What is a 'MultiFactor Model'
A multifactor model is a financial model that employs multiple factors in its computations to explain market phenomena and/or equilibrium asset prices. The multifactor model can be used to explain either an individual security or a portfolio of securities. It does so by comparing two or more factors to analyze relationships between variables and the resulting performance.
BREAKING DOWN 'MultiFactor Model'
Multifactor models are used to construct portfolios with certain characteristics, such as risk, or to track indexes. When constructing a multifactor model, it is difficult to decide how many and which factors to include. Also, models are judged on historical numbers, which might not accurately predict future values.Categories of MultiFactor Models
Multifactor models can be divided into three categories: macroeconomic models, fundamental models 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.
Beta
The beta of a security measures the systemic risk of the 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.
MultiFactor Model Formula
Factors are compared using the following formula:
Ri = ai + _i(m) * Rm + _i(1) * F1 + _i(2) * F2 +...+_i(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
_ is the beta with respect to each factor including the market (m)
e is the error term
a is the intercept
Fama and French ThreeFactor Model
One widely used multifactor model is the Fama and French threefactor model. The Fama and French model has three factors: size of firms, booktomarket values and excess return on the market. In other words, the three factors used are SMB (small minus big), HML (high minus low) and the portfolio's return less the risk free rate of return. SMB accounts for publicly traded companies with small market caps that generate higher returns, while HML accounts for values stocks with high booktomarket ratios that generate higher returns in comparison to the market.

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