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# Multi-Factor Model

A financial model that employs multiple factors in its computations to explain market phenomena and/or equilibrium asset prices. The multi-factor model can be used to explain either an individual security or a portfolio of securities. It will do this by comparing two or more factors to analyze relationships between variables and the security’s resulting performance.

Factors are compared using the following formula:

Ri = ai + βi(m) Rm + βi(1)F1 + βi(2)F2 +…+βi(N)FN + ei

Where:
Ri is the returns of security i
Rm is the market return
F(1,2,3…N) is each of the factors used
β is the beta with respect to each factor including the market (m)
e is the error term
a is the intercept

Multi-factor models are used to construct portfolios with certain characteristics, such as risk, or to track indexes. When constructing a multi-factor model, it is difficult to decide how many and which factors to include. One example, the Fama and French model, has three factors: size of firms, book-to-market values and excess return on the market. Also, models will be judged on historical numbers, which might not accurately predict future values.

Multi-factor models can be divided into three categories: macroeconomic, fundamental and statistical models. Macroeconomic models compare a security’s return to such factors as employment, inflation and interest. Fundamental models analyze the relationship between a security's return and its underlying financials (such as earnings). Statistical models are used to compare the returns of different securities based on the statistical performance of each security in and of itself.

Investment dictionary. . 2012.

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