Linear relationship

  Earnings Surprises. The main focus on the literature on earnings announcement has been on the response of investors to new information. Several measures have been proposed in the literature to quantify the new information. In this project, we will focus on one measure that compares the earnings announcement 𝑒𝑞,𝑘 for company 𝑘 in quarter 𝑞 with the corresponding analyst forecast 𝑒̂𝑞,𝑘. The analyst forecast is defined as the median forecast among all the analysts that make a forecast in the last 60 (trading) days before the earnings announcement. If an analyst made multiple forecasts in this time horizon, we consider the most recent one. The earnings surprise is defined as the difference between the earnings announcement and the forecast divided by the lagged price 5 trading days before the announcement date: 𝑠𝑞,𝑘 = 𝑒𝑞,𝑘 − 𝑒̂𝑞,𝑘 𝑝𝑞,𝑘 The price of a share works as a renormalization factor: the earnings are measured as earnings in dollar per share. The division by lagged price measures the earnings surprise as a fraction of the value of the company. If 𝑠𝑞,𝑘 = 0.01, it means that the company earned unexpected profits equal to 1 percent of the value of the company. Returns. We consider the response of stock returns to earnings surprises at different horizons. To capture the immediate response, one could look at window [0,0], that is the stock return of the same day as the announcement. However, since announcements are often made after the markets are closed, one should look at [0,1], that is the return for the same day and the next day. If one wants to look at the delayed response to the earnings announcement, a typical measure is [3,75], that is the stock returns for the period three days to 75 days after the announcement (where days are always meant as trading days). As for the measure of returns, we will simply consider market-adjusted return defined as the difference between the raw return and the market return. For example, the marketadjusted return for stock 𝑘 for window [0,1] of quarter 𝑞 is defined as 𝑟𝑞,𝑘 [0,1] − 𝑟𝑞,𝑚 [0,1] Data. For convenience, I have already merged for you the information from Compustat, CRSP, and IBES. All data could be obtained from Wharton Research Data Service (https://wrds-www.wharton.upenn.edu). In this project, you will use “earnings.csv” (or “earnings.dta” for Stata), which you can download from canvas. The first row of the file contains the variable names. The dataset includes earnings, corresponding earnings forecast, and returns around earnings announcements from 1995 through 2004. Each row represents one earnings announcement. (In order to make the data set small enough, the dataset contains only companies with name up to “M”.) It contains the following variables: - permno (or cusip): company identifier. - coname: company name - siccode: SIC code of industry - date: earnings announcement date - year: the year of the earnings announcement date - medact: actual earnings per share - medest60: median earnings forecast in the last 60 days - adj: adjustment factor (which will be used to adjust earnings and price from different periods) - lagprice: lagged price - netwin1: market-adjusted return for window [0,1] - netwin2: market-adjusted return for window [3,75] 2. Assignment While a coding language is generally easier for this type of task and strongly encouraged, this problem set can be completed using Excel. Softwares (e.g. Stata, MATLAB) can be accessed through the Virtual Computer Lab. More information can be found: https://sites.wustl.edu/olinit/virtual-lab/ Please submit your code or log file (or your working excel file) along with the write-up for the questions through Canvas by team. In the write-up, you only need to include related information requested in the question subsections. Part 1: data preparation A. Compute earnings surprises (s) = 𝑎𝑑𝑗×(𝑚𝑒𝑑𝑎𝑐𝑡−𝑚𝑒𝑑𝑒𝑠𝑡60) 𝑙𝑎𝑔𝑝𝑟𝑖𝑐𝑒 B. Look at the summary statistics of main variables (refer to the question below). C. Winsorize s, netwin1, netwin2 at 0.5% and 99.5% level (winsorization is to set all outliers to a specified percentile of the data; for example, the winsorization here would set all data below the 0.5th percentile set to the 0.5th percentile, and data above the 95.5th percentile set to the 95.5th percentile) For your convenience, I've done A and C for you. I’ve included the winsorized variables to the dataset, they are named as sw, netwin1w and netwin2w. Question: Report the summary statistics (mean, standard deviation, min, p10, p25, median, p75, p90, max) of earnings surprises (s), netwin1, and netwin2 (variables before the winsorization). Do you see outliers that may affect your analysis? Part 2: short-run response For each year, sort the announcements by earnings surprise (𝑠𝑤) into 11 quantiles: - Define quantile 6 as the group of announcements with no surprise (𝑠𝑤 = 0) - Divide the announcements with negative surprises (𝑠𝑤 < 0) in 5 equal-sized groups, with group 1 being the one with the most negative announcements and group 5 the one with least negative. The breakpoints for the quantiles are determined separately for each year. - Similarly, divide announcements with positive surprises 𝑠𝑤 > 0 in 5 equal sized groups (groups 7 through 11). Group 11 will be the one with the most positive surprises. The breakpoints for the quantiles are determined separately for each year. Compute average market-adjusted returns [0,1] ( 𝑛𝑒𝑡𝑤𝑖𝑛1𝑤 ) and average earnings surprises across earnings announcements within each quantile for each year. Next, for each of the eleven quantiles separately, calculate the average of year-by-year market-adjusted returns, and the average of year-by-year average earnings surprises. Finally, plot the following two figures. The "average" mentioned here refers to the average of year-by-year averages: - Figure 1: Average market-adjusted returns [0,1] (𝑛𝑒𝑡𝑤𝑖𝑛1𝑤) against average earnings surprises for these 11 quantiles (similar to figure 1d in DellaVigna and Pollet (2009), without separating the plot by Fridays/Other Days) - Figure 2: Average market-adjusted returns [0,1] (𝑛𝑒𝑡𝑤𝑖𝑛1𝑤) as a function of these 11 quantiles (similar to figure 1a in DellaVigna and Pollet (2009), without separating the plot by Fridays/Other Days) Question: (1) Plot the two figures (Figures 1 and 2) as described above. (2) Is the relationship between the market-adjusted return and the earnings surprise shown in Figure 1 linear? Provide one interpretation for the observed non-linearity. That is, what features does the information contained in the earnings news have to have to justify this shape? (No need to be behavioral here.) (3) Is the relationship in Figure 2 linear? How do you interpret the economic magnitude here? How do you explain this linear relationship?