How to do a financial event study

Event studies, the financial professors favorite tool in Efficient Market Hypothesis (EMH) tests. If you don't use it you lose it, so I figured I'd detail the process now while I remember it.

The Event

So the above is the event study and its' many possibilities. Lets use a earnings release date as an example. The tallest vertical line is the actual release date, we will call this time 0. The left vertical line will be the end of the development period and we will say this is day -30. This means that the left line is 30 trading days before the earnings release date. Between the left line and the right line is the event window and it is symmetrical which means the event window ends on day +30. Now lets talk stats.

The Development Period
As said above the development period ends at day -30, the left vertical line, and is begins around 100 days before that, lets say day -130. Through this period you need to develop your expected returns model - the CAPM.

The intuition of this is you want to find out if the company has returns that are different than what you would normally expect on a average trading day. You could simply suggest it would return the average daily historical return for the company, but there is a much better way. By regressing your companies returns against the market (the S&P 500 usually) you can create a one parameter model that will predict the expected return for your stock based on how the market is performing.

E[Rj] = A + B(Rm - Rf). Where E means 'expected', Rj is the return of your 'j'th company, A is the 'alpha' AKA predicted abnormal return, B is the 'beta' the parameter that acts upon your independent variable to estimate your company return, Rm is the S&P 500 return and Rf is the risk free return for the period understudy. Many practitioners set their 'intercept' or A to zero so their regression simply is B(Rm - Rf). If this doesn't hurt the R2 of your test to much, it is an acceptable simplifying assumption.

At the end of this you might have a formula that says Rj = 1.2*(Rm - 0) for a daily return. In words this says that the return of the S&P 500 multiplied by 1.2 will be your best estimate of your stock return.

The last note on the development period is it needs to be 'sterile' or free of any big events. For instance if the company announced a bid to take over another company you will have some pretty irregular earnings in that period and your regression will not predict the event window very well.

The Event Window
Okay so why did we stop our development period at day -30 instead of day 0. The answer is leakage. Often corporate 'events' will leak into the industry before they are widely disseminated by the press. This is sloppily shown by the brown line, which starts to rise before day 0. If the brown line were to rise as it does before day 0 but then flatten off you may be able to make the following statement. "The earnings announcement was responsible for positive abnormal returns, however these returns were not tradeable by the general public because they occurred before the announcement.  This effect is closely monitored when the focus of your event study is the affect of insider trading.

The red line that oscillates around the blue time-line represents a case where the company does not experience abnormal returns. It is important to remember this is not the same as saying the company has 0 return, if the market is going up or down the stock is following it with a closeness that is determined by its beta.

The yellow line represents what the EMH predicts (red line too). As soon as the information is released the price adjusts and nobody has time to trade on it, unless they were holding the stock before the event, in which case they still were exposed to the risk of the abnormal return being negative. Unlike the brown or burgundy line the change has no drift. In reality sometimes events have drift, where the original bump continues of the following days. This is evidence for 'weak form efficiency' because a trader could just buy stocks who had an abnormal bump and sell stocks who had abnormal losses.

Prove it
So lets say you think you can make money by always buying/selling a company after a certain event happens. You name it, it could be changing auditors, a technical indicator, a product announcement, whatever. Before you go dumping your money after seeing it work once, you should figure out the strength of the effect. Run the numbers on 30 firms who have gone through the event, calculating the CAPM for each and recording the abnormal returns. Add all of the abnormal returns in your chosen trading window (perhaps day 0 to day 45), this is the stocks 'cumulative abnormal  return' or CAR. Then average all of the CAR's for each firm, and get your CAR_bar (bar means average in stats lingo). You also need the standard deviation of the sample of CAR's, call this Sigma_car.

Test it with the following formula, Tstat = (CAR_bar)/(Sigma_car/(sqrt(N - 1))) where N is the 30 because you have 30 firms. If this Tstat is 2, you have a bomber strategy that is going to work with 90% certainty. Tstat of 2.56 works with 95% certainty. Lower Tstats means that your CAR_bar might not be significantly 'not zero' enough to gaurentee you a pay day.

So What
Good point. Besides being a key component to any 4th year finance semester or grad school event studies aren't that common in the real world. They can however really simplify your search for indicators that affect stock prices, and if you find a match that has significant CAR with a lot of persistence or drift, you've got yourself a winning ticket.