SDFCoefficients {intrinsicFRP}

SDF Coefficients

Description

Computes the SDF coefficients of Fama-MachBeth (1973) doi:10.1086/260061 ⁠FMSDFcoefficients = (C' * C)^{-1} * C' * E[R]⁠ or the misspecification-robust SDF coefficients of Gospodinov-Kan-Robotti (2014) doi:10.1093/rfs/hht135: ⁠GKRSDFcoefficients = (C' * V[R]^{-1} * C)^{-1} * C' * V[R]^{-1} * E[R]⁠ from data on factors F and test asset excess returns R. These notions of SDF coefficients minimize pricing errors: ⁠argmin_{d} (E[R] - Cov[R,F] * d)' * W * (E[R] - Cov[R,F] * d)⁠, with W=I, i.e., the identity, and W=V[R]^{-1}, respectively. Optionally computes the corresponding heteroskedasticity and autocorrelation robust standard errors (accounting for a potential model misspecification) using the Newey-West (1994) doi:10.2307/2297912 plug-in procedure to select the number of relevant lags, i.e., n_lags = 4 * (n_observations/100)^(2/9).

Usage

SDFCoefficients(
  returns,
  factors,
  misspecification_robust = TRUE,
  include_standard_errors = FALSE,
  hac_prewhite = FALSE,
  target_level_gkr2014_screening = 0,
  check_arguments = TRUE
)

Arguments

returns

A ⁠n_observations x n_returns⁠-dimensional matrix of test asset excess returns.

factors

A ⁠n_observations x n_factors⁠-dimensional matrix of factors.

misspecification_robust

A boolean: TRUE for the "misspecification-robust" Kan-Robotti-Shanken (2013) GLS approach using the inverse covariance matrix of returns; FALSE for standard Fama-MacBeth risk premia. Default is TRUE.

include_standard_errors

A boolean: TRUE if you want to compute the SDF coefficients' HAC standard errors; FALSE otherwise. Default is FALSE.

hac_prewhite

A boolean indicating if the series needs pre-whitening by fitting an AR(1) in the internal heteroskedasticity and autocorrelation robust covariance (HAC) estimation. Default is false.

target_level_gkr2014_screening

A number indicating the target level of the tests underlying the factor screening procedure in Gospodinov-Kan-Robotti (2014). If it is zero, then no factor screening procedure is implemented. Otherwise, it implements an iterative screening procedure based on the sequential removal of factors associated with the smallest insignificant t-test of a nonzero SDF coefficient. The threshold for the absolute t-test is target_level_gkr2014_screening / n_factors, where n_factors indicate the number of factors in the model at the current iteration. Default is 0., i.e., no factor screening.

check_arguments

A boolean: TRUE for internal check of all function arguments; FALSE otherwise. Default is TRUE.

Value

A list containing n_factors-dimensional vector of SDF coefficients in "sdf_coefficients"; if include_standard_errors = TRUE, then it further includes n_factors-dimensional vector of SDF coefficients' standard errors in "standard_errors";

Examples

# import package data on 6 risk factors and 42 test asset excess returns
factors = intrinsicFRP::factors[,-1]
returns = intrinsicFRP::returns[,-1]

# compute GKR SDF coefficients and their standard errors
frp = SDFCoefficients(returns, factors, include_standard_errors = TRUE)