Medics Inc, JC Penney and Rexx Energy Corp had long term negative returns over their public existence within the timeframe, while the S&P500 returned 0.0514% on average daily.
One can observe that the S&P500 had relatively low volatility, as well as extreme values compared to the sample. Its maximum one-day loss of 11.98% of S&P500, as well as the 9.38%
increase are the former in reaction and the latter in recovery of the 2020 COVID-19 Crisis.
The remaining variables’ statistical characteristics should be interpreted separate from the previous stock market returns. Their values are less clearly interpreted as their formulisation is not as clear. The FF3F model specific SMB and HML factors have by far the highest standard deviation and extreme values out of all variables. This tells us that within the time window of the dataset the return of small versus big firms varies strongly and can reach highly different levels. The difference in returns of high book-to-value versus low book-to-value firms also seems to fluctuate strongly within the data sample. Both can be explained to the highly different reactions to market events of firms being attributed to either of these groups.
To sum up, the firm returns behave as expected and are highly volatile with high extrema.
The benchmark index is less volatile and experienced its relatively low extrema during the COVID-19 crisis in 2020.
5.1. Short squeeze
Table IV.
The short squeeze
This table presents the results regarding the short-term effect of a short squeeze on a firm’s abnormal return. It provides insight on the significance of the abnormal returns experienced over a 3-day event window centred around the short squeeze. The table presents the findings of performing a parametric KP-test as well as a GRANK test on each individual firms’ CAR, as well as on the CAAR on the whole sample conjunctively, with the ‘CAAR (11 securities)’ variable. The table provides the C(A)AR estimated with three different estimation models: The historical mean model (HMM), a single index model; the market-model (SIM), and finally, a multi-factor model;
the Fama French 3-Factor model (FF3F-model). The table provides each firm’s specific event date, as well as the span of each C(A)ARbetween brackets [-1,1]. In column (1) and (4) the C(A)ARis calculated with the HMM. In column (2) and (5) the C(A)AR is calculated with the SIM. In column (3) and (6) the C(A)ARis calculated with the FF3F. (1), (2) and (3) show the significance level of C(A)ARdetermined by the KP-test. (4), (5) and (6) show the significance level of C(A)ARdetermined by the GRANK test. Each C(A)ARis given in percentage points and below it is provided its significance level with *s. One * indicating an alpha of 10%, ** indicating an alpha of 5%
and *** indicating an alpha of 1%.
The CAR and CAAR results are consistent across estimation models. One can observe that the CARs of the individual firms are within a 10% range across estimation models. While the CAAR vary by less than two percentage points. This is a sign that all three estimation models
Parametric KP-test Non-parametric GRANK test
HMM SIM FF3F HMM SIM FF3F
(1) (2) (3) (4) (5) (6)
SECURITY EVENT DATE CAAR[-1,1] CAAR[-1,1] CAAR[-1,1] CAAR[-1,1] CAAR[-1,1] CAAR[-1,1]
AMC Entertainment Holdings Inc 27-Jan-21 255.9742%
***
254.4327%
***
259.0950%
***
255.9742%
***
254.4327%
***
259.0950%
***
Bank Atlantic Corp 01-Nov-11 99.1684% *** 102.4245%
***
101.5749%
***
99.1684%
***
102.4245%
***
101.5749%
***
Chesapeake Energy Corp 03-Mar-16 69.0600% *** 67.1819% *** 58.0983% *** 69.0600% *** 67.1819% *** 58.0983% ***
Cliffs Natural Resources Inc 31-May-16 31.4997%
**
30.9193%
**
24.1574%
**
31.4997%
**
30.9193%
**
24.1574%
**
Entero Medics Inc 05-Jan-17 236.8067%*** 236.6690%
***
242.5994%
***
236.8067%
***
236.6690%
***
242.5994%
***
EP Energy Corp 03-Mar-16 80.4122% *** 78.5755% *** 63.2516% *** 80.4122% *** 78.5755% *** 63.2516% ***
Gamestop 25-Jan-21 157.3324%*** 157.0023%
***
155.4159%
***
157.3324%
***
157.0023%
***
155.4159%
***
JC Penney 27-Feb-14 30.4448%
***
29.9021%
***
30.2689%
***
30.4448%
***
29.9021%
***
30.2689%
***
Quidel Corp 26-Oct-11 12.8502% *** 9.9270% *** 9.5388% *** 12.8502% *** 9.9270% *** 9.5388% ***
Rexx Energy Corp 02-Mar-16 80.3340% *** 75.0663% *** 64.4349% *** 80.3340% *** 75.0663% *** 64.4349% ***
Tesla 09-May-13 34.4414%
***
34.2158%
***
33.4338%
***
34.4414%
***
34.2158%
***
33.4338%
***
CAAR (11 securities) - 167.8759%*** 167.2498%
***
166.3034%
***
167.8759%
***
167.2498%
***
166.3034%
***
*** p-value < .01, ** p-value <.05, * p-value <.1
capture very similar price variation, which hints at a low level of confounding effects coming from overall market movement. This speaks in favour of the robustness of the analysis and show that the simple HMM model still provides reliable results compared to the more complex market and FF3F model.
All, except for Cliffs Natural Resources Inc, individual CAARs are significant on a 1%
alpha, providing further evidence that short squeezes took place on the event date. The Cliffs Natural Resources INC’s CAAR is significant on a 5% alpha, still providing strong evidence for abnormal positive returns due to the event. The stock experienced a 30% cumulative price movement over a 3-day period, which holds its significance across all three estimation models, with the two latter models incorporating various levels of systematic risk.
Looking at the CAAR (11 securities), one can see that the results as a sample tested together are significant on a 1% significance level, with a CAAR ranging from 166,3034% to 167.8759% across estimation models. The CAAR (11 securities) variable can be interpreted that the short squeeze had a statistically significant impact on short term returns. The null hypothesis for both performed tests, CAAR = 0 is rejected on a 1% significance level.
The results can be given high degrees of robustness, as both the parametric KP-test and the non-parametric GRANK test, overline in regards of their significance levels (Kolari &
Pynnönen, 2011). Statistical significance levels are also consistent across estimation models.
This analysis concludes that the short squeeze had a statistically significant, on a 1% alpha, effect on the return of each security and the sample of securities together.
5.2. Medium term
Table V.
Medium term post-event returns
This table presents the findings regarding the medium-term change in returns after a short squeeze, over a 6-day post-event window. The table shows results of the parametric KP-test as well as a non-parametric GRANK test on the sample firms individual CAR as well as on the whole sample conjunctively, with the ‘CAAR (11 securities)’
variable. The table provides the CAAR estimated with three different estimation models: The historical mean model (HMM), a single index model; the market-model (SIM), and finally, a multi-factor model; the Fama French 3-Factor model (FF3F-model). The table provides each firm’s specific event date, as well as the range of each C(A)AR between brackets [1,6]. The table provides each firm’s specific event date, as well as the span of each C(A)AR between brackets [-1,1]. In column (1) and (4) the C(A)AR is calculated with the HMM. In column (2) and (5) the C(A)AR is calculated with the SIM. In column (3) and (6) the C(A)AR is calculated with the FF3F.
(1), (2) and (3) show the significance level of C(A)AR determined by the KP-test. (4), (5) and (6) show the significance level of C(A)AR determined by the GRANK test. Each C(A)AR is given in percentage points and below it is provided its significance level with *s. One * indicating an alpha of 10%, ** indicating an alpha of 5%
and *** indicating an alpha of 1%.
The CARs and CAARs were computed over six trading day long window. One can observe that this event window measures twice the length of the 3-day event window in Table IV. The event window starts one trading day after the event date, as such the performance of the stock is analysed in the post-event timeframe opposing to Table 4. that looked at an event window
Parametric KP-test Non-parametric GRANK test
HMM SIM FF3F HMM SIM FF3F
(1) (2) (3) (4) (5) (6)
SECURITY EVENT DATE CAAR[1,6] CAAR[1,6] CAAR[1,6] CAAR[1,6] CAAR[1,6] CAAR[1,6]
AMC Entertainment Holdings Inc 27-Jan-21 "-51.7763%
**
"-50.9921%
**
"-53.6547%
**
"-51.7763%
**
"-50.9921%
**
"-53.6547%
***
Bank Atlantic Corp 01-Nov-11 -4.1376% -5.7219% -5.5631% -4.1376% -5.7219% -5.5631%
Chesapeake Energy Corp 03-Mar-16 15.9626% 13.4641% 9.5800% 15.9626% 13.4641% 9.5800%
Cliffs Natural Resources Inc 31-May-16 19.0239% 17.6188% 6.9925% 19.0239% 17.6188% 6.9925%
Entero Medics Inc 05-Jan-17 233.5755%
***
233.6611%
***
239.8623%
***
233.5755%
***
233.6611%
***
239.8623%
***
EP Energy Corp 03-Mar-16 84.1101%
***
81.6667%
***
72.3787%
***
84.1101%
***
81.6667%
***
72.3787%
***
Gamestop 25-Jan-21 151.2046%
***
151.0621%
***
154.5026%
***
151.2046%
***
151.0621%
***
154.5026%
***
JC Penney 27-Feb-14 19.2055%
*
18.4364%
*
19.2901%
*
19.2055%
*
18.4364%
*
19.2901%
*
Quidel Corp 26-Oct-11 0.2257% -2.1745% -3.5765% 0.2257% -2.1745% -3.5765%
Rexx Energy Corp 02-Mar-16 77.6951%
***
77.4268%
***
67.7587%
***
77.6951%
***
77.4268%
***
67.7587%
***
Tesla 09-May-13 27.4957%
***
24.9755%
***
24.5488%
***
27.4957%
***
24.9755%
***
24.5488%
***
CAAR (11 securities) - 86.8922%
**
85.7917%
**
83.7598%
**
86.8922%
**
85.7917%
**
83.7598%
**
*** p-value < .01, ** p-value <.05, * p-value <.1
surrounding the event date. This specification allows the analysis to look at the medium-term impact of the event, instead of the immediate effect (Benninga, 2008).
The individual CARs show less consistent and significant results as the short-term analysis but are still favourable to the analysis. Out of the 11 individual stocks, five experienced significant positive medium-term abnormal returns on a 1% alpha, while one experienced them on a 10% alpha across all estimation models. The remaining either have either a below 10%
significance level and/or negative returns, which are both contradictory to the expected relationship. AMC Entertainment Holdings INC and Bank Atlantic Corp experienced negative CARs in the medium term, with a 5% alpha for the former and below 10% for the latter one.
This can be interpreted as a market correction of the high price levels found in Table 4.
immediately after the event. AMC and Bank Atlantic both had experienced above average, in the context of the sample, short term abnormal returns. These results are mostly consistent across the parametric and non-parametric tests. Only the CAR of AMC is found to have stronger significance for the FF3F model with the GRANK test compared to the KP-test.
Otherwise, significance levels remain constant across estimation models.
The CAAR (11 securities) supports the alternative hypothesis (1). The CAAR is significant on a 5% significance level, with a CAAR ranging from 83.7598% to 86.8922% across estimation models. It measures approximately 85%, when averaged between 3 estimation methods. It shows an approximate decrease by the factor of 2 compared to the short-term analysis. The CAAR (11 securities) variable positive sign, and significance level can be interpreted as evidence in favour of hypothesis (1). It shows that there is statistical proof that the event, short squeeze, increased medium-term abnormal returns of the sample of stocks.
These results can be given high degrees of robustness, as both, the parametric KP-test and the non-parametric GRANK test, overline regarding their significance levels. Moreover, statistical significance levels are also consistent across all three estimation models. From these results, this paper concludes that the short squeezes had a statistically significant positive effect, on a 5% significance level, on the return of 45.45% of individual securities of the sample and on the sample of securities together.
5.3. Long term
Table VI.
Long term post-event returns
This table presents the findings regarding the medium-term change in returns after a short squeeze, over a 101-day post-event window The table shows results of the parametric KP-test as well as a non-parametric GRANK test on the sample firms individual CAR as well as on the whole sample conjunctively, with the ‘CAAR (11 securities)’ variable. In addition, there is an addition of a ‘CAAR (10 securities)’ variable, which present the GRANK and KP-test on the whole sample conjunctively, minus AMC Entertainment Holdings Inc. The table provides the C(A)AR estimated with three different estimation models. HMM, the historical mean model, SIM, a single index model: Market-model, and finally a multi-factor model, FF3F-model. The table provides each firm’s specific event date, as well as the range of each C(A)AR between brackets, [6, 106]. In column (1) and (4) the C(A)AR is calculated with the HMM. In column (2) and (5) the C(A)AR is calculated with the SIM. In column (3) and (6) the C(A)AR is calculated with the FF3F. (1), (2) and (3) show the significance level of C(A)AR determined by the KP-test. (4), (5) and (6) show the significance level of C(A)AR determined by the GRANK test. Each C(A)AR is given in percentage points and below it is provided its significance level with *s. One * indicating an alpha of 10%, ** indicating an alpha of 5% and *** indicating an alpha of 1%.
Both the KP-test and GRANK test are performed on CAR and CAAR 120 consecutive trading days. The post-event window starts six trading days after the event date, at the end of the medium-term window. As such, the analysis has a longer scope compared to Table IV. and
Parametric KP-test Non-parametric GRANK test
HMM SIM FF3F HMM SIM FF3F
(1) (2) (3) (4) (5) (6)
SECURITY EVENT DATE CAAR[6,106] CAAR[6,106] CAAR[6,106] CAAR[6,106] CAAR[6,106] CAAR[6,106]
AMC Entertainment Holdings Inc 27-Jan-21 232.7924%
*
232.5474%
*
208.7361%
***
232.7924%
*
232.5474%
*
208.7361%
***
Bank Atlantic Corp 01-Nov-11 35.4559% 15.5690% 16.1150% 35.4559% 15.5690% 16.1150%
Chesapeake Energy Corp 03-Mar-16 78.4296% 63.8397% 14.8470% 78.4296% 63.8397% 14.8470%
Cliffs Natural Resources Inc 31-May-16 -71.3485% -70.9803% -93.3373% -71.3485% -70.9803% -93.3373%
Entero Medics Inc 05-Jan-17 82.3214% 82.1940% 157.0492%
* 82.3214% 82.1940% 157.0492%
* EP Energy Corp 03-Mar-16 44.1182% 29.8497% -26.9700% 44.1182% 29.8497% -26.9700%
Gamestop 25-Jan-21 -26.3300% -26.4379% 9.1094% -26.3300% -26.4379% 9.1094%
JC Penney 27-Feb-14 73.5624% 80.6629% 78.7644%
* 73.5624% 80.6629% 78.7644%
* Quidel Corp 26-Oct-11 -22.5125% "-46.7820%
*
"-45.3310%
**
-22.5125% "-46.7820%
*
"-45.3310%
**
Rexx Energy Corp 02-Mar-16 72.4428% 58.5542% 1.5547% 72.4428% 58.5542% 1.5547%
Tesla 09-May-13 32.1909% 45.4033% 39.8678%
* 32.1909% 45.4033% 39.8678%
*
CAAR (11 securities) - 86.9183%
** 80.0442% 69.7805% 86.9183%
** 80.0442% 69.7805%
CAAR (10 securities) - 61.9968%
* 54.4951% 45.5354% 61.9968%
* 54.4951% 45.5354%
*** p-value < .01, ** p-value <.05, * p-value <.1
Table V., which looked at shorter timeframes. This specification allows the analysis to look at the long-term impact of the event instead of the immediate or medium-term effect (Benninga, 2008).
The results indicate that daily abnormal returns diminish over the longer timeframe. One can observe that the event window measures 40 times the length of the short-term and 20 times of the medium-term window. All firms experienced less high price changes proportional to event window length, compared to the short-term and medium-term results.
Out of the 11 firms, 72.72% produced a positive CAR, with the remaining firms producing negative long-term returns. AMC and Bank Atlantic experienced positive returns in the long term compared to their previous medium-term negative CAR.
Regarding the individual firms, there is no strong evidence in favour of the expected relationship. Out of the positive CAR’s, AMC Entertainment Holdings Inc, is the only one is found to be significant on a 10% alpha across all 3 estimation models. Three other firms, Entero Medics Inc, JC Penney and Tesla achieved 10% alpha for one out of three estimation models, showing no strong signs in favour of the alternative hypothesis (2). Quindel Corp achieved 5%
significance on its negative returns with the FF3F model and 10% with the market model, providing further evidence against the alternative hypothesis (2) and in favour of the null hypothesis (2).
As a collection, the CAAR (11 securities) only shows significant positive returns with the HMM model at a 5% alpha, which a model that ignores market movements. These results are consistent across both significance testing models. The other two estimation models find CAAR to be non-significant, as their significance level is below 10%. This is evidence against the expected relationship. The results do not hint at a positive long-term impact of short squeezes on the collective returns of the sample.
AMC’s results merit a deeper look. AMC’s KP-test and GRANK test reached 10% with the HMM and market-model while passing 1% for the FF3F estimation model, while also having a positive CAAR. As the FF3F model incorporates market trends the most, these findings indicate that AMC Entertainment Holdings Inc, outperformed the market significantly. This can most likely be attributed to macro-economic trends, as AMC Entertainment Holdings Inc’s cashflow suffered immensely due to the COVID-19 crisis. The company was forced to close all its cinema venues (Q.ai a Forbes Company, 2021). However, during the measured post-event window lockdown measures were lifted, which raised hope that AMC could generate
cashflows again. This contributed to the optimism in the market regarding its stock and the price rose again. The increase in CAR should not be interpreted as being mainly attributed to the short squeeze event but is most likely mainly due to confounding effects.
Removing AMC’s abnormal return from the sample indicates even stronger evidence in favour of the null hypothesis (2). The resulting ‘CAAR 10 securities’ is lower compared to the whole sample, and the significance level of the HMM decreases to a 10% significance level.
This indicates that the previous 5% significance level was influenced by the inclusion of AMC and consequently the confounding affects expected to be included in its abnormal returns.
The results can be given high degrees of robustness. Both, the parametric KP-test and the non-parametric GRANK test, overline in regards of their significance levels. From these results, this paper concludes that the short squeezes had no statistically significant positive effect on the returns of individual securities or on the sample of securities altogether. Any found significance levels can be argued to be caused by macro-economic variables. The null hypothesis (2) is not rejected.
To conclude, this statistical analysis finds that the selected sample of firms experiences significant positive returns directly around the event date (+/- 1 day). Furthermore, there is sufficient evidence to state that the short squeeze has a positive relationship with stock returns in the medium term (6 trading days). Finally, there is no evidence for a change in long term abnormal returns. Thus, this paper rejects its null hypothesis (1) on a 5% significance level and does not reject its null hypothesis (2).