FRP {intrinsicFRP}

Factor risk premia.

Description

Computes the Fama-MachBeth (1973) doi:10.1086/260061 factor risk premia: ⁠FMFRP = (beta' * beta)^{-1} * beta' * E[R]⁠ where beta = Cov[R, F] * V[F]^{-1} or the misspecification-robust factor risk premia of Kan-Robotti-Shanken (2013) doi:10.1111/jofi.12035: ⁠KRSFRP = (beta' * V[R]^{-1} * beta)^{-1} * beta' * V[R]^{-1} * E[R]⁠, from data on factors F and test asset excess returns R. These notions of factor risk premia are by construction the negative covariance of factors F with candidate SDF ⁠M = 1 - d' * (F - E[F])⁠, where SDF coefficients d are obtained by minimizing pricing errors: ⁠argmin_{d} (E[R] - Cov[R,F] * d)' * (E[R] - Cov[R,F] * d)⁠ and ⁠argmin_{d} (E[R] - Cov[R,F] * d)' * V[R]^{-1} * (E[R] - Cov[R,F] * d)⁠, 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). For the standard error computations, the function allows to internally pre-whiten the series by fitting a VAR(1), i.e., a vector autoregressive model of order 1. All the details can be found in Kan-Robotti-Shanken (2013) doi:10.1111/jofi.12035.

Usage

FRP(
  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 factor risk premia 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 factor risk premia in "risk_premia"; if include_standard_errors = TRUE, then it further includes n_factors-dimensional vector of factor risk premia standard errors in "standard_errors"; if target_level_gkr2014_screening >= 0, it further includes the indices of the selected factors in selected_factor_indices.

Examples

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

# compute KRS factor risk premia and their standard errors
frp = FRP(returns, factors, include_standard_errors = TRUE)