Linear Factor Model

A Linear Factor Model is a factor model that ..

• See: Non-Linear Factor Model, Multivariate Linear Factor Model, Bilinear Factor Model.

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References

1999

• http://web.stanford.edu/~wfsharpe/mia/fac/mia_fac2.htm
  • A linear factor model relates the return on an asset (be it a stock, bond, mutual fund or something else) to the values of a limited number of factors, with the relationship described by a linear equation. In its most generic form, such a model can be written as: :[math]\displaystyle{ r_i = bi1*f_1 + bi2*f_2 + .... + b_{im}*f_m + e_i }[/math]

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  • Factor models are used in many domains in the field of investments, so it should not be surprising that different factors are used and different terms employed to describe the key components.
  • Factors (the fj's) may be::
    • macro-economic variables
    • returns on pre-specified portfolios,
    • returns on zero-investment strategies (long and short positions of equal value) giving maximum exposure to a fundamental or macro-economic factors,
    • returns on benchmark portfolios representing asset classes,
    • or something else.
  • The bij coefficients may be called:
    • factor exposures,
    • factor sensitivities,
    • factor loadings,
    • factor betas,
    • asset exposures.
    • style
    • or something else.
  • The ei term may be called:
    • idiosyncratic return,
    • security-specific return,
    • non-factor return,
    • residual return,
    • selection return
    • or something else.
  • Different problems require different factors and emphasize different economic relationships. The job of the Analyst is to either construct and apply an appropriate factor model for the task at hand or to at least understand the underlying structures and economic meanings of models constructed by others.

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