Before we commence the cross-sectional analysis, we will briefly consider the average transaction costs that prevail during the event window. This is done to determine whether investors can earn a profit from exploiting the significantly negative ACAR of -1.1%. The average transaction costs (calculated as the percentage bid-ask spread relative to the bid price) and absolute value of ACAR for the event window are shown in Table 4 below.
30 There is a slight upward skew incorporated in the average AAV for this post-lockup period (+3, +8). The median AAV for the same period is 103.9%.
31 See footnote 29 where we explain the selected range of trading days to be depicted in Figure 2 and Figure 3
56 As shown in Table 4, the average transaction cost for the entire sample amounts to 1.31%. At a first glance, this exceeds the absolute value ACAR and thus implies that it is too costly to profit off the abnormal mispricing.
However, when assessing the 95% confidence interval for average transaction costs, it becomes evident that there only is a difference of 0.04 percentage points between the absolute value of ACAR and the lower bound of the confidence interval for average transaction costs. Furthermore, a 99% confidence interval would yield a lower bound of 1.03%, which thereby would overlap with the absolute value of ACAR. It is therefore of great importance to expand the analysis and consider the daily development of the average transaction costs and absolute values of AAR, which is depicted in Figure 4 and tabulated by Table 5.
When assessing the daily development of the average transaction costs and absolute values of AAR throughout the event window, it becomes clear that (on average) one cannot benefit off the abnormal price reaction at lockup expiration. One should especially consider the absolute values of AAR at 𝑡 = −2 and 𝑡 = +2 since
TABLE 4: Transaction costs and absolute ACAR for the event window (-2, +2)
Event window ABS(ACAR) Mean SD N Lower 95% Upper 95%
(-2, +2) 1.06% 1.31% 1.3% 141 1.10% 1.53%
FIGURE 4: Transaction costs and absolute AARtwithin the event window (t= -2, +2)
The solid red line represents the daily average transaction costs throughout the event window, whereas the red dotted lines represent the upper- and lower bounds of the associated 95% confidence interval. The solid blue line represents the absolute value of average abnormal returns throughout the event window, whereas the blue dotted line represents the upper bound of the associated 95% confidence interval.
-2 -1 0 1 2
Trading day (t)
TABLE 5: Transaction costs and absolute AARt within the event window (-2, +2)
Event window ABS(AAR) Mean SD N Lower 95% Upper 95%
-2 0.51% 1.25% 2.0% 141 0.9% 1.6%
-1 0.08% 1.29% 1.4% 141 1.1% 1.5%
0 0.21% 1.26% 1.4% 141 1.0% 1.5%
1 0.19% 1.31% 1.5% 141 1.1% 1.6%
2 0.64% 1.30% 1.5% 141 1.0% 1.6%
ACAR is depicted by its absolute value to optimally compare with transaction costs. The table depicts the trading days that are included in the event window.
57 these estimates were found to be statistically significant in the event study on abnormal returns. On both trading days, the transaction costs are on average too large to exploit the mispricing.
Furthermore, it can be observed in Figure 4 that the lower bound of the 95% confidence interval for transaction costs does not overlap the upper bound of the 95% confidence interval for the abnormal value of AAR.
Although the difference seems to be narrow at 𝑡 = −2, it can be observed in Table 5 that there exists a 0.01 percentage point difference between the two bounds. There could arguably be observed an overlap between the two bounds if one were to apply a 99% confidence interval. However, this will not be applied since we accepted our results from the event study on abnormal returns at a 5% significance level.
Due to the findings from our event study on abnormal returns, which suggest a significantly negative ACAR of -1.1%, it is possible that the market is neither rationally nor optimally incorporating public information into their valuation of stocks. Hence, since the abnormal returns at lockup expiration were found to be significant, the question prevails on why such an abnormality in stock prices is not eradicated by arbitrageurs. While we cannot attain a comprehensive answer to this question, it is possible to assess the limitations of arbitrage in a lockup context, and how such limitations can explain the stock price reaction at lockup expiration.
Our findings on transaction costs suggest that there is an immensely limited opportunity for arbitrageurs to benefit off any mispricing in stock prices at lockup expiration (ceteris paribus). In line with this observation, Espenlaub et al. (2001) argue that the relatively small magnitude of abnormal returns implies that any mispricing of stocks cannot not be exploitable through arbitrage. Investors generally face holding costs (e.g.
opportunity cost of capital) in addition to trading costs (e.g. brokerage fees) which bear the combined effect of impeding investors from exploiting any such inefficiencies in the market (Pontiff, 2006).
In addition, Ofek and Richardson (2000) emphasize that the creation of short positions is often hampered in a lockup context, as a limited free float prior to lockup expiration can render any arbitrage opportunities obsolete.
Hence, apart from the complications from transaction costs, it may be the case that investors only have access to an insufficient number of lendable shares throughout the lockup period in the IPO aftermarket.
In conclusion, even if market participants can predict the number of shares that are sold at lockup expiration with great certainty, their actions for profiting off abnormal stock reactions will likely be impeded by costly arbitrage, unfavourable holding costs, as well as fundamental risk factors. When combined, these issues may suggest that arbitrageurs (and investors alike) choose not to undertake an exploitative trading strategy, thus implying that mispricings (on average) still will prevail at lockup expiration.
6 Cross-sectional analysis
Our event study on abnormal returns yielded significant evidence of a negative ACAR of -1.1% at lockup expiration when applying a 5-day event window (-2, +2). As the next step of our analysis, we will now advance to the cross-sectional analysis to investigate a selection of underlying characteristics among our sampled firms that are likely to have an impact on CAR.
Firstly, we will inspect our sample by performing statistical, descriptive, and graphical analyses which will substantiate a thorough understanding of the sample distribution. Secondly, we will through an iterative stepwise regression procedure narrow down our model specification, starting with a Base Model that includes all explanatory variables. Herein, we will derive the Final Model according to statistical analyses, theoretical concepts, as well as our own financial and logical reasoning, which will jointly ensure that we arrive at a final model that is optimally fitted to our dataset. Finally, when the Final Model is adequately specified we will provide a thorough assessment and interpretation of our results.