This is good work Asteroiders. I have been looking at short selling for the past 18months (14 months for my honours research and now refining the research for two journal publications). To start, I have looked at a different study period to yours which looked at a period from December 08 to June 09 (142 trading days).
The research I conducted actually provided the first statistical test to determine if a relationship exist between short selling and abnormal returns.
In short, yes there is a statistical and significant relationship. However, I have found this relationship depends on many factors (market size, issued capital, level of short selling activity and the use of different proxies to measure short selling activity).
During my study period 63 companies reported a short sale for every day. I used this data to test if a granger causality relationship exists for each of these 63 companies. As you have shown a graph for NCM I will use this company as an example.
The first hypothesis was short selling do not granger cause abnormal returns (H1) and the 2nd hypothesis was abnormal returns do not granger cause short selling. I have over 20 variables to test different levels of short selling activity. However, the 2 main proxies are total shares sold long TSS(L) given by total shares sold minus short sell volume and short sell volume (SSV). This provided a direct comparison between short sellers and non short sales.
Results for H1 was TSS(L) was significant and therefore reject the null hypothesis and SSV was not sign (only just with p-value .11) meaning the null is not rejected and short selling does not granger cause abnormal returns for NCM during my study period. However, I did get several results for when short selling is over its mean and mean+1 st.dev. meaning when SSV is abnormally high, it does granger cause abnormal returns.
Results for H2 did not show a sign relationship for abnormal returns cause short selling.
Of the 63 companies a total of 47 companies (74.6%) found sign results for SSV meaning of the 63 companies short selling granger causes abnormal returns for 47 companies. however, I also found a total of 41 sign results for TSS(L) or 65% of companies. Overall, SSV was only just more sign but both proxies either long or short sales granger cause short selling.
For H2 only 26 for SSV were sign and 21 for TSS(L).
These companies were then pooled within a panel model and a number of results were found - mostly both a negative and positive relationship between short selling and returns for the contemporaneous trading day. When I tested SSV and TSS(L) in a multivariate I only got a sign result for TSS(L) and SSV was not sign. BUT, using LAGS in this model is another story and SSV is sign and NEGATIVE coefficient for a number different models when TSS(L) is not. Therefore, SSV has a statistically sign and NEGATIVE relationship with abnormal returns while TSS(L) is not sign in all models.
