# Regression taking in account size of earnings surprises

I'm trying to regress earnings surprises on variable x. However, absolute earnings surprises are mostly influenced by company total earnings and the number of shares outstanding. So I can't just use this in the regression. Relative surprise also doesn't work as the sign of relative surprises does not really say anything if both the actual and forecasted values can be either negative or positive. My current idea is to make 3 categories: good, neutral and bad. For the calculations I will use conditions which solves the aforementioned problem. However, I was wondering if there might be another way in which the size/severity of the surprise is more accurately accounted for as this gives a more detailed view of the effect of variable x on earnings surprises? Do you maybe know of a way in which to do this? Thanks for reading :)

Kind regards

• If there are many analysis covering the stock, the standard deviation of their prediction is helpful (i.e. being 10 std above is not the same same 1/2 std above). As a side note, you should consider the history of surprises, e.g. if the company play a game where they surprise a little every period, then it's not quite a surprise. Commented Jun 21, 2022 at 14:19
• Thank you for the comment! I am going to look into it
– JMK
Commented Jun 23, 2022 at 13:37

Ok so this is bit of a half-answer but perhaps you can find some use in it. I've done some work on earnings surprises so I'll recap common ways to define it.

The first way to look at earnings surprises is by taking a $$[-1,+1]$$ day window centered around the earnings announcement date. Your feature will then be the excess return over that period:

$$\text{EAR} = r_S - r_f$$

where $$r_S$$ is the cumulative stock return and $$r_f$$ the return of a Fama-French portfolio. This is documented in many papers but take for example Brand et al. (2008) - Earnings Announcements are full of Surprises.

The other way to look at earnings surprises is by using realised changes in EPS, however, you might get more interesting results by including earnings forecasts (e.g. median forecasts or broker composites). A popular database is I/B/E/S but common data vendors like Bloomberg or TR have their own aggregates.

In Chan et al. (1995), the authors define earnings revisions $$ER$$ as

$$\text{ER} = \frac{\text{E}_{t}-\text{E}_{t-1}}{\sigma_E}$$

where the numerator uses the absolute growth in EPS from one period to the next and the denominator captures the standard deviation of earnings (forecasts) over a 12 month interval (similar to what Dimitri mentioned in his comment). You can also scale the earnings surprise by the stock returns which is what Baule et al. (2014) call Misvaluation $$Q$$:

$$Q = \frac{1+r_{E}}{1+r_{S}}$$

where $$r_E$$ refers to the earnings (forecast) growth over the previous period and $$r_{S}$$ the stock return over the same window. The authors also propose an adjusted $$Q$$ to deal with companies with negative/low EPS.

Finally, there's the Standardised Unexpected Earnings factor which is discussed here and also in the Brandt paper. The $$\text{SUE}$$ scales the expected earnings growth by the standard deviation of realised earnings over 8 quarters.

Personally, I haven't had much luck with any of factors for a variety of equity universes (i.e. very low IC's no matter the parameter choice).

• Thanks a lot for your comprehensive answer! I think I will use that first part (EAR) in addition to a regression with a dummy variable taking on value one if the earnings surprise is positive. And I will have a further look into the other methods!
– JMK
Commented Jun 23, 2022 at 13:35