What is an earnings surprise?
One of my goals for this blog is to provide a minimally watered-down resource for technical but common financial terms. It annoys me when I see technical jargon thrown around in articles without any references.
My audience for a post like this is someone who is somewhat mathematically trained, but not necessarily mathematically sophisticated, and certainly not knowledgeable about finance. I already wrote a similar post about what it means for a statistic to be seasonally adjusted here.
By way of very basic background, publicly traded companies (i.e. companies you can buy stock on) announce their earnings once a quarter. They each have a different schedule for this, and their stock price often has drastic movements after the announcement, depending on if it’s good news or bad news. They usually make their announcement before or after trading hours so that it’s more difficult for news to leak and affect the price in weird ways minutes before and after the announcement, but even so most insider trading is centered around knowing and trading on earnings announcements before the official announcement. (Don’t do this. It’s really easy to trace. There are plenty of other ways to illegally make money on Wall Street that are harder to trace.)
In fact, there’s so much money at stake that there’s a whole squad of “analysts” whose job it is to anticipate earnings announcements. They are supposed to learn lots of qualitative information about the industry and the company and how it’s managed etc. Even so most analysts are pretty bad at forecasting earnings. For that reason, instead of listening to a specific analyst, people sometimes take an average of a bunch of analysts’ opinions in an effort to harness the wisdom of crowds. Unfortunately the opinions of analysts are probably not independent, so it’s not clear how much averaging is really going on.
The bottomline of the above discussion is that the concept of an earnings surprise is really only borderline technical, because it’s possible to define it in a super naive, model-free way, namely as the difference between the “consensus among experts” and the actual earnings announcement. However, there’s also a way to quantitatively model it, and the model will probably be as good or better than most analysts’ predictions. I will discuss this model now.
[As an aside, if this model works as well or better as most analysts' opinions, why don't analysts just use this model? One possible answer is that, as an analyst, you only get big payoffs if you make a big, unexpected prediction which turns out to be true; you don't get much credit for being pretty close to right most of the time. In other words you have an incentive to make brash forecasts. One example of this is Meredith Whitney, who got famous for saying in October 2007 that Citigroup would get hosed. Of course it could also be that she's really pretty good at learning about companies.]
An earnings surprise is the difference between the actual earnings, known on day t, and a forecast of the earnings, known on day t-1. So how do we forecast earnings? A simple and reasonable way to start is to use an autoregressive model, which is a fancy way of saying do a regression to tell you how past earnings announcements can be used as signals to predict future earnings announcements. For example, at first blush we may use last earning’s announcement as a best guess of this coming one. But then we may realize that companies tend to drift in the same direction for some number of quarters (we would find this kind of thing out by pooling data over lots of companies over lots of time), so we would actually care not just about what the last earnings announcement was but also the previous one or two or three. [By the way, this is essentially the same first step I want to use in the diabetes glucose level model, when I use past log levels to predict future log levels.]
The difference between two quarters ago and last quarter gives you a sense of the derivative of the earnings curve, and if you take an alternating sum over the past three you get a sense of the curvature or acceleration of the earnings curve.
It’s even possible you’d want to use more than three past data points, but in that case, since the number of coefficients you are regressing is getting big, you’d probably want to place a strong prior on those coefficients in order to reduce the degrees of freedom; otherwise we would be be fitting the coefficients to the data too much and we’d expect it to lose predictive power. I will devote another post to describing how to put a prior on this kind of thing.
Once we have as good a forecast of the earnings knowing past earnings as we can get, we can try adding macroeconomic or industry-specific signals to the model and see if we get better forecasts – such signals would bring up or bring down the earnings for the whole industry. For example, there may be some manufacturing index we could use as a proxy to the economic environment, or we could use the NASDAQ index for the tech environment.
Since there is never enough data for this kind of model, we would pool all the data we had, for all the quarters and all the companies, and run a causal regression to estimate our coefficients. Then we would calculate a earnings forecast for a specific company by plugging in the past few quarterly results of earnings for that company.