SDF_gmm {BayesianFactorZoo} | R Documentation |
GMM Estimates of Factors' Risk Prices under the Linear SDF Framework
Description
This function provides the GMM estimates of factors' risk prices under the linear SDF framework (including the common intercept).
Usage
SDF_gmm(R, f, W)
Arguments
R |
A matrix of test assets with dimension |
f |
A matrix of factors with dimension |
W |
Weighting matrix in GMM estimation (see Details). |
Details
We follow the notations in Section I of Bryzgalova et al. (2023).
Suppose that there are factors,
.
The returns of
test assets are denoted by
.
Consider linear SDFs (), that is, models of the form
.
The model is estimated via GMM with moment conditions
and the corresponding sample analog function . Different weighting matrices deliver different point estimates. Two popular choices are
where is the covariance matrix of returns and
is a large constant so that
.
The asymptotic covariance matrix of risk premia estimates, Avar_hat
, is based on the assumption that
is independent over time.
Value
The return of SDF_gmm
is a list of the following elements:
-
lambda_gmm
: Risk price estimates; -
mu_f
: Sample means of factors; -
Avar_hat
: Asymptotic covariance matrix of GMM estimates (see Details); -
R2_adj
: Adjusted cross-sectional;
-
S_hat
: Spectral matrix.
References
Bryzgalova S, Huang J, Julliard C (2023). “Bayesian solutions for the factor zoo: We just ran two quadrillion models <https://doi.org/10.1111/jofi.13197>.” Journal of Finance, 78(1), 487–557.