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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.