While I have an undergrad degree in Statistics, I haven’t had to use much of what I learned for over 20 years. In my company, we’ve recently been trying to come up with a more optimal executive compensation structure.
As with most bonus plans, the idea to align management’s goals with those of the shareholder. Our CFO requested that we perform a regression analysis of various financial metrics versus our stock price. The metrics that I’ll be using for the simple regression versus stock price are EBITDA (Earnings before Interest, Taxes and D&A), Operating Cash Flow and ROIC (Return on Invested Capital). Financial theory tells us that ROIC, over the long run, should have the highest correlation with changes to the stock price.
I understand that the stock price, on its own, doesn’t mean much. However, I can say that our capital structure and cost of capital haven’t changed significantly over the past 10 years.
Using the Data Analysis tool in Excel, I ran 10-year regressions of stock price on each of the metrics and got very high R-squareds (>75%) for each. However, I felt that I should also look at the change in stock price versus the changes to each of the metrics. I got much lower R-squareds using this method.
I’d love to hear any recommendation/advice on what the most appropriate methodology would be in assessing the metrics that are most closely correlated with stock price.
I’m imagining that your data set consists of a series of dates, each of which has a value for stock price and each of the other metrics. I would avoid trying to model day to day changes in stock price as that is likely to be very noisy. Either a straight regression (as you did) or one that looked at changes over long periods (say monthly or quarterly) is probably better. Another thought is that if you are looking a something like stock price where it is natural to talk about % change rather than absolute change, you are probably better looking at the data on a log scale.
Thanks. I’m only using annual metrics vs. year-end stock price for 10 years, i.e. 10 pairs of data for each of the three regressions. While the stock prices are volatile, the corresponding metrics are accounting-based, and don’t change frequently. One potential follow-up to get more data points is to use quarterly stock prices vs. rolling quarterly metrics (since accounting results are produced quarterly). I understand that none of these is perfect, but I’m just trying to get some confidence that I’m moving in the right direction.
Remember to take into account any corporate actions (stock splits etc) that would change the share of the company each stock represents.
Also (in my opinion) you should also use inflation adjusted prices or add inflation rates as one of the explanatory variables so that you can look at the real value apparently added by the executive.
It doesn’t strike me as improbable that your 3 variables will predict stock price. EBITDA, for example, SHOULD have a high correlation with stock price. Taking inflation into account would be good but you need to do it for all variables, not stock price.
Therefore, I think you are really setting out to prove the obvious…like that light levels increase as the sun rises. I’m not sure how this gets to executive compensation. Ok, I do have a cynical theory…that your CFO knows exactly what he is doing/knows this and so whats a high r^2 so he can justify high salaries. (SEE! EBITDA is important so…[confused logic] executives should be paid extremely well!!!)
If that is the case, just give it to him. It’s what he wants.
However, if he is serious, then why is EBITDA even looked at? Where the hell are the executive compenation variables? So many variables missing here.
If you are serious and find out that EBITDA (for example) has a high correlation with stock price…then what predicts EBITDA? Does executive compensation explain EBITDA well? $10 your CFO won’t want to go there
As an FYI I was asked to do this once (I am a statistician). They didn’t ask me again {I found the largest contributor to the r^2 was GDP}
Have you considered using a natural log transformation? Logging all the variables will give you an elasticity interpretation, where your beta coefficient on eg EBITDA would tell you that a 1% change in EBITDA yields a beta% change in stock price.
No splits and materially the same cap structure, so these aren’t an issue. I’m not sure how inflation plays into this. Everything is measured in dollars, so they all inflate equally, as do the opportunity costs. I probably didn’t need to mention the exec comp part, since that’s not really my question.
I would argue very strongly that you should be using the change in stock price exclusively. and not be using the level stock price at all. I would also argue that you should be using changes in EBITA and cash flow.
For one thing, you’re trying to find out what affects the stock price, and that means you’re trying to find out what makes it change.
For another, all of the above variables tend to rise over time simply because of that pesky inflation thing. Your high R-squared values when you use levels may well be just because an external variable (inflation) is causing all of them to rise over time. Your terms are correlated but the cause (inflation) may be external.
Consumption of ice cream is highly correlated with the consumption of sun tan lotion. But that doesn’t mean that we can get our customers to eat more ice cream by giving away sun tan lotion.
Edited to add: Actually, you can remove that pesky inflation problem simply by measuring everything in constant rather than current dollars.
I’m with you here, but it is quite common amongst American companies to use financial metrics as the backdrop of bonus structures. I’m certainly familiar with the many potential flaws of such incentive plans, but at the very least, we’re competing for talent versus other firms that use similar structures.
Individual, but certainly not independent, 10-year periods (with no overlap). Of the three metrics, the lowest R-Square was .75, and the highest was .83
This sounds like it could be a spurious regression. If you take two independent but autocorrelated time series (e.g., random walks or Brownian motions) and regress one on the other, you can get some very high R[sup]2[/sup] values simply by chance. I’m actually somewhat surprised that Buck Godot didn’t point this out, but maybe it’s not as well-known as I thought.
IMO, the right thing to do is to fit some kind of time series model, but at the very least you should be looking at how changes in the stock price track the changes in your metrics. I expect that those changes are at least a little bit correlated with each other, so you really ought to be fitting a multiple regression. You also really ought to be including economic variables as BlinkingDuck suggested, but that’s not going to lead to a story that your boss likes.
