1+{v}_2 $ , where $ {v}_2\sim N\left(0,{\sigma}^2\right) $ . Here, $ {v}_2 $ innovation represents the long-term information. We assume that $ {v}_1 $ and $ {v}_2 $ are independent.Footnote ⁷ The information about the realization of $ {v}_2 $ is not available to the arbitrageurs in period 1; they can only observe the distribution of $ {v}_2 $ . In period 2, the value of $ {v}_2 $ becomes known to the arbitrageurs but not to the market maker. This means that the long-term information becomes after some time known to some market participants, in addition to the insider. In period 3, the firm is liquidated and the dividends are paid to all shareholders at price $ {p}_3={v}_0+{v}_1+{v}_2 $ .

In periods 1 and 2, some liquidity traders need to trade $ {u}_1 $ and $ {u}_2 $ shares of the stock to cover their private liquidity shocks, with $ {u}_t\sim N\left(0,{\sigma}_u^2\right) $ , $ t=1,2 $ . We assume that variables $ {u}_1 $ , $ {u}_2 $ , $ {v}_1 $ and $ {v}_2 $ are mutually independent and that the two types of informed traders experience liquidity shocks during both periods. That is, at the beginning of period $ t $ , for $ t=1,2 $ , the insider receives an endowment shock $ {w}_t^i\sim N\left(0,{\sigma}_w^2\right) $ and each arbitrageur receives $ {w}_t^a\sim N\left(0,{\sigma}_w^2\right) $ .Footnote ⁸

The $ NLI $ benchmark assumes the insider chooses not to trade upon signal $ {v}_2 $ due to being afraid to be prosecuted by the regulator. In contrast, the $ AI $ benchmark assumes that the insider takes signal $ {v}_2 $ fully into account and strategically trades based on both $ {v}_1 $ and $ {v}_2 $ pieces of information. Given that the insider and arbitrageurs know $ {v}_1 $ and $ {v}_2 $ in period 2 in both benchmarks, the derivation for period 2 price and demands is identical. The two benchmarks have different implications only for period 1 prices and quantities.

Let $ {\zeta}_1 $ and $ {\zeta}_2 $ denote the number of shares traded by the insider in periods 1 and 2, respectively, and let $ {\xi}_{1j} $ and $ {\xi}_{2j} $ denote the number of shares traded by arbitrageur $ j $ in period 1 and 2, respectively. The insider optimally trades $ {\zeta}_1 $ and $ {\zeta}_2 $ shares to maximize his consumption

(1) $$ {C}^i=\left({\zeta}_1+{\zeta}_2+\eta \right){p}_3-{\zeta}_1{p}_1-{\zeta}_2{p}_2, $$

where $ {p}_t $ refers to the price of the stock in period $ t $ . Similarly, each arbitrageur $ j $ trades optimally $ {\xi}_{1j} $ and $ {\xi}_{2j} $ shares in periods 1 and 2 by maximizing his consumption

(2) $$ {C}_j^a=({\xi}_{1j}+{\xi}_{2j}){p}_3-{\xi}_{1j}{p}_1-{\xi}_{2j}{p}_2,\hskip1em j=1,\dots, n. $$

In period 2, before the trading occurs, the market observes $ {p}_1 $ , which is the last period’s trading price. Given the linear pricing rule, Proposition 1 characterizes the equilibrium price in period 2 and the arbitrageurs’ orders. All proofs are in the Supplementary Material.

Proposition 1 ( $ NLI $ and $ AI $ benchmarks). In period 2, the pricing rule and the demands are:

(3) $$ {\displaystyle \begin{array}{c}{p}_2={p}_1+{\lambda}_2{x}_2,\\ {}{\zeta}_2=\frac{v_2+{v}_1+{v}_0-{p}_1}{\lambda_2(n+2)}+\frac{w_2^i}{2},\\ {}{\xi}_{2j}=\frac{v_2+{v}_1+{v}_0-{p}_1}{\lambda_2(n+2)}+\frac{w_{2j}^a}{2},\hskip1em j=1,\dots, n,\end{array}} $$

where $ {x}_2={\zeta}_2+{\sum}_{j=1}^n{\xi}_{2j}+{u}_2 $ is the total order imbalance in period 2 and the price impact $ {\lambda}_2 $ is

(4) $$ {\lambda}_2=\sqrt{\frac{\left(n+1\right)}{{\left(n+2\right)}^2}}\left(\frac{{\tilde{\sigma}}^2}{\frac{n{\sigma}_w^2}{2}+{\sigma}_u^2}\right),\hskip1em {\tilde{\sigma}}^2=\mathit{\operatorname{var}}\left[{v}_1+{v}_2|{p}_1\right]. $$

Proposition 2 characterizes the equilibrium price and the insider’s and arbitrageurs’ orders in period 1 in the $ NLI $ benchmark—when the insider ignores the information about $ {v}_2 $ in period 1.

Proposition 2 ( $ NLI $ benchmark). Suppose that the insider ignores information about $ {v}_2 $ . The pricing rule and the insider’s and each arbitrageur’s orders in period 1 are:

(5) $$ {\displaystyle \begin{array}{c}{p}_1={p}_0+{\lambda}_1{x}_1,\\ {}{\zeta}_1={\beta}_1{v}_1+{\delta \lambda}_1{w}_1^i,\\ {}{\xi}_{1j}={\beta}_1{v}_1+{\delta \lambda}_1{w}_{1j}^a,\hskip3em j=1,\dots, n,\end{array}} $$

where $ {x}_1={\zeta}_1+{\sum}_{j=1}^n{\xi}_{1j}+{u}_1 $ denotes the total order imbalance in period 1, the parameters $ {\beta}_1 $ , $ \delta $ and $ {\lambda}_1 $ solve the system of equations:

(6) $$ {\displaystyle \begin{array}{c}{\lambda}_1=\frac{\left(n+1\right){\beta}_1{\sigma}^2}{{\left(n+1\right)}^2{\beta}_1^2{\sigma}^2+n{\delta}^2{\lambda}_1^2{\sigma}_w^2+{\sigma}_u^2},\\ {}{\beta}_1=\frac{1-2{\alpha \lambda}_1}{\lambda_1\left(n+2-2{\alpha \lambda}_1\left(n+1\right)\right)},\\ {}\delta =\frac{1-2{\alpha \lambda}_1}{2{\lambda}_1\left(1-{\alpha \lambda}_1\right)},\hskip3em \alpha =\frac{1}{{\left(n+2\right)}^2{\lambda}_2},\end{array}} $$

and $ {\lambda}_2 $ is as given in equation (4).

Finally, Proposition 3 characterizes the equilibrium price and the insider’s and arbitrageurs’ orders in period 1 in the $ AI $ benchmark—under the assumption that the insider does not ignore $ {v}_2 $ and strategically trades on this information in period 1.

Proposition 3 ( $ AI $ benchmark). Suppose that the insider conditions his demand on knowledge of $ {v}_2 $ , then the pricing rule and the insider’s and each arbitrageur’s orders in period 1 are:

(7) $$ {\displaystyle \begin{array}{c}{p}_1={p}_0+{\lambda}_1{x}_1,\\ {}{\zeta}_1={\beta}_1{v}_1+\delta {v}_2+{\delta \lambda}_1{w}_1^i,\\ {}{\xi}_{1j}={\beta}_1{v}_1+{\delta \lambda}_1{w}_{1j}^a,\hskip1em j=1,\dots, n\end{array}} $$

where $ {x}_1={\zeta}_1+{\sum}_{j=1}^n{\xi}_{1j}+{u}_1 $ denotes the total order imbalance in period 1, and the parameters $ {\lambda}_1 $ , $ {\beta}_1 $ , and $ \delta $ solve the system equations:

(8) $$ {\displaystyle \begin{array}{c}{\lambda}_1=\frac{\left(\left(n+1\right){\beta}_1+\delta \right){\sigma}^2}{\left({\left(n+1\right)}^2{\beta}_1^2+{\delta}^2\right){\sigma}^2+n{\delta}^2{\lambda}_1^2{\sigma}_w^2+{\sigma}_u^2},\\ {}{\beta}_1=\frac{1-2{\alpha \lambda}_1}{\lambda_1\left(n+2-2{\alpha \lambda}_1\left(n+1\right)\right)},\\ {}\delta =\frac{1-2{\alpha \lambda}_1}{2{\lambda}_1\left(1-{\alpha \lambda}_1\right)},\hskip3em \alpha =\frac{1}{{\left(n+2\right)}^2{\lambda}_2},\end{array}} $$

and $ {\lambda}_2 $ is as given in equation (4).

B. Hypotheses

In this section, we develop testable hypotheses based on the predictions derived for the two benchmarks. From now on, we set $ {p}_0=0 $ and define returns as price changes. We are interested in $ {r}_{1,3}={p}_3-{p}_1 $ , the long-term future return after the insider and arbitrageurs learn their private information. As the long-term information is observed only by the insider, we contrast return sensitivities to insider’s and arbitrageurs’ demands to determine whether the insider does or does not trade based on foreknowledge of future material information. We denote the observed insider’s demand after he/she learns the short-term and long-term information as $ {\zeta}_1 $ and the observed aggregate demand of the arbitrageurs after they learn the short-term information as $ {\xi}_1={\sum}_{j=1}^n{\xi}_{1j} $ .

To examine the sensitivities between the demands of the two types of informed traders and future stock returns, we consider three different tests. First, we consider return sensitivities of insider’s and arbitrageurs’ demands as reflected in coefficients $ b $ and $ c $ in equation (9). Second, we differentiate the signs of insider’s and arbitrageurs’ demands and consider their interactions. Equation (10) regresses returns on a set of dummy variables interacting the direction of each type’s net demand (e.g., $ {\unicode{x1D540}}_{\zeta_1>0,{\xi}_1<0} $ treats the case when the insider buys and arbitrageurs sell). Finally, equation (11) considers the sensitivities of the insider’s demand to the short-term and long-term information and complements the return equations.

(9) $$ {r}_{1,3}={b}_0+b{\zeta}_1+c{\xi}_1+\unicode{x025B} $$

(10) $$ {r}_{1,3}={b}_{++}{\unicode{x1D540}}_{\zeta_1>0,{\xi}_1>0}+{b}_{+-}{\unicode{x1D540}}_{\zeta_1>0,{\xi}_1<0}+{b}_{-+}{\unicode{x1D540}}_{\zeta_1<0,{\xi}_1>0}+{b}_{--}{\unicode{x1D540}}_{\zeta_1<0,{\xi}_1<0}+\unicode{x025B} $$

(11) $$ {\zeta}_1={d}_{++}{\unicode{x1D540}}_{v_1>0,{v}_2>0}+{d}_{+-}{\unicode{x1D540}}_{v_1>0,{v}_2<0}+{d}_{-+}{\unicode{x1D540}}_{v_1<0,{v}_2>0}+{d}_{--}{\unicode{x1D540}}_{v_1<0,{v}_2<0}+\unicode{x025B} $$

In order to evaluate signs and relative magnitudes of the demand sensitivities on future returns (coefficients $ b $ and $ c $ in equation (9)), we solve the model numerically. Figure 1 presents the values of coefficients $ b $ and $ c $ as predicted by the two benchmarks for $ {\sigma}_v^2/{\sigma}_u^2=1 $ , $ {\sigma}_v^2/{\sigma}_w^2=1 $ and $ n=3 $ .Footnote ⁹

Figure 1Sensitivity of Future Returns to Order Flows

Figure 1 plots the values of sensitivity coefficients $ b $ and $ c $ of future returns $ {r}_{1,3} $ on insider’s and informed traders’ demands $ {\zeta}_1 $ and $ {\xi}_1 $ , respectively. The coefficients are computed based on the multivariate regression $ {r}_{1,3}={b}_0+b{\zeta}_1+c{\xi}_1+\unicode{x025B} $ . Graph A corresponds to the $ NLI $ benchmark of the model and Graph B corresponds to the $ AI $ benchmark. The primitive parameters are: $ {\sigma}_v^2/{\sigma}_u^2={\sigma}_v^2/{\sigma}_w^2=1 $ and $ n=3 $ . The remaining parameters are computed numerically by solving the system of equations (6) and (8) for the $ NLI $ and $ AI $ benchmark, respectively.

Figure 1 Long description

A two-panel bar chart. Both panels share a y-axis ranging from negative 0.2 to 0.7 with increments of 0.1. The x-axis for both panels contains two categories: b and c.

Graph A, titled N L I Benchmark, shows two small positive bars of equal height. Bar b and bar c both reach approximately 0.05 on the y-axis.

Graph B, titled A I Benchmark, shows much larger values with opposing directions. Bar b is a tall positive bar reaching approximately 0.65. Bar c is a negative bar extending downward to approximately negative 0.2.

In the $ NLI $ benchmark, both types of informed traders use only the short-term information $ {v}_1 $ , which positively correlates with the long-term fundamental value $ {v}_0+{v}_1+{v}_2 $ . This means that the demands of both types of traders positively predict future stock returns. If insiders trade also on the long-term information $ {v}_2 $ , as in the $ AI $ benchmark, arbitrageurs are able to predict future returns relatively less well, and therefore the coefficient $ c $ is negative. When both $ {v}_1 $ and $ {v}_2 $ are either positive or negative, the arbitrageurs’ prediction has a correct sign. However, when $ {v}_1 $ and $ {v}_2 $ have opposite signs, arbitrageurs’ demands and future returns are negatively correlated. On average, the negative correlation in the latter case dominates the positive correlation in the former case, and the overall effect, as reflected in the coefficient $ c $ , is negative. In summary, our first hypothesis highlights the relative informational advantage of the insider over arbitrageurs. We formulate a null hypothesis and two alternative hypotheses corresponding to the two benchmarks.

Figure 2 provides predictions for categorical rather than continuous demand variables as reflected in equation (10)), assuming $ {\sigma}_v^2/{\sigma}_u^2=1 $ , $ {\sigma}_v^2/{\sigma}_w^2=1 $ , and $ n=3 $ . We consider separately demand sensitivities when the insider and arbitrageurs both buy or sell ( $ {b}_{++} $ and $ {b}_{--} $ ) versus when their demands have opposite signs ( $ {b}_{+-} $ and $ {b}_{-+} $ ).

Figure 2Future Expected Returns Conditional on Signs of Order Flows

Figure 2 plots the expectations of future returns $ {r}_{1,3} $ conditional on signs of order flow variables $ {\zeta}_1 $ and $ {\xi}_1 $ . Coefficient $ {b}_{++} $ , $ {b}_{+-} $ , $ {b}_{-+} $ and $ {b}_{--} $ are computed based on the multivariate regression $ {r}_{1,3}={b}_{++}{\unicode{x1D540}}_{\zeta_1>0,{\xi}_1>0}+{b}_{+-}{\unicode{x1D540}}_{\zeta_1>0,{\xi}_1<0}+{b}_{-+}{\unicode{x1D540}}_{\zeta_1<0,{\xi}_1>0}+{b}_{--}{\unicode{x1D540}}_{\zeta_1<0,{\xi}_1<0}+\unicode{x025B} $ . The primitive parameters are: $ {\sigma}_v^2/{\sigma}_u^2={\sigma}_v^2/{\sigma}_w^2=1 $ and $ n=3 $ . The remaining parameters are computed numerically by solving the system of equations (6) and (8) for the $ NLI $ and $ AI $ benchmark.

Figure 2 Long description

The image consists of two side-by-side bar charts. Both charts share a Y-axis ranging from negative 0.5 to 0.5 with increments of 0.1. The X-axis for both charts lists four variables: b sub plus plus, b sub plus minus, b sub minus plus, and b sub minus minus.

Graph A, titled N L I Benchmark, shows relatively low magnitude coefficients. The first bar, b sub plus plus, is positive at approximately 0.13. The second bar, b sub plus minus, is slightly negative at approximately negative 0.03. The third bar, b sub minus plus, is slightly positive at approximately 0.03. The fourth bar, b sub minus minus, is negative at approximately negative 0.13.

Graph B, titled A I Benchmark, shows significantly higher magnitude coefficients. The first bar, b sub plus plus, is positive at approximately 0.36. The second bar, b sub plus minus, is positive at approximately 0.46. The third bar, b sub minus plus, is strongly negative at approximately negative 0.46. The fourth bar, b sub minus minus, is negative at approximately negative 0.36.

Both benchmarks imply that whenever insider’s and arbitrageurs’ demands have the same sign, demands of the two types correctly forecast the future return: $ {b}_{++} $ is positive and $ {b}_{--} $ is negative. However, in the case of opposite signs of insider’s and arbitrageurs’ demands, the $ NLI $ benchmark predicts that the expected future stock return is positive whenever the arbitrageurs’ aggregate demand is positive and vice versa: $ {b}_{-+} $ is positive, while $ {b}_{+-} $ is negative. The higher predictive power of arbitrageurs’ demand stems from the fact that their demands are aggregated over $ n $ arbitrageurs and the noise in the arbitrageurs’ demands, which is due to independent shocks to their initial endowments, is diversified away. The $ AI $ benchmark in the case of opposite signs of insider’s and arbitrageurs’ demands predicts that the expected future stock return is positive whenever the insider’s demand is positive because the insider is informed about the long-term innovation to the fundamental value, while arbitrageurs are not. This implies that $ {b}_{+-} $ is positive, while $ {b}_{-+} $ is negative. As a result, Hypothesis 2 concerns the predictive ability of informed demands when the two types of informed traders disagree on the direction of trading.

Hypothesis 3 is somewhat different. It does not concern return-demand sensitivities but focuses on the relationship between the insider’s demand and the short-term and long-term information. Estimation of the direct sensitivity of insider’s demand to the two types of information complements Hypothesis 2. Figure 3 presents the model’s predicted sensitivities to information as represented by coefficients $ {d}_{++} $ to $ {d}_{--} $ in equation (11). We again differentiate the $ NLI $ and $ AI $ benchmarks and assume $ {\sigma}_v^2/{\sigma}_u^2=1 $ , $ {\sigma}_v^2/{\sigma}_w^2=1 $ and $ n=3 $ .

Figure 3Expected Insider’s Demand Conditional on Signs of Innovations

Figure 3 plots the conditional expectations of insider’s demand $ {\zeta}_1 $ conditional on signs of fundamental innovations $ {v}_1 $ and $ {v}_2 $ . The primitive parameters are: $ {\sigma}_v^2/{\sigma}_u^2={\sigma}_v^2/{\sigma}_w^2=1 $ and $ n=3 $ . The remaining parameters are computed numerically by solving the system of equations (6) and (8) for the $ NLI $ and $ AI $ benchmark.

Figure 3 Long description

The image consists of two side-by-side bar graphs, Graph A and Graph B. Both graphs share a y-axis ranging from negative 0.8 to 0.8 with increments of 0.2 and an x-axis with four categories: d sub plus plus, d sub plus minus, d sub minus plus, and d sub minus minus.

Graph A. N L I Benchmark:

* d sub plus plus: Positive bar at approximately 0.35.

* d sub plus minus: Positive bar at approximately 0.35.

* d sub minus plus: Negative bar at approximately negative 0.35.

* d sub minus minus: Negative bar at approximately negative 0.35.

Graph B. A I Benchmark:

* d sub plus plus: Positive bar at approximately 0.75.

* d sub plus minus: Negative bar at approximately negative 0.3.

* d sub minus plus: Positive bar at approximately 0.3.

* d sub minus minus: Negative bar at approximately negative 0.75.

The $ NLI $ benchmark implies that the insider’s demand is positive only when the short-term information $ {v}_1 $ is positive. This happens because the insider does not use the long-term information $ {v}_2 $ and hence buys only when $ {v}_1 $ signal commands so. In the $ AI $ benchmark, the insider optimally forms a positive demand whenever the long-term information $ {v}_2 $ is positive, anticipating a positive future return. In the case of $ {v}_1<0 $ and $ {v}_2>0 $ ( $ {v}_1>0 $ and $ {v}_2<0 $ ), the fundamental asset value is on average zero. However, the insider buys (sells) to exploit the selling (buying) pressure coming from arbitrageurs who act on the basis of $ {v}_1 $ only. As a result, insider’s demand is contrarian to the short-term information when the short-term and long-term signals are of opposite signs.

Overall, our hypotheses aim to establish whether insider’s trading strategies take into account the short-term and/or long-term information. The main identification strategy is comparing his/her demand to the demand of traders who use only the short-term information. Using short-sellers’ demand to proxy for arbitrageurs’ trades, we are able to estimate the sensitivity of insider trades to the short-term versus long-term information.

A. Predictability of Future Returns

To test Hypothesis 1 on the relative predictive power of informed trading, we regress future returns on insider-trading and short-selling intensity dummies simultaneously:

(12) $$ {aret}_{k,t+5,t+6+h}={b}_1{is}_{kt}+{b}_2{ip}_{kt}+{c}_1{ssh}_{kt}+{c}_2{ssl}_{kt}+{X}_{kt}\gamma +{u}_{kt}, $$

where $ {aret}_{k,t+5,t+6+h} $ denotes abnormal return in stock $ k $ from $ t+5 $ to $ t+6+h $ relatively to the earnings announcement at $ t $ , with $ h\in \left\{\mathrm{20,40,60,130,250}\right\} $ ; $ {is}_{kt} $ and $ {ip}_{kt} $ denote dummy variables for intensive net insider sales and purchases, respectively, in firm $ k $ over the $ \left(0,+5\right) $ response window relatively to $ t $ ; and $ {ssh}_{kt} $ and $ {ssl}_{kt} $ denote short selling in the highest and lowest quintiles, respectively, in firm $ k $ over the $ \left(0,+5\right) $ response window. Figure 6 shows the timings. Variables $ {X}_{kt} $ include firm-specific characteristics including the past 1-year return $ {pastret}_{k,t-1y,t-2} $ , the earnings announcement abnormal return $ {eaar}_{k,t-2,t+1} $ , the change in earnings-per-share $ \Delta {eps}_{k,t-q4,t} $ as well as firm and year fixed-effect dummies. Standard errors are clustered within firms.

Figure 6Timings of Earnings Announcements and Related Abnormal Returns

Figure 6 shows relative timings of informed trading during the response window and timings of future abnormal returns. Everything is arranged relatively to the earnings announcement that is set as day $ t $ . We take into account only trading days. Accordingly, we establish i) the earnings-announcement window, which starts on day $ t-1 $ and ends on day $ t+1 $ ; ii) the response window when insiders and short sellers trade, which starts on day $ t $ and ends on day $ t+5 $ ; and iii) the future-return window, which runs between days $ t+5 $ and $ t+6+h $ .

Hypothesis 1 highlights the relative informational advantage of insiders over short sellers in the $ AI $ benchmark. In particular, Hypothesis 1 _AI predicts that future returns are negatively correlated with short-sellers’ demand, which means that $ {c}_1 $ should be positive and $ {c}_2 $ negative. In contrast, Hypothesis 1 _NLI predicts negative $ {c}_1 $ and positive $ {c}_2 $ .

Table 3 shows the results with the first 2 columns summarizing Hypothesis 1 predictions. Future abnormal returns are significantly more negative for stocks with insider selling and significantly more positive for stocks with insider buying. Similarly, future abnormal returns are significantly more negative for intensively shorted stocks (except for the shortest horizon $ h=20 $ ) and significantly more positive for stocks with the lowest levels of short selling for all horizons.Footnote ¹⁸ This shows that both insiders’ and short-sellers’ demands predict future returns, which is in line with existing literature (Huddart et al. (Reference Huddart, Ke and Shi2007), Akbas et al. (Reference Akbas, Jiang and Koch2020)). More importantly, we reject the null hypothesis (Hypothesis 10) for all horizons $ h $ in favor of the alternative Hypothesis 1 _NLI . Coefficient $ {c}_1 $ is significantly negative and $ {c}_2 $ is significantly positive at the 1% level after controlling for insider trading, which provides initial evidence in favor of the $ NLI $ benchmark that insiders abstain from trading on the foreknowledge of future material information, but take advantage of short-term mispricing.

Table 3Predictive Ability of Insider Trading and Short Sales

Table 3 Long description

The table consists of 8 columns and 11 rows. The header row includes columns for H 1 sub N L I, H 1 sub I S S, and time horizons h = 20, h = 40, h = 60, h = 130, and h = 250.

Row 1: i s. Values for h = 20 to h = 250 are -0.006***, -0.008***, -0.014***, -0.026***, and -0.031***.

Row 2: i p. Values for h = 20 to h = 250 are 0.015***, 0.016***, 0.021***, 0.034***, and 0.036***.

Row 3: s s h (c sub 1). H 1 sub N L I is c sub 1 < 0. H 1 sub I S S is c sub 1 > 0. Values for h = 20 to h = 250 are -0.001, -0.006***, -0.011***, -0.023***, and -0.029***.

Row 4: s s l (c sub 2). H 1 sub N L I is c sub 2 > 0. H 1 sub I S S is c sub 2 < 0. Values for h = 20 to h = 250 are 0.005***, 0.011***, 0.018***, 0.036***, and 0.046***.

Row 5: p a s t r e t. Values for h = 20 to h = 250 are -0.004***, -0.009***, -0.026***, -0.050***, and -0.072***.

Row 6: e a a r. Values for h = 20 to h = 250 are 0.046***, 0.071***, 0.050***, 0.042***, and 0.051***.

Row 7: Delta eps. Values for h = 20 to h = 250 are 0.033***, 0.024***, 0.022*, 0.001, and 0.005.

Row 8: Constant. Values for h = 20 to h = 250 are -0.106, -0.061, -0.095, -0.203, and -0.234.

Row 9: Nr. of obs. All values are 130,240.

Row 10: R-squared. Values for h = 20 to h = 250 are 0.71%, 0.92%, 1.11%, 1.83%, and 1.99%.

To test Hypothesis 2 concerning the predictive power of a disagreement between the two types of informed traders, we interact insiders’ and short sellers’ intensive trading dummies:

(13) $$ {\displaystyle \begin{array}{c}{aret}_{k,t+5,t+6+h}={b}_{++}\left({ip}_{kt}\times {ssl}_{kt}\right)+{b}_{+-}\left({ip}_{kt}\times {ssh}_{kt}\right)\\ {}+{b}_{-+}\left({is}_{kt}\times {ssl}_{kt}\right)+{b}_{--}\left({is}_{kt}\times {ssh}_{kt}\right)+{X}_{kt}\gamma +{u}_{kt},\end{array}} $$

where matrix $ {X}_{kt} $ contains the same control variables as in model (12), but we add interaction terms for the no insider trading dummy $ noit $ and the middle short-selling quintiles dummy $ ssm $ . The regression constant reflects the remaining category of quarters $ ssm\times noit $ . As we focus on the predictive power of the two informed traders’ demands when they are in disagreement, Hypothesis 2 _NLI suggests a higher predictive power for short-sellers’ demands: $ {b}_{+-} $ should be negative and $ {b}_{-+} $ positive. Hypothesis 2 _AI predicts the opposite signs as insiders’ predictive power is higher when they use foreknowledge of future material information.

Panel A of Table 4 shows the results with the first 2 columns summarizing Hypothesis 2 predictions. We reject the null Hypothesis 2 ₀ at all horizons $ h $ , but this time it is rejected in favor of Hypothesis 2 _NLI or Hypothesis 2 _AI , depending on whether insiders buy or sell. Specifically, the coefficient $ {b}_{+-} $ corresponding to the interaction term $ ip\times ssh $ (insiders are buying while short sellers are selling intensively) is positive and statistically significant for all horizons. This means that when insiders and short sellers disagree and insiders buy, future returns are positive—insiders predict future returns better than short sellers. Hence, insiders’ demand is based on foreknowledge of future material information. The null Hypothesis 2 ₀ is rejected in favor of the alternative Hypothesis 2 _AI for insider purchases. It is noteworthy that this result applies under the assumption that short sellers are as good as insiders in processing the short-term public information. Section VI discusses alternative scenarios.

Table 4Predictive Ability of Disagreement Among Informed Traders’ Demands

Table 4 Long description

The table is divided into two main sections: Panel A and Panel B.

Header Row: The columns represent different time horizons or hypotheses, labeled H 2 sub N L I, H 2 sub I, h = 20, h = 40, h = 60, h = 130, and h = 250.

Panel A: Predictive Regression of Disagreement Among Traders on Future Returns.

* i p times s s l (b sub plus plus): Values increase from 0.020 at h = 20 to 0.063 at h = 250.

* i p times s s h (b sub plus minus): Values range from 0.016 at h = 20 to 0.018 at h = 250.

* i s times s s l (b sub minus plus): Values range from -0.001 at h = 20 to 0.015 at h = 250.

* i s times s s h (b sub minus minus): Values decrease from -0.007 at h = 20 to -0.064 at h = 250.

* Additional rows include i p times s s m, i s times s s m, n o i t times s s l, n o i t times s s h, p a s t r e t, e a a r, Delta e p s, Constant, Number of observations (132,240 for all), and R-squared (increasing from 0.70% to 1.99%).

Panel B: Net Dollar Profits per Trade.

* i p times s s l: Ranges from -$172 at h = 20 to $1,614 at h = 250.

* i p times s s m: Ranges from -$433 at h = 20 to $1,243 at h = 250.

* i p times s s h: Ranges from -$1,163 at h = 20 to $2,430 at h = 250.

* i s times s s l: Ranges from $2,683 at h = 20 to $1,268 at h = 250.

* i s times s s m: Increases significantly from $4,671 at h = 20 to $28,727 at h = 250.

* i s times s s h: Increases significantly from $5,391 at h = 20 to $48,105 at h = 250.

Statistical significance is indicated by asterisks, with three asterisks representing the highest level of significance.

In contrast, the coefficient $ {b}_{-+} $ for the interaction term $ is\times ssl $ (insiders are selling while short sellers are “buying”) is positive for $ h\ge 40 $ and significant for $ h=40 $ . This means that when demands of insiders and short sellers have opposite signs and insiders sell, future returns are positive—insiders do not predict future returns well. Insider selling is not based on foreknowledge of future material information. In the case of insider sales, the null Hypothesis 2 ₀ is rejected in favor of the alternative Hypothesis 2 _NLI .

Overall, Panel A suggests that when insiders and short sellers disagree in their trading, insiders tend to abstain from selling on foreknowledge of future material information. Also, insiders’ sales forecast future returns when their demand is aligned with short-sellers’ demand; they effectively hide behind the high short-sellers’ demand. In contrast, insiders are sometimes able to take advantage of foreknowledge of future material information when buying. As shareholders are usually more determined to sue when suffering from negative returns, the differing pattern across purchases and sales minimizes insiders’ chances of legal jeopardy in the future (Ke et al. (Reference Ke, Huddart and Petroni2003), Cheng and Lo (Reference Cheng and Lo2006), Kallunki, Kallunki, Nilsson, and Puhakka (Reference Kallunki, Kallunki, Nilsson and Puhakka2018)).

Still, it is important to check whether insiders are able to earn significant dollar amounts during periods of their agreement or disagreement with short sellers, as positive correlation between trades and future returns is not necessarily translated into significant dollar profits for insiders (Cziraki and Gider (Reference Cziraki and Gider2021)). This is due to variation in trading volumes that differ significantly across different categories, as we show in Table 1, but also across different percentage returns. We calculate the dollar profit for each trade within the (0,+5) response window as the inflation-adjusted dollar value expressed in 2017 U.S. dollars and multiplied by the buy-and-hold abnormal return over the corresponding time horizon, which is size and book-to-market adjusted. In order to express profits with positive values, we multiply the resulting number for sales by $ -1 $ . For each firm-quarter, we average over all trades that fall within the (0,+5) response window.

Panel B of Table 4 shows averages of dollar profits per trade across different trading categories and horizons.Footnote ¹⁹ The unconditional average dollar profit per trade in our sample (untabulated) is $3,202 for the $ h=20 $ horizon and $23,375 for the $ h=250 $ horizon. This compares to $4,000 and $12,000, respectively, in Cziraki and Gider (Reference Cziraki and Gider2021). Most of this profitability comes from quarters when insiders sell together with high or medium sort selling ( $ is\times ssh $ and $ is\times ssm $ categories), that is, when insiders sell in agreement with short sellers. The average per-trade profit in the $ is\times ssh $ category is $5,391 for the 20-day horizon, while the annual profit ( $ h=250 $ ) in this category reaches $48,105 per trade. Insiders do not make significant profits when selling in disagreement with short sellers. The average net profit in categories where insiders actively purchase shares is small and insignificant, and even negative for short horizons. It seems that insiders do not purchase shares in order to make large profits. Overall, Panel B supports Hypothesis 2 _NLI that insiders do not profit from using foreknowledge of private information, but they still make relatively sizable profits when selling in agreement with short sellers.

There are three other interesting points to make here. First, our results in Panel B show that even when insiders agree with short sellers, they make dollar profits only from sales and not from purchases. This suggests that insiders often have high motivation to sell due to liquidity or diversification needs, but are very cautious when making sales to avoid unnecessary losses. Insiders take every opportunity to sell when they do not face high legal jeopardy. The second point is that in Panel B, the $ is\times ssm $ category also exhibits a similar and almost as strong dollar profits as the $ is\times ssh $ category. This could be because our classification of high short-selling is too conservative. Alternatively, it may highlight that insiders are better at identifying public information than short sellers and use long-term information only when it is correlated with the short-term information (hiding behind short sellers). Third, insiders do not suffer losses when they sell in disagreement with short sellers; coefficients for $ is\times ssl $ in Panel A are all but 1 (for $ h=40 $ ) insignificant. This is in sharp contrast with positive and highly significant coefficients for $ noit\times ssl $ , which is for the same low short-seller trading but when insiders decide not to trade. This pattern suggests that insiders stop selling strategically.

B. Insiders’ Demand Predictions

Finally, we test Hypothesis 3 concerning the relationship between the insiders’ demand and the long-term information following equation (11). It predicts that when the short-term and long-term information exhibit opposite signs, insiders’ demand is positively correlated with the long-term private information in the $ AI $ benchmark, while it is negatively correlated with the long-term information in the $ NLI $ benchmark. We measure the direction of the short-term information using the demand of short sellers. We base this approximation on our earlier conjecture that short sellers typically trade on a superior interpretation of public news contained in earnings announcements (Engelberg et al. (Reference Engelberg, Reed and Ringgenberg2012)). This conjecture is indeed confirmed in the previous section. Applying this interpretation for quintiles by short-selling demand, dummy variables $ ssl $ , $ ssm $ , and $ ssh $ correspond to positive, neutral, and negative short-term information, respectively.

To measure the direction of the long-term information, we use future realizations of earnings innovations following Piotroski and Roulstone (Reference Piotroski and Roulstone2005). We define future earnings innovation as $ \Delta {earn}_{k,t,t+q4}=\frac{earn_{k,t+q4}-{earn}_{kt}}{TA_{kt}} $ , which is the difference between earnings 4 quarters ahead $ {earn}_{k,t+q4} $ and the current quarter earnings $ {earn}_{kt} $ , scaled by the firm’s total assets $ {TA}_{kt} $ at the current quarter. We set the dummy variable $ longh $ equal to 1 for all observations in the highest quintile by $ \Delta {earn}_{k,t,t+q4} $ . Similarly, $ longl $ is equal to 1 for the lowest quintile and $ longm $ is equal to 1 for the middle 3 quintiles by $ \Delta {earn}_{k,t,t+q4} $ .Footnote ²⁰

Panel A of Table 5 shows insider trading patterns depending on short-term information (short sellers’ trading) and long-term information ( $ \Delta {earn}_{k,t,t+q4} $ ). We aim to show deviations of insider sale and purchase frequencies from their expected frequencies. The data set covers 115,997 firm-quarters, and insiders on average sell in 18.3% and purchase in 7.7% of them. 74% of firm-quarters are without any insider trading activity. Both short-term and long-term information are sorted into three bins, where high and low bins represent around 20% of firm-quarter observations and the medium bin around 60%. Based on these frequencies, we compute the expected frequencies for all combinations of short-term information, long-term information, and insider trading. For example, the expected frequency of a quarter with insider sales when both short- and long-term information are low is $ 0.0071=0.183\times 0.198\times 0.196 $ . We then compute the realized frequency of the type (in this case, it is 0.0109), take the deviation from the expected value ( $ 0.0038=0.0109-0.0071 $ ), and express it as a percentage deviation ( $ +54\%=0.0038/0.0071 $ ). The interpretation of the number is that the actual frequency of quarters when insiders sell and short- and long-term information is low is 54% higher than its expected frequency.

Table 5Relationship Between Insiders’ Demand and Private Information

Table 5 Long description

Panel A, titled Percentage Deviations from the Benchmark, compares Sales and Purchases across three categories: long h, long m, and long l.

* For the row ssl: Sales are minus 79.9 percent, minus 70.7 percent, and minus 74.8 percent; Purchases are 13.5 percent, 23.4 percent, and minus 8.9 percent.

* For the row ssm: Sales are minus 9.1 percent, 24.5 percent, and minus 14.4 percent; Purchases are minus 9.4 percent, minus 4.7 percent, and minus 19.5 percent.

* For the row ssh: Sales are 48.6 percent, 23.8 percent, and 54.1 percent; Purchases are 22.1 percent, 3.5 percent, and 33.0 percent.

Panel B, titled Multivariate Regression Setting, analyzes nispos (Sales) and nisneg (Purchases) with columns for H 3 sub N L I, H 3 sub A I, and Coefficients.

* ssl times long h (d sub plus plus): Sales coefficient is minus 0.140; Purchases coefficient is 0.016.

* ssl times long l (d sub plus minus): Sales coefficient is minus 0.198; Purchases coefficient is minus 0.025.

* ssh times long h (d sub minus plus): Sales coefficient is 0.209; Purchases coefficient is 0.102.

* ssh times long l (d sub minus minus): Sales coefficient is 0.189; Purchases coefficient is 0.060.

* ssm times long h: Sales coefficient is minus 0.016; Purchases coefficient is 0.046.

* ssm times long l: Sales coefficient is 0.037; Purchases coefficient is 0.024.

* ssl times long m: Sales coefficient is minus 0.162; Purchases coefficient is minus 0.048.

* ssh times long m: Sales coefficient is 0.147; Purchases coefficient is 0.069.

* pastret: Sales coefficient is 1.050; Purchases coefficient is minus 0.196.

* eaar: Sales coefficient is 5.212; Purchases coefficient is minus 0.881.

* Delta eps: Sales coefficient is minus 0.513; Purchases coefficient is minus 0.306.

* Number of observations: 115,997 for both.

* R-squared: 3.48 percent for Sales and 1.64 percent for Purchases.

Panel A of Table 5 shows the percentage deviations for insider sales and purchases. We can see that insider sales are clearly aligned with the short-term information: the frequency of quarters with insider sales is increased by 24% to 54% when the short-term information is negative ( $ ssh $ ), regardless of the long-term information. At the same time, the frequency of quarters with insider sales decreases between 71% and 80% when the short-term information is positive ( $ ssl $ ), again regardless of the nature of the long-term information. The bins with medium short-term information show the smallest changes, and only the bin for positive long-term information is aligned with insider sales. Purchases show a somewhat higher reliance on long-term information. For example, when short-term information is positive ( $ ssl $ ), insiders increase purchases when long-term information is positive, but decrease purchases when it is negative. During periods of negative short-term information, insiders tend to increase their purchases irrespective of the long-term information.

Panel B of Table 5 tests Hypothesis 3 in a multivariate setting with insider trading demand as the dependent variable. We separate insider selling and buying demands and use $ nispos $ and $ nisneg $ , both measured in basis points, respectively. For easier interpretation, we take the absolute value of $ nisneg $ so that a higher $ nisneg $ means higher net purchases. We run two separate regressions:

(14) $$ {\displaystyle \begin{array}{l}{nispos}_{k,t,t+5}={d}_{++}{ssl}_{kt}\times {longh}_{kt}+{d}_{+-}{ssl}_{kt}\times {longl}_{kt}\\ {}\hskip9.36em +{d}_{-+}{ssh}_{kt}\times {longh}_{kt}+{d}_{--}{ssh}_{kt}\times {longl}_{kt}+{X}_{kt}\gamma +{u}_{kt},\end{array}} $$

(15) $$ {\displaystyle \begin{array}{l}{nisneg}_{k,t,t+5}={d}_{++}{ssl}_{kt}\times {longh}_{kt}+{d}_{+-}{ssl}_{kt}\times {longl}_{kt}\\ {}\hskip9.36em +{d}_{-+}{ssh}_{kt}\times {longh}_{kt}+{d}_{--}{ssh}_{kt}\times {longl}_{kt}+{X}_{kt}\gamma +{u}_{kt}.\end{array}} $$

As before, matrix $ {X}_{kt} $ includes control variables $ {pastret}_{k,t-1y,t-2} $ , $ {eaar}_{k,t-2,t+1} $ , $ \Delta {eps}_{k,t-4q,t} $ , and firm and year fixed effects. It also includes the remaining interaction terms with medium short-term and long-term information dummies, $ ssm $ and $ longm $ . The reference category is the group of $ ssm\times longm $ with neutral short-term or long-term information.

Panel B shows coefficient estimates, using $ \Delta earn $ 4 quarters ahead as the measure of long-term information. The first 2 columns show Hypothesis 3 predictions for insider sales, followed by a column with coefficients. We can see that stocks with negative short-term information $ ssh $ and positive long-term information $ longh $ experience insider selling in line with the short-term information and against the long-term information. Insiders increase their net sales: coefficient $ {d}_{-+} $ is positive. Similarly, for stocks with positive short-term information $ ssl $ and negative long-term information $ longl $ , insiders tend to decrease their net sales: coefficient $ {d}_{+-} $ is negative and statistically significant. Insiders follow the short-term information despite the opposite sign of the long-term information. The same pattern prevails for sales when we measure $ \Delta earn $ 1 and 3 quarters ahead or use earnings announcement abnormal returns 1, 3, and 4 quarters ahead as a measure of long-term information (see Table A1 in the Supplementary Material). For insider sales, we reject the null Hypothesis 3 ₀ in favor of the alternative Hypothesis 3 _NLI . It is noteworthy that these results for Hypothesis 3 are not just consistent with Hypothesis 2 results, but reinforce them because this time the conclusion is not based on a “non-rejection” of the null hypothesis.

Coefficients for purchases in Panel B show a different pattern. We can see that coefficient $ {d}_{+-} $ is negative while $ {d}_{-+} $ is positive. This suggests that insider purchases decrease with bad but increase with good long-term information. Even though $ {d}_{+-} $ is not statistically significant in Panel B, Table A1 shows statistical significance for $ \Delta earn $ 1 quarter ahead and for all three $ eaar $ specifications. We reject the null Hypothesis 3 ₀ for insider purchases in favor of the alternative Hypothesis 3 _AI .

In summary, our results in this section suggest that insider sales versus purchases take advantage of different information. Insider sales follow closely patterns of short-selling demands, which suggests that insiders exploit short-term mispricing stemming from public information rather than foreknowledge of material information. This is not the case for insider purchases: insiders seem to trade on foreknowledge of future material information when buying. We believe the difference is due to insiders more carefully avoiding trading on the long-term undisclosed information when selling because the chances and cost of being prosecuted are higher with sales than with purchases (Ke et al. (Reference Ke, Huddart and Petroni2003), Cheng and Lo (Reference Cheng and Lo2006), and Kallunki et al. (Reference Kallunki, Kallunki, Nilsson and Puhakka2018)). Instead, they skillfully take advantage of the short-term mispricing stemming from public information that is not illegal but still profitable.

C. Routine Versus Opportunistic Insider Trades

Our conclusion so far is that insider sales rely on exploiting mispricing stemming from the market’s misinterpretation of public information, and only insider purchases rely on foreknowledge of material information. This section explores whether this trading pattern prevails for opportunistic trades. In particular, we want to check whether our results hold even after excluding routine insider sales, which should be independent of any information (Cohen et al. (Reference Cohen, Malloy and Pomorski2012)). If the results hold, it would reinforce the claim that sales carry higher legal jeopardy and insiders avoid using the foreknowledge of material information when selling to minimize their legal prosecution cost.

Following Cohen et al. (Reference Cohen, Malloy and Pomorski2012), we identify insiders who trade in the same calendar (routine) month in at least 3 consecutive years. We classify all trades by the insider following this 3-year period as routine if they happen in the same routine month. Trades made in non-routine months are classified as opportunistic. Then, in each quarter, we add routine (opportunistic) net insider sales over the response window and set routine (opportunistic) insider selling and buying dummies to 1 when routine (opportunistic) net insider selling is positive and negative, respectively. This adjustment of Cohen et al. (Reference Cohen, Malloy and Pomorski2012) covers all quarters in our data set and fits our setting of insider trading in concise response windows. Table A2 in the Supplementary Material shows that routine insider trading is less frequent than opportunistic insider trading. In line with Table 2, both opportunistic and routine insider trading are higher when short-selling demand is in the highest and lowest quintiles than when it is in the middle 3 quintiles.

Table A3 in the Supplementary Material replicates Tables 3 and 4 replacing $ is $ and $ ip $ with decomposed dummies for opportunistic ( $ isopp $ and $ ipopp $ ) and routine ( $ isrt $ and $ iprt $ ) trades. We conclude that opportunistic purchases and sales predict significantly future returns in the right direction. Insiders are informed when making their opportunistic purchases and sales. All the coefficients for routine purchases $ iprt $ are insignificant, which confirms that they do not predict future abnormal returns. Routine insider sales $ isrt $ , however, are significantly negatively correlated with future returns for all horizons except the longest horizon. The coefficients are smaller in size than the coefficients for the opportunistic sales, but they suggest that insiders are able to sell in line with future returns even in the case they sell regularly in a particular month of the year. This is because insiders have the option not to trade in some years—our results suggest that insiders abstain from selling when future returns are particularly large and keep their pattern of trading when future returns are small.

Panel B of Table A3 tests Hypothesis 2 separately for opportunistic and routine insider trades. When insiders and short sellers disagree, future returns align with insiders’ trades in case of opportunistic insider purchases, but they align with short sellers’ trades in case of routine insider purchases. The null Hypothesis 2 ₀ is rejected in favor of Hypothesis 2 _AI in the former case, but in favor of Hypothesis 2 _NLI in the latter case. Note that when the two types of informed traders agree, they predict future information regardless of whether insider purchases are routine or opportunistic. Focusing on insider sales, even the most informed transactions do not show any signs of usage of long-term private information. We conclude that insider sales rely on exploiting short-term mispricing.

Finally, Table A4 tests Hypothesis 3 concerning the relationship between insiders’ demand and private information, again separately for opportunistic and routine insider trades. We can see that insider selling aligns with the short-term rather than the long-term information, even when we restrict to opportunistic transactions that are more informative. Routine sales do not adjust to information. Opportunistic net purchases decrease with negative long-term information and increase with positive long-term information. Again, we see evidence of insiders relying on foreknowledge of material long-term information when buying, but only opportunistically. Routine insider purchases do not adjust to long-term information. Table A5 in the Supplementary Material shows results when we measure opportunistic insider trades on the insider instead of the trade level.Footnote ²¹ Intuitively, this definition gains a higher fraction of routine trading. Our conclusions pertain.

To summarize, this section suggests that insider sales exploit mispricing stemming from short-term public information rather than foreknowledge of material information, even when we drop less information-driven routine insider sales and focus on opportunistic sales. Opportunistic insider purchases tend to take advantage of foreknowledge of material information.

D. Robustness Tests

In this section, we perform four robustness tests to further support our main results. First, we check that our results are not driven by high short-selling constraints. In particular, low short-selling activity, reflected in our $ ssl $ dummy, may not measure positive short-term information, but it may rather capture short sellers refraining from trading because it is too costly to do so. We classify short-selling constrained stocks as stocks with loan fees exceeding 200 bp during the response windowFootnote ²² and repeat tests in Tables 4 and A1, but drop all stock-quarter observations with high loan fees. Table A6 in the Supplementary Material shows that our conclusions hold; insider purchases link with the long-term information while insider sales with the short-term information.

Second, we show that our results are not substantially affected by the fact that not all short selling is driven by speculative motives. For example, market makers, who do not want to hold costly inventory, rely on short selling during episodes of intensive public buying pressure. This part of the short-selling demand is not informationally motivated. In order to isolate short selling that is due to market making, we follow Diether et al. (Reference Diether, Lee and Werner2009) and define residual relative short selling as the error term in the regression: $ {ss}_{i,t}={\alpha}_i+{\beta}_i\times {oimb}_{it}^{+}+{\varepsilon}_{i,t} $ , which is run for every stock $ i $ and day $ t $ and where $ ss $ is the number of shares shorted divided by the number of shares outstanding and $ {oimb}^{+} $ is the daily positive order imbalance of a stock, with negative values replaced with zeros. $ oimb $ is computed as daily purchases minus sales scaled by daily volume and purchases and sales are defined as in Lee and Ready (Reference Lee and Ready1991). We replace relative short selling in Tables 4 and A1 by residual relative short selling $ ess $ to better proxy for informationally motivated short selling. Table A7 in the Supplementary Material shows that even the composition of short-selling quintiles changes (Panel A), our main conclusions remain broadly unchanged.

Third, we address a concern that some insider trades are not informationally motivated ex ante and including them in our sample may add noise to our tests. In the previous section, we dropped routine insider trades but not all non-informationally motivated trades are classified as routine; many plan trades executed under Rule 10b5-1 are classified as opportunistic if they are not repeated over 3 consecutive years. To mitigate this concern, we exclude plan trades from opportunistic trades and test that the remaining opportunistic non-plan trades are indeed not based on foreknowledge of material information. About 7.60% of opportunistic insider sales are plan trades, while only about 0.63% of opportunistic purchases are plan trades. Table A8 in the Supplementary Material shows that the main conclusions hold for the stricter definition of opportunistic trades.

Finally, we show that our results do not change when considering a longer response window (0,+20) for informed trading and an alternative adjustment for abnormal returns. Table A9 in the Supplementary Material replicates Tables 4 and A1, but measures informed traders’ demands during the (0,+20) response window. Table A10 replicates Table 4 using market-adjusted returns instead of book-to-market and size adjustment. It is worth noting that the longer response window does not affect the signs of the coefficients, but coefficient magnitudes drop somewhat. This suggests that most of the informed trading is indeed happening during the shorter response window of (0,+5).