The Structure of Fundamental Factor Models

Beyond macroeconomic factor models, there are also fundamental factor models and statistical factor models. __Statistical factor models__ are pretty easy to summarize: they don't make many assumptions, and they just plow through data using portfolios of the securities being examined as the factors themselves—so interpretation ranges from difficult to impossible. End of story.

__Fundamental factor models__ are much more intuitive, since they use fundamentals of the companies themselves as factors. What might be an example?

No. That may be included in a multifactor model, but it's not a fundamental attribute of a company.

No. A consumer confidence index isn't specific to a firm. It's information about the state of the economy.

That's right. This is one of many fundamental variables that can be used as factors in a fundamental factor model, along with size, growth, earnings variability, financial leverage, and many others.

Whatever factors are chosen can be put into the same sort of model that you've seen with a macroeconomic factor model. $$\displaystyle R_i = a_i + b_{i1}F_1 + b_{i2}F_2 + ... + b_{iK}F_K + \epsilon_i $$ But now there are some differences. These factors aren't unexpected changes; they're just values used with sensitivity factors to provide pieces of total return. With this in mind, how do you think the intercept value will most likely compare to the intercept value of a macroeconomic factor model?

No. Smaller, actually.

Yes.

The intercept isn't an expected return here, and it's not the risk-free rate either. It's just an intercept with little real interpretation.

A notable feature of fundamental factor models is that most factor sensitivities (betas) can be interpreted in the same way, since they are standardized. $$\displaystyle b_{ik} = \frac{\mbox{Value of Attribute } k \mbox{ for Asset } i - \mbox{ Average Value of Attribute } k}{\sigma (\mbox{Values of Attribute } k)} $$ What beta do you think would result from a company value that is average?

You got it.

No. It would be 0.

The two numerator pieces would be equal in this case, leaving the beta at zero. If the value was a standard deviation below, then it ends up as -1. If it's two standard deviations above, then 2. They are all really like z-scores. The exception is dummy variables like whether a company belongs to a certain industry or not. Once the factor sensitivities are calculated for each, then the factor returns are estimated through regressions. So there's another difference from the macroeconomic factor model.

Factors in fundamental factor models can be grouped different ways. Sometimes these models are used for return attribution, risk attribution, or performance attribution, so it's helpful to group things into __company fundamental factors__ like earnings growth and variability, __company share-related factors__ like earnings yield and dividend yield, and __macroeconomic factors__ like a CAPM beta, sector, and industry. Where would you place a financial leverage ratio?

No. Financial leverage exists at the company level.

Not quite. This isn't a valuation measure like a book-to-market value ratio.

Exactly! Of course this isn't the only grouping. Other models can group factors into country, industry, and style factors. There are a lot of potential factors in a fundamental factor model, so they can be used to often produce some better information than others. But each type has its use, and you never know where that little extra piece of valuable information will come from in your valuation efforts.

To summarize: [[summary]]

Market risk

Earnings to price

Consumer confidence index

It will be bigger

It will be smaller

0

1

Into macroeconomic factors

Into company fundamental factors

Into company share-related factors

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