I am reading that Statistical factors have no basis in finance theory for return-generating models. I am not quite what is meant by Statistical factors. I believe it means historical average mean return and historical annual sd. Am I correct? I read and re-read Schweser and Curriculum, but I wasn’t too sure what Statistical factors mean. I’d appreciate any thoughts.
Without reading what you’re reading, my best guess is a statistical factor derived from something called a… Factor Analysis. Essentially, you’re trying to find an unknown common structure (or structures) between certain observed variables. In other words, X1, X2, and X3 are variables we measured, and it could be the case that some how X1 and X2 share factor A, that causes them to covary, and X1 X2 X3 might all share factor B that causes them to covary. An important point is that A and B are orthogonal to one another (factors are independent). We would run a factor analysis to see what and how many underlying factors there might be, then we have to think about what the statistical factors might represent (a lot is subjective since these are unknown factors).
Although, without knowing what you read, I probably can’t be certain. I do know that I’ve seen factor analysis used and reference in MS finance courses.
I believe that you’re misinterpreting what you’re reading, or else Schweser’s interpretation of the curriculum is wrong.
Statistical factors can be anything:
- The GDP of Sri Lanka
- How fast (in lbs. / week) our puppy’s weight increases
- The 6-month GBP LIBOR rate
- The nationality of the driver who wins the Monaco Grand Prix
- The trailing 12-month moving average unemployment rate in Argentina
- Detroit’s per capita annual income divided by Hong Kong’s per capita annual credit card purchases
- Whatever
You build a mathematical model for the returns on McDonald’s common stock with all of these (and more) as independent variables and do a lot of fancy statistical analysis to determine which inputs have statistically significant coefficients and which ones don’t, then use that information to decide which inputs you’ll use in your predictive model.
The point that the curriculum makes (or tries to make) is that you may get many input variables that have statistical significance, but no economic basis for that significance. It’s unlikely, for example, that Geordie’s growth rate has any economically valid relation to the return on McDonald’s common stock, even though you may get a very high positive correlation between the two. On the other hand, statistical factors such as population growth, GDP growth, interest rates, unemployment rates, and so on are like to have both statistical significance and an economic basis for inclusion in such a model.
I still haven’t ruled out my suggestion. I’ve seen (and heard of) people doing a factor analysis to find this unknown factor (or a few)-- they then go ahead and use the factor(s) in another model to predict something else (like a regression). Essentially, they’ve taken something that, like you said, may not have grounding in reality (but it’s in the data), and they try to use it in another model to predict something (like a return). A more concrete example: say we measure GDP and interest rates and do a factor analysis, which suggests that there’s some underlying link (factor, covariance structure) and we happen to call it “A”. We then try to take A and use it in a regression model to predict returns. The problem is, we don’t necessarily know what “A” is–it may be real and it may not be real.
It’s also possible that the initial author used the term “statistical factor” as anything influencing the outcome–as most people would use it if they haven’t heard of a factor analysis.
Nor have I.
I was simply trying to give an example of the breadth of the term “statistical factor”.
Unfortunately, we don’t know exactly what he’s reading… 
Sorry for the delayed response, S2000magician and tickersu. The sentence I have quoted is from Book 4; Schweser; Page #167; First paragraph under LOS 44.d. I think they have qualified their statement by saying, “Statistical factors often have no basis in finance theory and are suspect in that they may represent only relations for a specific time period which have been identified by data mining (repeated tests on a single data set).”
I would appreciate your thoughts. Thanks in advance.
They’re saying that over the period of time that my puppy’s weight went up, the S&P 500 went up. Strong positive correlation (for that period of time), but no economic reason to think that it will continue: puppies eventually stop growing.
Well, it’s very unlikely they’re talking about a factor analysis then. S2000 is right with the example he gave (and schweser more references artifacts or spurious relationships).