Macroeconomic Factor Models, Fundamental Factor Models, And Statistical Factor Models

Portfolio Management 8 min readModule 2 of 3Save

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  • LOS 37.d
    Describe and compare macroeconomic factor models, fundamental factor models, and statistical factor models.

The CAPM could be described as a single factor model because it assumes asset returns are explained by a single factor: the return on the market portfolio. A multifactor model assumes asset returns are driven by more than one factor. There are three general classifications of multifactor models: (1) macroeconomic factor models, (2) fundamental factor models, and (3) statistical factor models:

  1. Macroeconomic factor models assume that asset returns are explained by surprises (or “shocks”) in macroeconomic risk factors (e.g., GDP, interest rates, and inflation). Factor surprises are defined as the difference between the realized value of the factor and its consensus predicted value.
  1. Fundamental factor models assume asset returns are explained by multiple firm- specific factors (e.g., P/E ratio, market cap, leverage ratio, and earnings growth rate). Fixed income securities may use fundamental factors such as duration, credit quality, currency and geography.
  2. Statistical factor models use statistical methods to explain asset returns. Two primary types of statistical factor models are used: factor analysis and principal component models.

In factor analysis, factors are portfolios that explain covariance in asset returns. In principal component models, factors are portfolios that explain the variance in asset returns. The major weakness is that the statistical factors do not lend themselves well to economic interpretation.

Therefore, statistical factors are mystery factors.

Because of the popularity of macroeconomic factor and fundamental factor models, we will provide a more expanded discussion of these models.

Macroeconomic Factor Models

Often used for fixed income, macroeconomic models can also be used for equities. The following model is an example of a two factor macroeconomic model in which bond returns are explained by surprises in GDP growth rates and credit quality spreads:

Let’s take a closer look at each of the components:

  • Each “F” is a factor surprise, the difference between the predicted value of the factor and the realized value. Each “b” is the sensitivity of the bond’s return to that surprise. The higher the sensitivity, the larger the change in return for a given factor surprise.
  • The firm specific surprise captures the part of the return that can’t be explained by the model. It represents unsystematic risk related to firm specific events like a strike or a warehouse fire.
EXAMPLE: Compute a stock return using a macroeconomic factor model
  • The following two factor model is used to explain the stock returns for Media Tech (MT):

RMT = E(RMT) + bMT,1FGDP + bMT,2 FQS + εMT

  • The expected return for Media Tech equals 10%. Over the past year, GDP grew at a rate that was 2 percentage points higher than originally expected, and the quality spread was 1 percentage point lower than originally expected. Media Tech’s sensitivity to the GDP rate factor equaled 2, and its sensitivity to the quality spread factor equaled −0.5.
  • Over the past year, Media Tech also experienced a 2% company- unique surprise return (i.e., unrelated to the two macro factors). Construct the macroeconomic factor model for Media Tech, and calculate its return for the year.
  • Answer:
  • The two factor model for Media Tech is:

RMT = 0.10 + 2(0.02) − 0.50(−0.01) + 0.02 =

0.100 (the expected return) + 0.040 (the return from the positive GDP surprise) + 0.005 (the return from the positive quality spread surprise) + 0.020 (the return from unexpected firm specific events) = 0.165, or 16.5%

  • The Media Tech return was higher than originally expected because MT was positively affected by higher than expected economic growth (GDP), lower than- expected credit quality risk spreads (QS), and positive company specific surprise events.

Be careful to interpret the signs properly. A decrease in the quality spread (a surprise less than zero) is good news for MT stock because it has a negative sensitivity to the factor. When credit quality spreads increase, MT’s return goes down, and when credit quality spreads decrease, MT’s return goes up.

The main features of the macroeconomic factor model include the systematic or priced risk factors and the factor sensitivities.

Priced Risk Factors

A risk that does not affect many assets (i.e., an unsystematic risk) can usually be diversified away in a portfolio and will not be priced by the market. “Not priced” means investors cannot expect to be rewarded for being exposed to that type of risk.

The factors in our example model, GDP and credit quality spread shocks, are systematic risk factors, meaning that they will affect even well diversified portfolios. Since they cannot be avoided, systematic factors represent priced risk (i.e., risk for which investors can expect compensation).

Factor Sensitivities In a macroeconomic multifactor model, asset returns are a function of unexpected surprises to systematic factors, and different assets have different factor sensitivities. For example, retail stocks are very sensitive to GDP growth and, hence, have a large sensitivity to the GDP factor. Small, unexpected changes in GDP growth cause large changes in retail stock prices because changes in income affect retail spending.

Other stocks are less sensitive to GDP and have smaller GDP factor sensitivities. Retail grocer stocks, for example, do not react as much to changes in GDP because spending on food items is less sensitive to changes in national income. The factor sensitivities of the model can be estimated by regressing historical asset returns on the corresponding historical macroeconomic factors.

Fundamental Factor Models

Consider the following fundamental factor model:

Let’s take a closer look at each of the components of a fundamental factor model.

Standardized sensitivities (bi1 and bi2). Sensitivities in most fundamental factor models are not regression slopes. Instead, the fundamental factor sensitivities are standardized attributes (similar to z statistics from the standard normal distribution).

For example, the standardized P/E sensitivity in a fundamental factor model is calculated as:

Also note that by standardizing the factor sensitivity, we measure the number of standard deviations that each sensitivity is from the average. For example, a stock with a standardized P/E sensitivity of 2.0 has a P/E that is 2 standard deviations above the mean; a stock with a sensitivity of −1.5 has a P/E that is one and a half standard deviations below the mean. This standardization process allows us to use fundamental factors measured in different units in the same factor model.

For example, P/E ratios are usually greater than 1.00, while dividend yields are in percentages (i.e., less than 1.00). The one exception is factors for binary variables (e.g., industry classification).

EXAMPLE: Calculating a standardized sensitivity in a fundamental factor model
  • The P/E for stock i is 15.20, the average P/E for all stocks is 11.90, and the standard deviation of P/E ratios is 6.30. Calculate the standardized sensitivity of stock i to the P/E factor.
  • Answer:
  • The sensitivity of stock i to the P/E factor is:
  • Therefore, the P/E ratio for the stock is 0.52 standard deviations higher than the average stock P/E.

Factor returns (FP/E and FSIZE). The fundamental factors are rates of return associated with each factor (e.g., the difference in rate of return between low and high P/E stocks). The return difference between low and high P/E stocks is commonly referred to as the return on a factor mimicking portfolio.

In practice, the values of the fundamental factors are estimated as slopes of cross sectional regressions in which the dependent variable is the set of returns for all stocks and the independent variables are the standardized sensitivities.

Intercept term (ai). In fundamental factor models, the factors are not return surprises. Hence, the expected factor values are not zero, and the intercept term is no longer interpreted as the expected return.

The Macroeconomic Factor Model vs. the Fundamental Factor Model

The key differences between the macroeconomic factor model and the fundamental factor model can be summarized as follows:

  • Sensitivities. The standardized sensitivities in the fundamental factor model (bi1 and bi2) are calculated directly from the attribute (e.g., P/E) data, they are not estimated. This contrasts with the macroeconomic factor model, in which the sensitivities are regression slope estimates.
  • Interpretation of factors. The macroeconomic factors (FGDP and FQS) are surprises in the macroeconomic variables (e.g., inflation shock and interest rate shock). In contrast, the fundamental factors (FP/E and FSIZE) are rates of return associated with each factor and are estimated using multiple regression.
  • Intercept term. The intercept in the macroeconomic factor model equals the stock’s expected return (based on market consensus expectations of the macro factors) from an equilibrium pricing model like the APT. In contrast, the intercept of a fundamental factor model with standardized sensitivities has no economic interpretation; it is simply the regression intercept necessary to make the unsystematic risk of the asset equal to zero.
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