E. Investor Sentiment
IV. Empirical Results
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IV. Empirical Results A. Hypothesis
Our main test is whether stock prices are affected by the trading consolidation or not.
Given that the warrants exercise on the expiration dates have no information content (we include only warrants that are deep in-the-money prior to expiration), our null
hypothesis is that the ARs on the stock is zero. Against the null, the first alternative hypothesis is:
H1. Stock prices should rise if consolidation of trading is beneficial.
However, it could be argued that warrants offer investors additional tools to diversify their investment portfolios, upon warrants exercise, might reduce investors’ incentive and interest to invest in the stocks. Therefore, we consider another alternative
hypothesis:
H2. Stocks prices should fall because of the elimination of investment tools of
diversifying afforded by warrants.
In fact, the both effects may be present. The results will show us which effect is stronger.
Hypothesis H1 posits that the rise in stock prices is due to the increase in the stock liquidity upon the consolidation of trading after the warrants expiration. We exam this hypothesis by testing the relation between CAR and variables that reflect the liquidity benefits of trading consolidation. Our hypothesis is:
H3. CAR is an increasing function of liquidity benefits from consolidation of trading following the warrants expiration.
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B. The Analysis of Abnormal Returns
As mentioned in the part of introduction, first we want to see the abnormal returns (ARs) of stocks around the issued dates, the first trading dates, and the expiration dates of all warrants. We could see the statistic results in Table 2, 3 and 4.
In Table 2, the results show that almost all the means of daily ARs of stocks around the issued dates of all warrants are significantly positive. These results are contrary to the paper written by 張啟容 (1998), which discovered that there are negative ARs on the issued dates significantly. The paper uses the data in the sample period from 1997 to 1998 in Taiwan, and the author considered that the events of issuing warrants would convey somehow a kind of negative signal to investors. However, in our sample period, the phenomenon does not exist anymore. Conrad (1989) finds that options would have positive price effects on stocks beginning approximately three days before introduction.
And the effects are significantly until the day after issuing. Although warrants are not exactly like options, the results from Conrad (1989) are somewhat consistent with ours.
We think that issuers might buy portions of stocks to build their positions for hedge before they issue the warrants. Therefore the behavior of inventory buildup may lead the stock prices rising. This explanation is consistent with the study from Chan and Wei (2001).
Table 2
The Abnormal Returns of Stocks around the Issued Dates of All Warrants
t-3 t-2 t-1 t t+1 t+2 t+3
Mean 0.2790*** 0.2894*** 0.0850*** 0.0874*** 0.0682*** 0.0248 0.0313*
Std. 2.5503 2.5101 2.3336 2.2985 2.2936 2.2453 2.2504
t-value 13.19 13.90 4.39 4.58 3.58 1.33 1.68
N 14528
Day t is the issued dates of warrants. The abnormal returns (ARs) of stocks are the daily returns of underlying stocks minus the daily market returns. The sample comprises 14528 warrants over the period 2006-2010. ***, **, and * indicate significant level 1%, 5%, and 10%, respectively.
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In Table 3, it shows the results of the means of the ARs of stocks around the first trading dates of all warrants are almost significantly positive. On average, issuers would sell out their issuing positions in the first three days after the warrants listing (王佩甄 (2000)). However, there is no strong evidence to explain the ARs of stocks after the first trading dates of warrants. We infer a possible explanation is that since most of warrants are issued out-of-money (showed in Table 1), if issuers want to sell out their issuing warrants as soon as possible, they might somewhat play a role of market makers in the stock market to stimulate the stock prices to go up.
Table 3
The Abnormal Returns of Stocks around the First Trading Dates of All Warrants
t-3 t-2 t-1 t t+1 t+2 t+3
Mean 0.0225 0.0340* 0.0878*** 0.1348*** 0.1850*** 0.1674*** 0.1945***
Std. 2.2778 2.2349 2.2599 2.2508 2.2879 2.2986 2.2617
t-value 1.19 1.83 4.68 7.22 9.74 8.78 10.36
N 14521
Day t is the first trading dates of warrants. The abnormal returns (ARs) of stocks are the daily returns of underlying stocks minus the daily market returns. The sample comprises 14521 warrants over the period 2006-2010. ***, **, and * indicate significant level 1%, 5%, and 10%, respectively.
In Table 4, we could see that the days before expiration dates and the event dates have negative ARs of stocks. But the days after expiration dates have significantly positive ARs of stocks. We infer that investors might prefer to invest in the same equity claim. Since the warrants expired, investors have to rebalance their positions. The results could be explained that stock prices are improved by trading consolidation. We will discuss the relation between prices, liquidity, and trading consolidation in detail in the following section.
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Table 4
The Abnormal Returns of Stocks around the Expiration Dates of All Warrants
t-3 t-2 t-1 t t+1 t+2 t+3
Mean 0.0662*** 0.0821*** -0.0003 -0.0327* 0.0703*** -0.0026 -0.0112
Std. 2.1241 2.1791 2.1095 2.1442 2.0433 2.0965 2.0704
t-value 3.70 4.47 0.02 1.81 4.08 0.15 0.64
N 14102
Day t is the expiration dates of warrants. The abnormal returns (ARs) of stocks are the daily returns of underlying stocks minus the daily market returns. The sample comprises 14102 warrants over the period 2006-2010. ***, **, and * indicate significant level 1%, 5%, and 10%, respectively.
Further, we want to see if different level of investor sentiment would affect the ARs of stocks or not. In Table 5, we could see that in the period of high VIX, the ARs of stocks before t+2 are all as significantly positive as the results in Table 2. There is no apparent difference when investor sentiment is relatively high.
Table 5
The Abnormal Returns of Stocks During the Issued Dates of All Warrants in the Period of High VIX
t-3 t-2 t-1 t t+1 t+2 t+3
Mean 0.2729*** 0.2919*** 0.0666* 0.1023*** 0.0936*** 0.0348 -0.0385
Std. 2.8675 2.7640 2.6204 2.6161 2.6087 2.5563 2.5529
t-value 7.33 8.14 1.96 3.01 2.76 1.05 1.16
N 5935
Day t is the issued dates of warrants. The abnormal returns (ARs) of stocks are the daily returns of underlying stocks minus the daily market returns. The sample comprises 5935 warrants in the period of high VIX (we calculate the mean value of VIX during the period of 30 trading days before and after the issued dates following the window of (－30, ＋30)) exercise over 2006-2010. ***, **, and * indicate significant level 1%, 5%, and 10%, respectively.
Next, we could see the ARs of stocks after t-1 in Table 6 are all as significantly positive as the results in Table 3. Apparently, the ARs of stocks after the first trading dates would not be significantly affected by investor sentiment.
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Table 6
The Abnormal Returns of Stocks During the First Trading Dates of All Warrants in the Period of High VIX
t-3 t-2 t-1 t t+1 t+2 t+3
Mean -0.0325 -0.0407 0.0423 0.0680** 0.1873*** 0.1317*** 0.2030***
Std. 2.5696 2.5313 2.5539 2.5796 2.5830 2.5998 2.5245
t-value 0.97 1.24 1.27 2.03 5.58 3.90 6.19
N 5924
Day t is the first trading dates of warrants. The abnormal returns (ARs) of stocks are the daily returns of underlying stocks minus the daily market returns. The sample comprises 5924 warrants in the period of high VIX (we calculate the mean value of VIX during the period of 30 trading days before and after the first trading dates following the window of (－30, ＋30)) exercise over 2006-2010. ***, **, and * indicate significant level 1%, 5%, and 10%, respectively.
In Table 7, we could see the ARs of stocks on the day t are different from the results in Table 4. So in the period of high VIX, the ARs of stocks on the expiration dates are not significantly negative.
Table 7
The Abnormal Returns of Stocks During the Expiration Dates of All Warrants in the Period of High VIX
t-3 t-2 t-1 t t+1 t+2 t+3
Mean 0.1493*** 0.1407*** 0.0297 0.0095 0.1310*** 0.1020*** 0.0565
Std. 2.5419 2.5865 2.5210 2.5370 2.4491 2.5355 2.4600
t-value 3.78 3.50 0.76 0.24 3.44 2.59 1.48
N 4133
Day t is the expiration dates of warrants. The abnormal returns (ARs) of stocks are the daily returns of underlying stocks minus the daily market returns. The sample comprises 4133 warrants in the period of high VIX (we calculate the mean value of VIX during the period of 30 trading days before and after the expiration dates following the window of (－30, ＋30)) exercise over 2006-2010. ***, **, and * indicate significant level 1%, 5%, and 10%, respectively.
In Table 8, we could see that the ARs of stocks during the issued dates before t+2 are all as significantly positive as the results in Table 2 and Table 5. It suggests no matter in what levels of VIX, the existence of ARs of stocks is lasting.
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Table 8
The Abnormal Returns of Stocks During the Issued Dates of All Warrants in the Period of Low VIX
t-3 t-2 t-1 t t+1 t+2 t+3
Mean 0.2832*** 0.2877*** 0.0977*** 0.0771*** 0.0507** 0.0179 0.0796***
Std. 2.3061 2.3188 2.1130 2.0506 2.0478 2.0026 2.0139
t-value 11.39 11.50 4.29 3.48 2.29 0.83 3.66
N 8593
Day t is the issued dates of warrants. The abnormal returns (ARs) of stocks are the daily returns of underlying stocks minus the daily market returns. The sample comprises 8593 warrants in the period of low VIX (we calculate the mean value of VIX during the period of 30 trading days before and after the issued dates following the window of (－30, ＋30)) exercise over 2006-2010. ***, **, and * indicate significant level 1%, 5%, and 10%, respectively.
Then we could see the results showed in Table 9, comparing with Table 3 and Table 6, the ARs of stocks are all as significantly positive as the results above. It proves again that the investor sentiment did not visibly affect the ARs of stocks during the first trading dates of warrants.
Table 9
The Abnormal Returns of Stocks During the First Trading Dates of All Warrants in the Period of Low VIX
t-3 t-2 t-1 t t+1 t+2 t+3
Mean 0.0604*** 0.0854*** 0.1192*** 0.1808*** 0.1834*** 0.1920*** 0.1887***
Std. 2.0521 2.0033 2.0324 1.9918 2.0602 2.0655 2.0614
t-value 2.73 3.95 5.44 8.42 8.25 8.62 8.49
N 8597
Day t is the first trading dates of warrants. The abnormal returns (ARs) of stocks are the daily returns of underlying stocks minus the daily market returns. The sample comprises 8597 warrants in the period of low VIX (we calculate the mean value of VIX during the period of 30 trading days before and after the first trading dates following the window of (－30, ＋30)) exercise over 2006-2010. ***, **, and * indicate significant level 1%, 5%, and 10%, respectively.
In Table 10, we could see that the ARs of stocks are almost as same as the results in Table 4. According to our results, we could infer that the effects of investor sentiment play a role in the ARs of stocks during the expiration dates of warrants. As we exam the
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variances of the ARs of stocks during the issued dates and the first trading dates in different levels of VIX, there is no visibly change among our statistic results.
Table 10
The Abnormal Returns of Stocks During the Expiration Dates of All Warrants in the Period of Low VIX
t-3 t-2 t-1 t t+1 t+2 t+3
Mean 0.0318* 0.0578*** -0.0128 -0.0502** 0.0451** -0.0459** -0.0393**
Std. 1.9236 1.9855 1.9132 1.9582 1.8486 1.8832 1.8849
t-value 1.65 2.90 0.67 2.56 2.44 2.43 2.08
N 9969
Day t is the expiration dates of warrants. The abnormal returns (ARs) of stocks are the daily returns of underlying stocks minus the daily market returns. The sample comprises 9969 warrants in the period of low VIX (we calculate the mean value of VIX during the period of 30 trading days before and after the expiration dates following the window of (－30, ＋30)) exercise over 2006-2010. ***, **, and * indicate significant level 1%, 5%, and 10%, respectively.
In this paper, we mainly focus on the warrants which are deep in-the-money. The exercise of those type of warrants is quite certain, it suggests that we can eliminate time value and information cost inside the warrants. In Table 11, comparing with the results in Table 4, the ARs of stocks on the expiration dates of deep in-the-money warrants are more significantly negative than the results of all warrants.
Table 11
The Abnormal Returns of Stocks During the Expiration Dates of All Deep In-the-money Warrants
t-3 t-2 t-1 t t+1 t+2 t+3
Mean 0.0211 0.0033 0.0283 -0.1327*** 0.1483*** 0.0399 0.0633*
Std. 2.0357 2.0373 2.0163 2.1160 2.0136 2.0608 2.1040
t-value 0.65 0.10 0.84 3.74 4.39 1.15 1.79
N 3549
Day t is the expiration dates of warrants. The abnormal returns (ARs) of stocks are the daily returns of underlying stocks minus the daily market returns. The sample comprises 3549 deep in-the-money warrants over the period 2006-2010. ***, **, and * indicate significant level 1%, 5%, and 10%, respectively.
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In Table 12, the ARs of stocks on the expiration dates are not as significantly negative as the results in Table 11. A possible explanation is that investors would certainly exercise their call warrants in the expiration dates, so the issuers need no more stocks to hedge their short positions of warrants. They would sell their present holding positions in the stock market.
Table 12
The Abnormal Returns of Stocks During the Expiration Dates of All Non-Deep In-the-money Warrants
t-3 t-2 t-1 t t+1 t+2 t+3
Mean 0.0810*** 0.1086*** -0.0100 0.0010 0.0440** -0.0169 -0.0363*
Std. 2.1529 2.2242 2.1400 2.1527 2.0526 2.1083 2.0585
t-value 3.87 5.01 0.48 0.05 2.20 0.82 1.81
N 10553
Day t is the expiration dates of warrants. The abnormal returns (ARs) of stocks are the daily returns of underlying stocks minus the daily market returns. The sample comprises 10553 non-deep in-the-money warrants over the period 2006-2010. ***, **, and * indicate significant level 1%, 5%, and 10%, respectively.
In the following sections, we discuss further how the warrant market affects the stock market in different levels of investor sentiment.
C. Liquidity Change and Cumulative Abnormal Returns
The results in Table 13 show that the mean DVOL is －0.0309 with t＝10.66, highly significant. The coefficient of VOLRWS is significantly positive. It means if the average daily trading volume of warrants relative to the average daily trading volume of the stock before the (days －30 to －1) warrant expired raise, the trading volume of stocks relative to the market volume would also raise. Even though the mean of DVOL is negative, the increase in average stock volume is significantly induced by the decrease of numbers of living warrants.
The mean DSPD is positive but insignificant. We could see the coefficient of
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VOLRWS is significantly negative. It is consistent with the results of DVOL which means
that the greater the trading volume of warrants is, the greater the trading volume of the underlying stock is. And it also improved the liquidity of the stock market since the bid-ask spread decreased.
Then we could see the mean DTRQ is －0.0493 with t＝16.22, highly significant.
However, the coefficient of VOLRWS is significantly positive which represents that the liquidity of the stock market is indeed improved.
Finally, the average Dstd is significantly positive. It means that the market depth of the stock market is poorer after the warrants expired, but the coefficient of VOLRWS is insignificant.
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Changes in The stock liquidity following the warrant Exercise Regression Estimation Results
Dependent Variable Mean Constant VOLRWS R2
DVOL -0.0309*** indicate stock j and the market, respectively. A indicates the period of 30 trading days after the warrant expiration, days ＋1 to ＋30, and B indicates the period of 30 days before expiration, days －30 to －1.
𝐷𝑆𝑃𝐷𝑗= 𝑆𝑃𝑅𝐸𝐴𝐷𝑗𝐴− 𝑆𝑃𝑅𝐸𝐴𝐷𝑗𝐵. Roll (1984) proposes that 𝑆𝑃𝑅𝐸𝐴𝐷𝑗= 2 ∙ �−𝐶𝑂𝑉𝑗, where COV is the ratio of the average daily trading volume of warrants to that of the stock in the period of 30 trading days (days －30 to －1) before the warrant expired. The sample comprises 3549 warrants exercise over the period 2006-2010.
The estimated models are
(7) 𝐷𝐿𝐼𝑄𝑈𝐼𝐷𝐼𝑇𝑌𝑗= 𝛾0+ 𝛾1𝑉𝑂𝐿𝑅𝑊𝑆𝑗+ 𝑢𝑗,
Where DLIQUIDITYj＝DVOLj, DSPDj, DTRQj, or Dstdj.
t-statistics are in parentheses. The t-statistics if the regression coefficients are calculated using robust estimation of the standard errors, following White (1980). ***, **, and * indicate significant level 1%, 5%, and 10%, respectively.
Table 14 shows how all the factors we use above affect the CAR. Our main test is whether stock prices are affected by the warrants expired.
Hypothesis H1 could be explained as following reasons. According to the results in Table 13, we have noticed that the trading volume would transfer from warrants to stocks. The liquidity of the stock market increased after the warrants expired. The ensuing improvement in liquidity should bring higher stock prices (Amihud and Mendelson (1986), Brennan and Subrahmanyam (1996), Amihud, Mendelson, and Lauterbach (1997)).
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However, according to the results in Table 11, the mean value of the CAR is significantly negative. So we further study the relation between the CAR and the liquidity of stocks by examining Hypothesis H3. In Table 14, the coefficients of DVOL are significantly positive in the model (1) and (3). It is consistent with Hypothesis H3 which suggests that the coefficient of DVOL should be positive. If investors anticipate that the consolidation of trading between the warrants and the stocks improves liquidity, the increase in stock price should be an increasing function of the increase in its trading volume.
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Determinants of the Cumulative Abnormal Return (CAR) on the Expiration of All Deep-in-the-Money Warrants
Model (1) (2) (3) (4) (5) (6) (7) (8) (9) 𝑙𝑜𝑔�𝑉𝑂𝐿𝑗𝐵∕ 𝑉𝑂𝐿𝐵𝑚�. VOL is the average daily volume, and j and m indicate stock j and the market, respectively. A indicates the period of 30 trading days after the warrant expiration, days ＋1 to ＋30, and B indicates the period of 30 days before expiration, days －30 to －1. 𝐷𝑆𝑃𝐷𝑗= 𝑆𝑃𝑅𝐸𝐴𝐷𝑗𝐴− 𝑆𝑃𝑅𝐸𝐴𝐷𝑗𝐵. Roll (1984) proposes that over the post-exercise increase in number of shares. The sample comprises 3549 warrants exercise over the period 2006-2010. t-statistics are in parentheses. The t-statistics if the regression coefficients are calculated using robust estimation of the standard errors, following White (1980). ***, **, and * indicate significant level 1%, 5%, and 10%, respectively.
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The second measure is bid-ask spread, DSPD. In model (2), (3), and (4), the coefficients of DSPD are all significantly positive. It is consistent with Hypothesis H2 but contrary to Hypothesis H3. Then we could see the coefficients of the third and forth measures in model (5), (6), (7), and (8). Hypothesis H3 suggests that the coefficients of DTRQ and Dstd should be positive and negative, respectively. The higher the turnover
rate is, the higher CAR is. It represents that the consolidation of trading improves liquidity, and further benefits CAR. Similarly, the deeper the market depth is, the higher CAR is.
The fifth measure is DVOLRAT, which is the difference between DVOL and RATWS. Since the number of shares of stocks naturally increases after the warrant
exercise, it may be expected that the trading volume of stocks would increase as well.
However, most of warrants use cash to implement the contracts instead of using stocks.
Besides, part of the trading volume in the stocks may be due to arbitrage or hedge transactions between stocks and warrants. We obtain that the mean of DVOLRAT is － 0.0335 with t＝11.57, significantly different from zero, and the median is －0.0363, implying that the trading volume of most stocks increases by less than the increase in the number of shares of stock after the warrants expired. The result inflects that the part of the trading volume before warrants exercise is due to arbitrage or hedge trading. The coefficients of DVOLRAT are significantly positive in model (4) and (9). The results are consistent with Hypothesis H3.
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D. Investor Sentiment
In this section, we want to see if there is any results change in different levels of investor sentiment. We use VIX as a proxy to measure investor sentiment. As we mentioned in the previous section, we use the mean value of VIX in the whole sample period as a criterion to define the period of high VIX and low VIX.
Table 15 shows changes in the stock liquidity following the warrant exercise in the high VIX period which we calculate the mean value of VIX during the period of 30 trading days before and after the expiration dates following the window of (－30, ＋30).
According to the results in Table 15, the main difference to the results in Table 13 is the coefficient of VOLRWS in the regression using Dstd as the dependent variable which is significantly positive in Table 15. It suggests when investor sentiment is relatively high, the market depth would be worse apparently.
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Changes in The stock liquidity following the warrant Exercise in the Period of High VIX
Regression Estimation Results
Dependent Variable Mean Constant VOLRWS R2
DVOL -0.0138*** indicate stock j and the market, respectively. A indicates the period of 30 trading days after the warrant expiration, days ＋1 to ＋30, and B indicates the period of 30 days before expiration, days －30 to －1.
DVOL -0.0138*** indicate stock j and the market, respectively. A indicates the period of 30 trading days after the warrant expiration, days ＋1 to ＋30, and B indicates the period of 30 days before expiration, days －30 to －1.