Does news travel slowly before a market crash? The role of margin traders

2.1 Attribution bias and investor overconfidence

The psychology literature finds the existence of pervasive attribution bias. People attribute success to their own dispositions and failure to external forces (Hastorf et al., 1970). Gervais and Odean (2001) indicate that traders become more overconfident and trade more actively after the market increases because they attribute returns from the overall market increases to their own acumen when assessing their trading ability. Daniel et al. (1998) show that when individuals observe the outcomes of their actions, they update their confidence in their own ability in a biased manner. They attribute events that confirm the validity of their actions to their high ability and events that disconfirm the action to external noise or sabotage. Investors adjust their beliefs and seek support for their past investment decisions to reduce psychological costs and cognitive dissonance (Shefrin and Statman, 1985; Goetzmann and Peles, 1997). While existing studies reveal the causes of investor overconfidence and attribution bias, the current study contributes to the literature by showing the effects of overconfidence and attribution bias on price discovery, especially during market rallies.

2.2 Investor overconfidence and trade behaviour

Daniel et al. (1998) show that investors tend to be overconfident about the information they have generated but not about public information. Although prior studies indicate that momentum occurs because the market is slow to react to news (Jegadeesh and Titman, 1993), Daniel et al. (1998) argue that overreaction can also cause momentum because public information can trigger further overreaction, and continuing overreaction causes momentum in security prices. Daniel and Titman (1999) also show that investor overconfidence generates momentum in stock returns, and the momentum effect is likely to be strongest in stocks whose valuations require the interpretation of ambiguous information. Odean (1998) shows that overconfident traders cause markets to underreact to the information of rational traders. They underreact to abstract, statistical, and highly relevant information, and overreact to information that is salient, anecdotal, and less relevant. Positive (negative) return serial correlation occurs when investors underweight (overweight) new information. Griffin and Tversky (1992) indicate that individuals overreact to a prolonged record of salient performance but underreact to intermittent news.

Hong and Stein (1999) show that one group of traders (news watchers) underreact to private information gradually, then a second group of traders (arbitrageurs) try to exploit this underreaction and create an excessive momentum in prices, leading to overreaction. The existence of underreaction sows the seeds for overreaction by making it profitable for momentum traders to enter the market. Mendel and Shleifer (2012) analyse the interaction of insiders, noise traders, and outsiders. Noise traders are vulnerable to sentiment shocks and trade on them; outsiders who possess no information trade rationally by learning from prices. Outsiders are also prone to chasing price increases caused by insiders with private information. However, as long as there are sufficiently few noise traders, outsiders may get confused and chase noise as if it were information, thereby suppressing the possible impact of informed trading on prices, amplifying sentiment shocks and moving prices away from fundamentals.

Stambaugh et al. (2012) show that overpricing is more prevalent when market-wide sentiment is high. Yu and Yuan (2011) find that the market is less rational during high-sentiment periods due to high participation by noise traders in such periods. Similarly, Antoniou et al. (2010) indicate that sentiment has an asymmetric effect on prices, with optimism producing greater mispricing (overvaluation) than pessimism (underpricing). Adebambo and Yan (2016) find that stocks held by more overconfident managers experience greater momentum profits and stronger return reversals than stocks held by less overconfident managers. Cooper et al. (2004) show that momentum profits exist only in the subsequent periods after prolonged market gains. Chui et al. (2010) further show that momentum profits are higher in countries with stronger individualism. Differing from these studies, we add to the literature by investigating and documenting that overconfidence reduces price discovery, which is a more direct measure of market efficiency.

2.3 Background information on margin trades in the US and in China and the related studies

After the Securities and Exchange Act of 1934, the US Federal Reserve System (Fed) was responsible for setting the margin requirement, which was set initially at 45 percent in October 1934 and adjusted 23 times between 1934 and 1974. The margin requirement reached the highest rate of 100 percent (i.e., 0 percent borrowing) during January 1946 and February 1947 and remained at 50 percent after January 1974 (Hsieh and Miller, 1990; Alexander et al., 2004). Before January 1999, the Fed published a quarterly list of newly margin-eligible securities. After January 1999, the Fed ceased publishing its list and abandoned the vetting process in favour of an automatic rule whereby all domestic securities became margin-eligible once they were listed on the market (Alexander et al., 2004).

Starting on 31 March 2010, the China Securities Regulatory Commission (CSRC) launched a pilot programme and allowed margin trading and short selling for the first time in China. Initially, only 90 stocks listed on the Shanghai Stock Exchange and the Shenzhen Stock Exchange were eligible for margin trading and short selling (see Figure 1). After the pilot programme, the number of stocks eligible for margin trading and short selling increased four times in November 2011, January 2013, September 2013, and September 2014. There are about 900 stocks and 16 exchange-traded funds (ETFs) available for margin trading since the most recent addition in September 2014.

Due to limited availability of detailed margin trade information at stock level, many studies use the changes in margin level requirement in the US before 1999 to investigate the effects of margin requirement on market volatility, and find mixed results. For example, Seguin (1990) finds that share prices increase and volatility decreases when a firm is added to the eligible list, implying that margin trading reduces volatility. The author argues that reducing trader wealth constraints enhances liquidity (also see Conrad, 1989). Hsieh and Miller (1990) find a weak negative association between the level of margin requirements and the level of volatility during the late 1930s and early 1940s. They also indicate that changes in margin requirements tended to follow rather than lead changes in volatility because the Fed tended to raise margins when the market was booming and cut them after markets fell, and volatility normally rises when a market falls; thus, apparently a negative relationship exists between margin requirements and volatility.

Alexander et al. (2004) show that trading volume increases and that market liquidity and volatility do not change after stocks become eligible for margin trading. They suggest that the information content of trading, informational environment, and the efficiency of a firm's share price improves when the margin level is lowered. However, Hardouvelis (1990) shows that higher or increasing margin requirements are associated with lower stock price volatility and smaller deviations of stock prices from their fundamental values. This result indicates that margin trading increases volatility. Hardouvelis and Theodossiou (2002) show that an inverse relationship between margin levels and volatility exists only during bull and normal markets, and that no relationship exists during bear markets. We use detailed margin trade information of individual stocks and overcome the weakness of the existing studies that rely on margin-level requirement for all eligible stocks. More importantly, our results indicate that margin traders are sentiment investors. They rely on market sentiment and generate more pressure in the market, which slows down price discovery.

4.1 Univariate analysis of price delay

As an initial test of how price delay is different before and after the market crash, we conduct univariate analyses and compare price delay between the pre- and post-crash periods. To analyse how margin trades affect price delay differently in the pre- and post-crash periods, we divide the stocks in our sample into three groups based on their margin trade ratios in the pre-crash period. Stocks ranked at the bottom (top) third based on the monthly MG bal./TRD ratio are included in the Low (High) group, and the rest of all other stocks are included in the Medium group. Similarly, we also classify stocks into Low, Medium, and High groups based on the ratios of monthly net margin trade to total trading amount (i.e., non-margin trade amount), MG/TRD, and the monthly MG bal./TA, which are defined in Section 33. Note that we intentionally do not reclassify stocks based on the margin trade ratios in the post-crash period because our primary focus is how investor sentiment for a stock, as measured by margin trade ratios, affects price delay and how the changes in price delay are different for stocks in different sentiment categories. This design reduces the sample to 627 stocks that have margin trade data in both the pre- and post-crash periods.

Table 2 reports the results, and we observe two clear patterns. First, the price delay in the pre-crash period is about twice the delay in the post-crash period, and the differences are significant both statistically and economically regardless of margin trade classification. For example, the price delays of the Low, Medium, and High groups based on the MG bal./TRD ratio (the first two columns) are 0.41, 0.43, and 0.44, respectively, in the pre-crash period. In sharp contrast, the delays are only 0.19, 0.18, and 0.20, respectively, in the post-crash period. The changes from the pre- to the post-crash periods are −0.21, −0.25, and −0.25, respectively. All these changes are significant both economically and statistically at the 0.01 level. The results based on MG/TRD (the middle two columns) and MG bal./TA ratios (the last two columns) are similar.

Second, the magnitude of the decrease in price delay is positively related to the margin trade ratios. For example, the change in price delay for the Low MG bal./TRD ratio group is −0.21, which is equivalent to a decrease of 51 percent (−0.21/0.41); whereas the change in the price delay for the High MG bal./TRD ratio group is −0.25, which is a decrease of 57 percent (−0.25/0.44). The difference in the changes between the Low and High groups (Diff 3 – Diff 1) is −0.03 and significant at the 0.1 level. When stocks are classified by the MG/TRD ratio, the changes in price delay for the Low and the High ratio groups are −0.22 (or a decline of 52 percent) and −0.28 (or a decline of 62 percent), respectively. The difference in the decreases between the High and Low groups (Diff 3 – Diff 1) is −0.05, which is significant at the 0.05 level. The changes in the price delay are more pronounced when margin trade is measured by the MG bal./TA ratio (the last two columns). The decrease in price delay for the Low MG bal./TA group is −0.14, which is equivalent to a 42 percent decline, but it is −0.27, or a 56 percent decline, for the High MG bal./TA group. The difference in the declines between the Low and High groups is −0.13 and significant at the 0.01 level.

The large price delay in the pre-crash period combined with the more pronounced decrease in price delay for the high-margin trade stocks indicate an adverse effect of investor sentiment and overconfidence on price discovery. This is consistent with the findings of Seybert and Yang (2012) and Coulton et al. (2016), which indicate that investor sentiment impacts their decision-making process and consequently the timeliness of price discovery. Walther and Willis (2013) further show that even financial analysts are more optimistic and least accurate in the presence of high sentiment.7

4.2 Regression analysis and control of firm characteristics

The univariate analyses in the previous section show the decline in price delay after the market crash and the decline is larger for high-margin trade stocks. However, this is possibly a manifestation of other factors, since margin trade could be endogenous and affected by firm characteristics. Thus, we investigate the effects of margin trade on price delay by controlling for firm factors through the following pooled regression:

(4)

where the dependent variable Delay_i,t is the price delay for firm i in month t. MG Rank_i,t is a ranking score (on a 1–3 scale) of firm i's margin trade ratio in month t. Instead of using the actual value of margin trade ratios, we use the ranking score to reduce potential noise. Specifically, we rank stocks in each month based on their margin trade ratios. Stocks that are ranked at the bottom (top) third take a value of 1 (3) and the other stocks take a value of 2. To capture the asymmetric effect of margin trade on price delay in the pre- and post-crash periods, we use an interaction variable MG Rank_i,t × Post_t, where Post_t takes a value of 1 if month t is in the post-crash period and 0 otherwise. Firm control variables include stock price (Log(Price_i,t)); total assets (Log(TA_i,t)); earnings to price ratio (E/P_i,t) and lagged E/P ratio (E/P_i,t−1); Herfindahl index of top 10 shareholders (HHI_TOP10_i,t); monthly stock turnover ratio (Turnover_i,t); stock return (Return_i,t), and lagged return (Return_i,t−1); and stock risk (β_i,t) estimated using the monthly returns from t−12 to t−1. We also include market return (R_m,t) and lagged market return (R_m,t−1) to control for market conditions.

Table 3 reports the regression results. In the first model (columns 1–2), the MG Rank is the ranking score of MG bal./TRD ratio, and the coefficient on MG bal./TRD is positive (0.006) but not significant at the 0.1 level. The coefficient on the interaction variable MG × Post is negative (−0.056) and significant at the 0.01 level. In terms of economic significance, this implies that the average declines in price delay after the market crash are about 0.168 (−0.056 × 3) for high-margin stocks ranked in the top third based on MG bal./TRD ratio, and the decline in price delay is only about 0.056 (−0.056 × 1) for the low-margin stocks ranked in the bottom third based on MG bal./TRD ratio. This is largely consistent with the univariate results reported in Table 2. Among the firm control variables, price, stock turnover, and the current and lagged stock returns are positively related to price delay. The coefficients on both the total asset (Log(TA)) and stock risk (β) are negative and significant at the 0.01 level. The coefficient on R_m,t is 0.625 and significant at the 0.01 level, whereas the coefficient on R_m,t−1 is −0.379 and also significant at the 0.01 level.

In the second model (the two middle columns), the MG Rank is the ranking score of MG/TRD ratio, and the coefficient on MG/TRD is 0.030 and significant at the 0.01 level. The coefficient on the interaction variable MG × Post is −0.054 and significant at the 0.01 level. The coefficients on all control variables are identical to those in the first regression. When the MG Rank is measured by MG bal./TA ratio (the last two columns), the coefficient on MG bal./TA is 0.036, and the coefficient on MG × Post is −0.072; both of these are significant at the 0.01 level. The coefficients on all control variables are identical to those in the other two regressions.

The results so far support our hypotheses 1 and 2, namely price delay is larger in the pre-crash period than in the post-crash period and that the decline in price delay after the market crash is more pronounced for high-margin trade stocks than that for low-margin trade stocks. Combined with the large increase in market sentiment before the Chinese market crash (Figure 2c), these findings imply that investors in general are more susceptible to overconfidence and attribution bias before the market crash, and this bias slows down price discovery. It also implies that margin trades before market crash are largely driven by sentiment investors, which is evidenced by the large decline in price delay. We offer additional discussions in later sections.

We are aware that some of the control variables are likely to be correlated with each other. For example, the stock price is related to the stock return and market returns. Thus, we use different methods to check for possible multicollinearity. First, we check the variance inflation factor (VIF) in each regression. The maximum VIF in these regressions is 3.03, which is smaller than 10, suggesting that multicollinearity is not severe.8 Second, we run similar regressions by including one of the possibly correlated variables at a time. The coefficients on the margin ratios remain largely the same. Third, another concern is reverse causality, namely, margin traders may target stocks with greater price inefficiency. To alleviate this endogeneity concern, we use orthogonal regressions by regressing the margin ratios on firm control variables in the first step. Then, we use the residuals from the first step regression to replace the margin ratio in the basic model. The unreported results are consistent with those reported in the current table.9 We also report Durbin–Watson statistics in Table 3, which range from 1.47 to 1.62, indicating weak autocorrelation in the error term.

4.3 Price delay on market up- and down-days in different markets

The results so far show that the price delay is significantly larger in the pre-crash period than in the post-crash period, and the driving forces are likely the two types of information biases as indicated by Peng and Xiong (2006): investor overconfidence of their own analysis and ignorance of public information in the pre-crash period. In contrast, in the post-crash period, constrained investors tend to allocate more attention to market-wide information and ignore firm-specific information. However, it is unclear whether such asymmetric effects on price delay exist under different market conditions. Following Boehmer and Wu (2013), we estimate price delays separately on market up- and down-days in both the pre- and post-crash periods. To estimate the price delay on market down-days, the unrestricted model (1) and the restricted model (2) are modified below:

(5)

(6)

where R_j,t and are the stock and market returns on down-day t, respectively. We classify trading days as down-days if the market return on a given day is negative. We obtain R² from Equations 5) and 6) for each stock and compute the price delay on down-days in the pre- and post-crash periods separately. In the same vein, we also compute price delay on market up-days.

Panel A of Table 4 reports the comparison of price delays on up- and down-days in the pre-crash period. For the Low MG bal./TRD ratio group, the average price delay is 0.36 on up-days and 0.43 on down-days. The difference (Diff 1 = Down – Up) is 0.07 and significant at the 0.05 level, which indicates that price delay on down-days is about 19.4 percent (0.43/0.36 – 1) larger than that on up-days. For the Medium MG bal./TRD ratio group, the average price delays on up- and down-days are 0.38 and 0.44, respectively, and the difference is 0.06 and significant at the 0.01 level. For the High MG bal./TRD ratio group, the price delays on up- and down-days are 0.36 and 0.47, respectively. The difference is 0.11 and significant at the 0.01 level, which indicates that the price delay on down-days is about 30.6 percent (0.47/0.36 – 1) larger than that on up-days. The difference in the changes of price delay between the High and Low-margin ratio groups (Diff 3 – Diff 1) is 0.04 (= 0.11 – 0.07), which is not statistically significant at the 0.1 level. The results based on MG/TRD and MG bal./TA classifications are similar. The price delay is about 26.3 percent (0.48/0.38 – 1) larger on down-days than on up-days for the High MG/TRD group and about 19.6 percent (0.55/0.46 – 1) larger on down-days than on up-days for the High MG bal./TA group.

Panel B of Table 4 reports the price delay on up- and down-days in the post-crash period. As reported in Table 2, the price delays are much smaller after the market crash. A sharp contrast to the results in the pre-crash period is that the differences in the price delays between up- and down-days are insignificant regardless of how margin trade is measured. In addition, no apparent significant difference in price delay exists between the Low and High margin groups. Although the literature suggests that bad news travels slowly (Hong et al., 2000), our evidence indicates that this is the case only when market sentiment is high, i.e., in the pre-crash period. These results suggest that overconfident investors overestimate their own information and ability and ignore market information in the pre-crash period (Peng and Xiong, 2006). This is also consistent with the findings of Coulton et al. (2016) that bad news is incorporated into price more quickly for firms that are more sensitive to market movement.

4.4 Investor attention and changes in price synchronicity and sensitivity to market information

To provide further evidence that market crashes make investors more vigilant and that investor attention affects market efficiency, we investigate the changes in price synchronicity and the sensitivity to market movements during the pre- and post-crash periods. We use and β₀ estimated from the restricted market model (2) as a measure of price synchronicity and sensitivity to market movement, respectively. Although and the price delay are related to one another, they capture two different aspects of market efficiency. The price delay measures the speed that the current market information is incorporated into the stock price, whereas captures how much firm-specific information or idiosyncratic risk is capitalised into the stock price. As indicated by Roll (1988), DeLong et al. (1990), and Morck et al. (2000), a large R² indicates that stock price variations are synchronous, and more (less) market-wide (firm-specific) information is incorporated in the stock price. Thus, these two measures provide additional insight regarding investor attention and its effect on information capitalisation and sensitivity to market movement in the context of Morck et al. (2000) and Roll (1988).

Panel A of Table 5 reports the results of price synchronicity. The average values of for the Low MG bal./TRD group are 0.33 and 0.61 in the pre- and post-crash periods, respectively, which is equivalent to an increase of 85 percent. The average increases of for both the Medium and High groups are 0.31, which represents a 97 percent increase for the Medium group and a 100 percent increase for the High group. The difference in the increase of between the Low and High groups (Diff 3 – Diff 1) is 0.03 and significant at the 0.10 level. The results based on the MG/TRD and MG bal./TRD ratios are similar. For example, the increase in for the Low MG bal./TA group is about 49 percent (0.61/0.41 −1), and the increase in for the High MG bal./TA group is about 122 percent (0.60/0.27 – 1). The difference in the increases between the Low and High groups (Diff 3 – Diff 1) is 0.13, which is significant at the 0.01 level.

The results on the sensitivity to market information are reported in Panel B of Table 5. It is obvious that the sensitivity to market movement increases substantially after the market crash, and the increases are significantly larger for the high-margin trade stocks. For example, the average betas for the Low MG bal./TRD ratio group are 0.98 and 1.36 in the pre- and post-crash periods, respectively, indicating a 39 percent increase. The average increases in betas for the Medium and High groups are 0.56 and 0.74, which represent increases of 67 and 101 percent, respectively. The difference in the increase of beta between the Low and High groups (Diff 3 – Diff 1) is 0.37, which is significant both economically and statistically at the 0.01 level. The results based on MG/TRD and MG bal./TRD are similar.

These results uncover several important factors regarding investor attention and trade behaviour. First, the large R² in the post-crash period indicate strong market co-movements and prevalent herding among investors. This is consistent with Peng and Xiong's (2006) argument that attention-constrained investors tend to allocate more attention to market-wide information than to firm-specific information. Second, the substantial increase in R² combined with the significant decrease in price delay reveals a dramatic shift in investor behaviour. Third, the large beta in the post-crash period indicates that investors are more sensitive to market movement in down markets than in up markets. Fourth, the positive relationships between margin trade ratios and the increases in R² and betas further indicate that investor overconfidence causes overreliance on their own judgement and less responsiveness to market information, resulting in long price delays before the market crash. This is consistent with the attribution bias literature (Hastorf et al., 1970; Thaler and Johnson, 1990; Gervais and Odean, 2001; Abreu and Brunnermeier, 2002). In contrast, after the market crash, investors pay much greater attention to market information, causing strong co-movement.

5.1 Do margin trades reflect informed traders’ information or investor overconfidence?

One of our assumptions is that margin trades reflect investor overconfidence, which leads to the price delay in the pre-crash period. However, it is possible that margin trades reflect informed traders’ information. If the larger price delays before the market crash are driven by high sentiment and investor overconfidence, we expect that declines in abnormal returns (ARs) are larger for stocks of high-margin trades. In contrast, if margin trades reflect informed traders’ private information, the price decline of high-margin trade stocks is expected to be small. We compute the AR by running a time series regression of the market model for each stock using the monthly returns from month t−11 to t in each month t (i.e., a 12-month rolling window regression) and use the regression intercept as the AR₀ for the stock in month t. The CAR_0,1 is the stock's cumulative abnormal returns from month t to t+1, and the CAR_0,2 is the summation of ARs from month t to t+2. Then, we compare the AR₀ and CARs of stocks in different margin trade groups based on their margin ratios in the pre-crash period.

Panel A of Table 6 reports the results for AR₀. For the Low MG bal./TRD group, the average values of AR₀ are 2.79 and 1.94 percent in the pre- and post-crash periods, respectively, and the change is −0.85 percent and significant at the 0.1 level. For the Medium and High MG bal./TRD groups, the declines in AR₀ are −1.94 and −2.69 percent, respectively, and both are significant at the 0.01 level. In addition, the difference in the declines between the Low and High MG bal./TRD groups (Diff 3 – Diff 1) is −1.84 percent, which is significant at the 0.01 level. For the Low and High MG/TRD groups, the declines in AR₀ are −2.15 and −2.18 percent, respectively, and both are significant at the 0.01 level, but the difference between the Low and High groups is not significant. For the Low MG bal./TA group, the decline in AR₀ is −0.03 percent and insignificant. However, the declines in AR₀ for the Medium and High MG bal./TA groups are −2.0 and −3.40 percent, respectively, and both are significant at the 0.01 level. In addition, the difference in the declines of AR₀ between the Low and High groups (Diff 3 – Diff 1) is −3.37 percent and significant at the 0.01 level.10

Panels B and C of Table 6 report the changes in CAR_0,1 and CAR_0,2, respectively. The CARs are significantly smaller in the post-crash periods than in the pre-crash periods, and the declines are larger for the high-margin groups, especially when margin trade is measured by MG bal./TRD and MG bal./TA ratios. For example, the declines in CAR_0,1 for the Low and High MG bal./TRD are −2.15 and −5.93 percent, respectively, and the difference in the declines between the Low and High groups is −3.78 percent, which is significant both economically and statistically. The declines in CAR_0,1 are −0.55, −4.56, and −7.23 percent, for the Low, Medium, and High MG bal./TA groups, respectively, and the difference in the declines between the Low and High groups is −6.68 percent and significant at the 0.01 level. The pattern of changes in CAR_0,2 is similar to that of CAR_0,1, and the difference in the changes of CAR_0,2 between the Low and High MG bal./TA groups is −9.45 percent.

To investigate whether the declines in the abnormal returns are caused by the changes in firm fundamentals rather than investor overconfidence proxied by margin trade, we conduct the following regression:

(7)

where the dependent variables are the changes in AR₀ (CAR_0,1 and CAR_0,2). The independent variables include the rank of margin trade ratio (MG Rank), which takes a value of 1, 2, or 3 if the stock is ranked at the bottom, medium, or top third based on its margin ratios (MG bal./TRD, MG/TRD, MG bal./TA) in the pre-crash period. Other independent variables are control variables of firm characteristics, which include the changes in earnings per share (∆EPS), debt ratio (∆D/TA), Herfindahl index of top 10 shareholders (∆HHI_Top10), turnover ratio (∆Turnover), and the changes in stock beta (∆β).

Panel A of Table 7 reports the regression results of the changes on AR₀. The coefficient on MG bal./TRD (the first two columns) is −0.574 and significant at the 0.05 level, indicating that high-margin stocks experience significantly large declines in abnormal returns, confirming the results reported in Table 6. The coefficient on MG/TRD (the two middle columns) is insignificant. The coefficient on MG bal./TA is −1.382 and significant at the 0.01 level. Panel B of Table 7 reports the results of regressions on the changes to CAR_0,1. The coefficients on MG bal./TRD and MG bal./TA ratios are −1.098 and −2.602, and these numbers are significant at the 0.05 and 0.01 levels, respectively; whereas the coefficient on MG/TRD is insignificant. In the CAR_0,2 regressions reported in Panel C, the coefficients on MG bal./TRD and MG bal./TA ratios are −1.239 and −3.635 and significant at the 0.05 and 0.01 levels, respectively. Among the control variables, only the coefficients on ∆β remain consistently negative and significant at the 0.01 level in all regressions. To save space, the coefficients on control variables are not reported.

In summary, both the univariate and the regression analyses show that stocks of high-margin trades in the pre-crash period experience larger declines in abnormal returns after the crash, and the declines are unlikely to be due to the contemporaneous changes in firm fundamentals. This additional evidence also suggests that the margin trades are less likely driven by informed traders.

5.2 Do margin trades predict or destabilise price?

If margin trades reflect investor sentiment rather than informed traders’ information, more margin trades are expected on extreme market up-days, and fewer or negative net margin trades are expected on extreme market down-days. In contrast, if margin traders trade based on their private information, they buy (sell) undervalued (overpriced) stocks. Thus, more margin trades are expected on extreme down-days, and fewer margin trades are expected on extreme up-days, especially when extreme days are transitory. We classify a trading day as an extreme up-day if the daily return of an individual stock on that day (R_t) is equal to or greater than 7 percent (R_t ≥ 7 percent) or equal to or greater than 2 times the standard deviation (R_t ≥ 2δ) of its daily returns in a 12-month benchmark period from December 2013 to November 2014 prior to the pre-crash period. Similarly, a trading day is classified as an extreme down-day if the daily return of an individual stock is equal to or smaller than −7 percent (R_t ≤ −7 percent) or R_t ≤ −2δ. To reduce any possible contamination effect of multiple extreme days, we include only the extreme days that are not preceded by another extreme day during the prior nine days from t−9 to t−1.11

Panel A of Table 8 reports the margin trades on extreme day t unconditional on the following day t+1. Obviously, margin trade is very high on extreme up-days, especially in the pre-crash period. The mean (median) value of the net margin trade to the daily total trading amount (excluding margin trades) ratio is 2.40 (1.67) on up-days in the pre-crash period, and 2.11 (1.25) on up-days in the post-crash period. In sharp contrast, the mean (median) value of the margin trade ratio is −0.29 (−0.23) on extreme down-days before the crash and −1.64 (−1.25) on extreme down-days after the market crash. The negative value of net margin trade ratios indicates that margin traders liquidate their margin positions on down-days.12 In addition, the differences in the margin trade ratios on up-days are not significant between the pre- and post-crash periods, but the differences on down-days are significant between the pre- and post-crash periods, suggesting that margin traders are more sensitive to negative information after the crash. As additional evidence, Figure 3 shows the median values of daily net margin trade to total trade ratios surrounding extreme days from 10 days before (t−10, t−1) to 10 days after (t+1, t+10).

Following Boehmer and Wu (2013), we further classify an extreme down-day t into four categories: a continuation, a small reversal, a large reversal, or an overshot, depending on what occurs on the following day, t+1. Specifically, a continuation is that the stock return on day t+1 is non-positive after the extreme down-day t. A small reversal is that the closing price on day t+1 is greater than the closing price on day t but the reversal is smaller than 20 percent of the stock's return on the down-day t, i.e., P_t < P_t+1 ≤ P_t + 0.2 × (P_t−1 − P_t). A large reversal is if the stock return on day t+1 reaches more than 20 percent of its down-day t's return but the closing price on day t+1 still remains either at or below the closing price of day t−1, i.e., P_t + 0.2 × (P_t−1 − P_t) < P_t+1 ≤ P_t−1. An overshot is that the closing price on day t+1 exceeds the closing price on day t−1, i.e., P_t+1 > P_t−1. Similarly, after an extreme up-day t, a continuation is that the stock return on day t+1 is non-negative. A small reversal is a reversal of smaller than 20 percent of the stock's return on the up-day t, i.e., P_t − 0.2 × (P_t − P_t−1) ≤ P_t+1 ≤ P_t. A large reversal is a reversal of more than 20 percent of the up-day t's return but still remains above the closing price on day t−1, i.e., P_t−1 ≤ P_t+1 < P_t − 0.2 × (P_t − P_t−1). An overshot after an extreme up-day t is that the stock's price on day t+1 is below the closing price on t−1, P_t+1 < P_t−1.

Panel B of Table 8 shows the daily net margin trade to total trade ratio in the pre-crash period. The average values of margin trade ratios on extreme down-days are −0.36, −0.26, and −0.32 when the following day is a small reversal, a large reversal, and a continuation, respectively, and these numbers are statistically significant at either the 0.05 or 0.1 levels. The net margin trade to total trade ratio is 0.64 and insignificant when the following day is an overshot. In sharp contrast, on extreme up-days, the net margin trade to total trade ratios are not only positive but also large regardless of the condition on the following day, and the mean values of the ratios range from 2.12, when the following day is a continuation, to 3.0, when the following day is a small reversal. Panel C reports the net margin trade to total trade ratios after the market crash. On extreme down-days, all of the ratios are negative and significant at the 0.01 level regardless of the following day condition. Compared with the results on the down-days in the pre-crash period, the net margin trade to total trade ratios are not only consistently negative but also have a larger magnitude, ranging from −1.22 when the following day is a large reversal to −1.99 when the following day is a continuation. On extreme up-days, all the ratios are positive and significant at the 0.1 level or higher, and the magnitude is similar to that on extreme up-days in the pre-crash period.

These results show that margin traders play a pyramiding and de-pyramiding role in the markets. They increase margin trades substantially on extreme up-days and reduce their margin position on extreme down-days. More importantly, margin traders are more sensitive to bad news in the down market, which is evidenced by the significantly large magnitude of the negative net margin trade to total trade ratios on extreme down-days in the bear market. This additional evidence rejects the argument that margin trades reflect informed traders’ private information.