linearmodels.asset_pricing.model.LinearFactorModel¶

Linear factor model estimator

Parameters:¶

portfolios: IVData | ndarray | DataArray | DataFrame | Series¶: Test portfolio returns (nobs by nportfolio)
factors: IVData | ndarray | DataArray | DataFrame | Series¶: Priced factor returns (nobs by nfactor)
risk_free: bool = False¶: Flag indicating whether the risk-free rate should be estimated from returns along other risk premia. If False, the returns are assumed to be excess returns using the correct risk-free rate.
sigma: ndarray | DataArray | DataFrame | Series | None = None¶: Positive definite residual covariance (nportfolio by nportfolio)

Notes

Suitable for traded or non-traded factors.

Implements a 2-step estimator of risk premia, factor loadings and model tests.

The first stage model estimated is

\[r_{it} = c_i + f_t \beta_i + \epsilon_{it}\]

where \(r_{it}\) is the return on test portfolio i and \(f_t\) are the traded factor returns. The parameters \(c_i\) are required to allow non-traded to be tested, but are not economically interesting. These are not reported.

The second stage model uses the estimated factor loadings from the first and is

\[\bar{r}_i = \lambda_0 + \hat{\beta}_i^\prime \lambda + \eta_i\]

where \(\bar{r}_i\) is the average excess return to portfolio i and \(\lambda_0\) is only included if estimating the risk-free rate. GLS is used in the second stage if sigma is provided.

The model is tested using the estimated values \(\hat{\alpha}_i=\hat{\eta}_i\).

Methods

`fit`([cov_type, debiased])	Estimate model parameters
`from_formula`(formula, data, *[, portfolios, ...])	param formula: Formula modified for the syntax described in the notes

Properties

`formula`