There is an important difference between the characteristic variable model and the multifactor models.That difference is that
A) in the multifactor models, the returns of the factor portfolios are observed, and we estimate the sensitivity of each stock to the different factors. In the characteristic variable model, the weight of each stock on each characteristic is observed, and then we estimate the return associated with each characteristic.
B) in the multifactor models, the returns of the factor portfolios are observed, and we estimate the return associated with each characteristic. In the characteristic variable model, the weight of each stock on each characteristic is observed, and then we estimate the sensitivity of each stock to the different factors.
C) in the characteristic variable model, the returns of the factor portfolios are observed, and we estimate the the return associated with each characteristic. In the multifactor models, the weight of each stock on each characteristic is observed, and then we estimate the sensitivity of each stock to the different factors.
D) in the multifactor models, the returns of the factor portfolios are not observed, and we estimate the sensitivity of each stock to the different factors. In the characteristic variable model, the weight of each stock on each characteristic is not observed, and then we estimate the return associated with each characteristic.
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