Dependent variables

5.4.1.1. Abnormal returns

The first dependent variable is abnormal stock returns. This study looks at two different measures of abnormal returns to strengthen the results. This study looks at daily return and short data as mentioned by (Daske et al., 2005), daily data will allow for more precise estimations. The first measure of abnormal returns uses a calculation similar to (Dechow et al., 2001; Desai et al., 2002; Christophe et al., 2010). First, daily returns are calculated by taking the adjusted closing price of stock i on day t+1 minus the adjusted closing price of stock i on day t divided by the adjusted closing price of stock i on day t.

Daily Return_i,t= ACPi,t+1− ACPi,t ACP_i,t

The daily return is then adjusted with a market return. The market return is calculated in the same way as the daily return, but instead using the AEX equal weighted market index. The abnormal return is then the daily return of stock i on day t minus the daily return of the market

m on day t.

ABRET_i,t= Daily Return_i,t− Market Return_m,t

The second measure for abnormal returns follows a Capital Asset Pricing Model (CAPM) as used by Figlewski and Webb (1993):

ALT_RET_i,t= R_i,t− [R_f,x + β_i,x(R_m,t− R_f,x)]

ALT_RET_i,t= Abnormal return of stock 𝑖 on day 𝑡

R_i,t= Daily return of stock 𝑖 on day 𝑡

R_f,x= Risk free rate, using a 1 year Dutch government bond

βi,x= Beta of stock 𝑖 in the year perceding the sample period

32 The daily return and the market return are calculated as mentioned before however a Beta to account for volatility of the stock is added and a risk free rate using a 1 year Dutch

government bond is added. Beta is calculated as the covariance between the monthly

returns of stock i and the monthly returns of market m, divided by the variance of the monthly returns of market m. Beta is calculated over a period of one year prior to the sample period (Figlewski and Webb, 1993).

Initially, abnormal returns are calculated from the adjusted closing price of the stock on the day of the announcement of a short position to the adjusted closing price of the stock on the day after the announcement (0,1). A short position is included in the sample on the first initial day it is announced and any change in the position thereafter until the position drops below 0,5%. However, as mentioned by Boehmer, Jones, & Zhang (2008) it may be relevant to look at the reaction of returns over a longer period of time instead of just looking at the day after the announcement. The market may take longer to react to the new information. Therefore, an additional period is analyzed which is the period (0,5). This period starts on the day of the announcement of the short sale and ends five days after the announcement. This period is calculated as cumulative returns.

An issue that may occur when looking at a longer period of time after the announcement is that there could be additional announcements of or changes to the short positions during this period. A contol variable is added to combat this as used by (Kersbergen, 2015). The control variable MULTIPLE_i,t will count how many new or changed short positions are present in the periods (0,5; 0,10; 0,22).

5.4.1.2. Stock volatility

The most commonly used measure of stock return volatility is standard deviation. This statistic measures the dispersion of returns. Financial economists find the standard deviation to be useful because it summarizes the probability of seeing extreme values of return. When the standard deviation is large, the chance of large positive or negative return is large (Schwert, 1990). The standard deviation of daily returns is used as the measure for stock volatility. The calculation for VOL_i,tis the standard deviation of the daily returns of company i

over period t (Christophe et al., 2010; Saffi and Sigurdsson, 2011). As mentioned before it may be interesting to look at different periods of volatility. Boehmer et al. (2008) look at returns of up to 20 days after the announcement of a short position. This study looks at three different periods of volatility. the first period looks at the volatility of the day of the

announcement until 5 days after the announcement (0,5). The second period looks at the day of the announcement until 10 days after the announcement (0,10). The final period looks

33 at the day of the announcement until 22 days after the announcement (0,22). Based on the data of the study, the standard deviation values are scaled because they come from different time periods. For example, one standard deviation is calculated over a 10 day period whilst another is calculated over a 5 day period. Scaling them with a certain factor allows for the final values to be compared on an equal level. In this study the values are annualized (Saffi and Sigurdsson, 2011). The model to test stock volatility is slightly adjusted, as mentioned before some autoregressive elements are added. The regression formula is as follows:

VOLi,t= α + β1SHORTi,t+ β2MCAPi+ β3BTMi+ β4OPTIONSi+ β5LEVi

+ β6MULTIPLE_i+ β7VOLWEEK_i,t-5,-1+ β8VOLMONTH_i,t-22,-1+ ε_i,t

These autoregressive variables take into account the autoregressive nature of stock volatility as mentioned by Corsi (2009). It is described that volatility is influenced by its own past values. For example, tomorrow‟s daily volatility can be partly explained by today‟s volatility, last week‟s volatility, and last month‟s volatility. As this study uses less frequent data than daily volatility, only control variables for the previous week‟s volatility and the previous month‟s volatility are included. The variable VOLWEEK_i,t-5,-1 controls for the previous week‟s volatility by calculating the standard deviation of daily adjusted closing stock prices of company i over the previous five days t-5,-1 before the announcement of the short position. The variable VOLMONTH_i,t-22,-1 controls for the previous month‟s volatility by calculating the standard deviation of daily adjusted closing stock prices of company i over the previous twenty-two days t-22,-1 before the announcement of the short position. Both these variables are also annualized.