where 
ri is the return of securityrm is the market returnf 1 2 3 n is each of the factors used is the beta with respect to each factor including the market m e is the error terma is the intercepttypes of multi factor modelsmulti factor models can be divided into three categories macroeconomic models fundamental models and statistical models macroeconomic models macroeconomic models compare a security s return to such factors as employment inflation and interest fundamental models fundamental models analyze the relationship between a security s return and its underlying financials such as earnings market capitalization and debt levels statistical models statistical models are used to compare the returns of different securities based on the statistical performance of each security in and of itself many times historical data is used in this type of modeling construction of multi factor modelsthe three most commonly used models to construct a multi factor model are a combination model a sequential model and an intersectional model combination model in a combination model multiple single factor models which utilize a single factor to distinguish stocks are combined to create a multi factor model for example stocks may be sorted based on momentum alone in the first pass subsequent passes will use other factors such as volatility to classify them sequential model a sequential model sorts stocks based on a single factor in a sequential manner to create a multi factor model for example stocks for a specific market capitalization may be sequentially analyzed for various factors such as value and momentum sequentially intersectional model in the intersectional model stocks are sorted based on their intersections for factors for example stocks may be sorted and classified based on intersections in value and momentum measurement of betathe beta of a security measures the systematic risk of a security in relation to the overall market a beta of 1 indicates that the security theoretically experiences the same degree of volatility as the market and moves in tandem with the market a beta greater than 1 indicates the security is theoretically more volatile than the market conversely a beta less than 1 indicates the security is theoretically less volatile than the market 