Calculating investor turnover with Gaspar's formula

[Vincent Hitchins]

Hi, I'm new to Stata so apologies if my question seems a bit 'simple'. I'm currently researching the relationship between earnings management and institutional ownership. I was able to calculate the earnings aspect, but i have trouble with my 'investor turnover' formula. I'm supposed to do the following:
A short-term investor should buy and sell his investments frequently, while a long-term investor should hold his positions unchanged for a considerable length of time. To implement this idea empirically, i calculate for each institutional investor a measure of how frequently he rotates his positions on all the stocks of his portfolio (churn rate). If we denote the set of companies held by investor i by Q, the churn rate of investor i at quarter t is

where Pj,t and Nj,i,t represent the price and the number of shares, respectively, of company j held by institutional investor i at quarter t.

I then use investor churn rates to construct a measure of investor turnover for the firm that measures the investment horizon of institutional shareholders in the firm prior to an acquisition announcement. Denote by S the set of shareholders in company k and by wk,i,t the weight of investor i in the total percentage held by institutional investors at quarter t. The investor turnover of firm k is the weighted average of the total portfolio churn rates of its investors over four quarters:

The data is panel data with multiple companies over a time frame of 15 years (2003-2017). I'm having a hard to even start with transforming these formulas into STATA code. Is there anyone who could help me with this? I have attached a small example of my data set below:

FileDate ManagerName ManagerNumber TypeCode ReportDate PriorReportDate Cusip SHARESHELD NetChangeinSharesSincePrior StockName IndustryCode SHAREPRICE SharesOutstandinginMillions SharesOutstandingin1000sas
20030331 ASB CAPITAL MANAGEMENT, INC. 185 5 20030331 20021231 11563720 46038 -6200 BROWN FORMAN CORP 106 76.9 32 31966
20030331 AELTUS INVESTMENT MGMT, INC. 500 5 20030331 20021231 11563720 63463 -738 BROWN FORMAN CORP 106 76.9 32 31966
20030331 THRIVENT FINL FOR LUTHERANS 650 5 20030331 20021231 11563720 6600 -900 BROWN FORMAN CORP 106 76.9 32 31966
20030331 ALLIED IRISH BANKS PLC 1285 4 20030331 20021231 11563720 780 BROWN FORMAN CORP 106 76.9 32 31966

[Phil Bromiley]

You will increase your chances of helpful answer by following the FAQ on asking questions – provide Stata code in code delimiters, readable Stata output, and sample data using dataex. I'm not going to trying to import your data and calculate these for you. You don't even provide enough data to do that. To actually program this for you, I would have to go to the trouble of generating sufficient artificial data to appropriately run the program, and there is a good chance I wouldn't get it right.

Here is how you can go about your calculations. First, you xtset your data. Then you can calculate all the values that go within the summations using generate and the appropriate lags. Having done that, you can use egen by the appropriate categories to do summations. While the second equation could be done with two egen statements, it could also just as easily be written out since the second summation only sums over four things. Then you can simply use generate to do the ratios.