OLS for expected return


New Member
Hello everyone, I am having some issues while conducting an event study regarding stock prices during Covid-19.

I am having trouble understanding why results from OLS gives me such different results compared to using the mean of the stock prices of a given stock.
I am trying to calculate abnormal return in an event window of 5 days, with an estimation period of 200 days prior to the event. Such that the basic formula would be the Return on day x - expected return.

I am using the formula below for expected return:

Rit = αi + βiRmt + εit

So, in order to find excess return I do as follows:

Stock X return day 1 - ( Intercept + Beta * Market return day 1) = x
Stock X return day 2 - ( Intercept + Beta * Market return day 2) = x

The problem is that even though I know that the results should be significant, they are not. My suspicion is that the difference from stock X and the benchmark is so little because that the market also went heavily down on the given days. While using the average stock price from an estimation period of 200 trading days I avoid this issue, and therefore the results become clearly significant. I have however understood that the OLS method is prefered, and therefore I would really like to understand what I should do differently.

Should I not somehow be able to use OLS to get a specific expected return, and not a variable which changes every day? Should i perhaps use the average of the market returns in the regression instead?
Sorry for the long text, I would really appreciate some guidance - please let me know if I should clarify anything.