# Multifactor Models

While the Market Model uses only a single risk factor to price a security’s return, Multifactor Models apply a set of risk factors to describe an asset’s returns.

## Multifactor Model Types

Macroeconomic Factor Models

Apply economic variable as the risk factors that explain a security’s returns.

• Surprise Factor for betas of macroeconomic factor models:
• These models will not apply the actual value for a variable such as forecasted GDP growth rate.  Rather macroeconomic factor models apply a beta for the surprise factor of GDP growth describing the security’s expected return response when the variable “surprises” expectations.
• Calculating portfolio returns in a two security portfolio with a macroeconomic factor model:
• For each security, calculate the surprise return from the model; apply the security’s weighting to the surprise return; and sum the two weighted values.
• Surprise R security i = Expected R security i +β1(actual factor 1 – expected factor 1) + … repeat for # of factors
• This formula shows how the surprise beta is applied to the surprise to the factor value.  When the actual values equal the expected values, then the security’s actual return will equal its expected return.
• The difference between the expected return and the actual return is the surprise return; this is the error term of the regression model.

Fundamental Factor Models

Apply asset-class specific variables (ex. stocks: P/E ratio, degree of financial leverage, market capitalization, etc.) to explain a security’s returns.

Statistical Factor Models

These models apply a variety of variables in a regression analysis to find the best fit of historical data in explaining a security’s returns.