Title:	An R Package for Factor Model Asset Pricing
Version:	2.1.0
Date:	2024-04-15
Maintainer:	Alberto Quaini <alberto91quaini@gmail.com>
Description:	Functions for evaluating and testing asset pricing models, including estimation and testing of factor risk premia, selection of "strong" risk factors (factors having nonzero population correlation with test asset returns), heteroskedasticity and autocorrelation robust covariance matrix estimation and testing for model misspecification and identification. The functions for estimating and testing factor risk premia implement the Fama-MachBeth (1973) <doi:10.1086/260061> two-pass approach, the misspecification-robust approaches of Kan-Robotti-Shanken (2013) <doi:10.1111/jofi.12035>, and the approaches based on tradable factor risk premia of Quaini-Trojani-Yuan (2023) <doi:10.2139/ssrn.4574683>. The functions for selecting the "strong" risk factors are based on the Oracle estimator of Quaini-Trojani-Yuan (2023) <doi:10.2139/ssrn.4574683> and the factor screening procedure of Gospodinov-Kan-Robotti (2014) <doi:10.2139/ssrn.2579821>. The functions for evaluating model misspecification implement the HJ model misspecification distance of Kan-Robotti (2008) <doi:10.1016/j.jempfin.2008.03.003>, which is a modification of the prominent Hansen-Jagannathan (1997) <doi:10.1111/j.1540-6261.1997.tb04813.x> distance. The functions for testing model identification specialize the Kleibergen-Paap (2006) <doi:10.1016/j.jeconom.2005.02.011> and the Chen-Fang (2019) <doi:10.1111/j.1540-6261.1997.tb04813.x> rank test to the regression coefficient matrix of test asset returns on risk factors. Finally, the function for heteroskedasticity and autocorrelation robust covariance estimation implements the Newey-West (1994) <doi:10.2307/2297912> covariance estimator.
License:	GPL (≥ 3)
URL:	https://github.com/a91quaini/intrinsicFRP
BugReports:	https://github.com/a91quaini/intrinsicFRP/issues
Encoding:	UTF-8
RoxygenNote:	7.3.1
LinkingTo:	Rcpp, RcppArmadillo
Imports:	glmnet, graphics, Rcpp
Depends:	R (≥ 4.3.0)
LazyData:	true
Suggests:	testthat (≥ 3.0.0)
Config/testthat/edition:	3
NeedsCompilation:	yes
Packaged:	2024-04-15 20:23:36 UTC; albertoquaini
Author:	Alberto Quaini [aut, cre, cph]
Repository:	CRAN
Date/Publication:	2024-04-15 21:10:02 UTC

Asset Pricing Model Identification via Chen-Fang (2019) Beta Rank Test

Description

Tests the null hypothesis of reduced rank in the matrix of regression loadings for test asset excess returns on risk factors using the Chen-Fang (2019) doi:10.3982/QE1139 beta rank test. The test applies the Kleibergen-Paap (2006) doi:10.1016/j.jeconom.2005.02.011 iterative rank test for initial rank estimation when target_level_kp2006_rank_test > 0, with an adjustment to level = target_level_kp2006_rank_test / n_factors. When target_level_kp2006_rank_test <= 0, the number of singular values above n_observations^(-1/4) is used instead. It presumes that the number of factors is less than the number of returns (n_factors < n_returns). All the details can be found in Chen-Fang (2019) doi:10.3982/QE1139.

Usage

ChenFang2019BetaRankTest(
  returns,
  factors,
  n_bootstrap = 500,
  target_level_kp2006_rank_test = 0.05,
  check_arguments = TRUE
)

Arguments

Value

A list containing the Chen-Fang (2019) rank statistic and the associated p-value.

Examples

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

# compute the model identification test
hj_test = ChenFang2019BetaRankTest(returns, factors)

Testing for the pricing contribution of new factors.

Description

Computes the three-pass procedure of Feng Giglio and Xiu (2020) doi:org/10.1111/jofi.12883, which evaluates the contribution to cross-sectional pricing of any new factors on top of a set of control factors. The third step is a OLS regression of average returns on the covariances between asset returns and the new factors, as well as the control factors selected in either one of the first two steps. The first stwo steps consists in (i) a Lasso regression of average returns on the ovariances between asset returns and all control factors and (ii) a Lasso regression of the covariances between asset returns and the new factors on the ovariances between asset returns and all control factors. The second selection aims at correcting for potential omitted variables in the first selection. Tuning of the penalty parameters in the Lasso regressions is performed via Cross Validation (CV). Standard errors are computed following Feng Giglio and Xiu (2020) 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.

Usage

FGXFactorsTest(
  gross_returns,
  control_factors,
  new_factors,
  n_folds = 5,
  check_arguments = TRUE
)

Arguments

Value

A list containing the n_new_factors-dimensional vector of SDF coefficients in "sdf_coefficients" and corresponding standard errors in "standard_errors"; it also returns the index of control factors that are selected by the two-step selection procedure.

Examples

# import package data on 6 risk factors and 42 test asset excess returns
control_factors = intrinsicFRP::factors[,2:4]
new_factors = intrinsicFRP::factors[,5:7]
returns = intrinsicFRP::returns[,-1]
RF = intrinsicFRP::risk_free[,-1]

gross_returns = returns + 1 + RF

output = FGXFactorsTest(
  gross_returns,
  control_factors,
  new_factors
)

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

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)

Factor screening procedure of Gospodinov-Kan-Robotti (2014)

Description

Performs the factor screening procedure of Gospodinov-Kan-Robotti (2014) doi:10.2139/ssrn.2579821, which is an iterative model screening procedure based on the sequential removal of factors associated with the smallest insignificant t-test of a nonzero misspecification-robust SDF coefficient. The significance threshold for the absolute t-test is set to target_level / n_factors, where n_factors indicates the number of factors in the model at the current iteration; that is, it takes care of the multiple testing problem via a conservative Bonferroni correction. Standard errors are computed with the heteroskedasticity and autocorrelation using the Newey-West (1994) doi:10.2307/2297912 estimator, where the number of lags is selected using the Newey-West plug-in procedure: 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 Gospodinov-Kan-Robotti (2014) doi:10.2139/ssrn.2579821.

Usage

GKRFactorScreening(
  returns,
  factors,
  target_level = 0.05,
  hac_prewhite = FALSE,
  check_arguments = TRUE
)

Arguments

Value

A list contaning the selected GKR SDF coefficients in SDF_coefficients, their standard errors in standard_errors, t-statistics in t_statistics and indices in the columns of the factor matrix factors supplied by the user 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]

# Perform the GKR factor screening procedure
screen = GKRFactorScreening(returns, factors)

Heteroskedasticity and Autocorrelation robust covariance estimator

Description

This function estimates the long-run covariance matrix of a multivariate centred time series accounting for heteroskedasticity and autocorrelation using the Newey-West (1994) doi:10.2307/2297912 estimator. The number is selected using the Newey-West plug-in procedure, where n_lags = 4 * (n_observations/100)^(2/9). The function allows to internally prewhiten the series by fitting a VAR(1). All the details can be found in Newey-West (1994) doi:10.2307/2297912.

Usage

HACcovariance(series, prewhite = FALSE, check_arguments = TRUE)

Arguments

Value

A symmetric matrix (or a scalar if only one column series is provided) representing the estimated HAC covariance.

Examples

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

# Fit a linear model of returns on factors
fit = stats::lm(returns ~ factors)

# Extract residuals from the model
residuals = stats::residuals(fit)

# Compute the HAC covariance of the residuals
hac_covariance = HACcovariance(residuals)

# Compute the HAC covariance of the residuals imposing prewhitening
hac_covariance_pw = HACcovariance(residuals, prewhite = TRUE)

Compute the HJ asset pricing model misspecification distance.

Description

Computes the Kan-Robotti (2008) <10.1016/j.jempfin.2008.03.003> squared model misspecification distance: ⁠square_distance = min_{d} (E[R] - Cov[R,F] * d)' * V[R]^{-1} * (E[R] - Cov[R,F] * d)⁠, where R denotes test asset excess returns and F risk factors, and computes the associated confidence interval. This model misspecification distance is a modification of the prominent Hansen-Jagannathan (1997) doi:10.1111/j.1540-6261.1997.tb04813.x distance, adapted to the use of excess returns for the test asset, and a SDF that is a linear function of demeaned factors. Clearly, computation of the confidence interval is obtained by means of an asymptotic analysis under potentially misspecified models, i.e., without assuming correct model specification. Details can be found in Kan-Robotti (2008) <10.1016/j.jempfin.2008.03.003>.

Usage

HJMisspecificationDistance(
  returns,
  factors,
  ci_coverage = 0.95,
  hac_prewhite = FALSE,
  check_arguments = TRUE
)

Arguments

Value

@return A list containing the squared misspecification-robust HJ distance in squared_distance, and the lower and upper confidence bounds in lower_bound and upper_bound, respectively.

Examples

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

# Compute the HJ model misspecification distance
hj_test = HJMisspecificationDistance(returns, factors)

Asset Pricing Model Identification via Iterative Kleibergen-Paap 2006 Beta Rank Test

Description

Evaluates the rank of regression loadings in an asset pricing model using the iterative Kleibergen-Paap (2006) doi:10.1016/j.jeconom.2005.02.011 beta rank test. It systematically tests the null hypothesis for each potential rank ⁠q = 0, ..., n_factors - 1⁠ and estimates the rank as the smallest q that has a p-value below the significance level, adjusted for the number of factors. The function presupposes more returns than factors (n_factors < n_returns). All the details can be found in Kleibergen-Paap (2006) doi:10.1016/j.jeconom.2005.02.011.

Usage

IterativeKleibergenPaap2006BetaRankTest(
  returns,
  factors,
  target_level = 0.05,
  check_arguments = TRUE
)

Arguments

Value

A list containing estimates of the regression loading rank and the associated iterative Kleibergen-Paap 2006 beta rank statistics and p-values for each q.

Examples

# import package data on 15 risk factors and 42 test asset excess returns
factors = intrinsicFRP::factors[,-1]
returns = intrinsicFRP::returns[,-1]

# compute the model identification test
hj_test = ChenFang2019BetaRankTest(returns, factors)

Oracle tradable factor risk premia.

Description

Computes Oracle tradable factor risk premia of Quaini-Trojani-Yuan (2023) doi:10.2139/ssrn.4574683 from data on K factors ⁠F = [F_1,...,F_K]'⁠ and test asset excess returns R: ⁠OTFRP = argmin_x ||TFRP - x||_2^2 + tau * sum_{k=1}^K w_k * |x_k|⁠, where TFRP is the tradable factor risk premia estimator, tau > 0 is a penalty parameter, and the Oracle weights are given by ⁠w_k = 1 / ||corr[F_k, R]||_2^2⁠. This estimator is called "Oracle" in the sense that the probability that the index set of its nonzero estimated risk premia equals the index set of the true strong factors tends to 1 (Oracle selection), and that on the strong factors, the estimator reaches the optimal asymptotic Normal distribution. Here, strong factors are those that have a nonzero population marginal correlation with asset excess returns. Tuning of the penalty parameter tau is performed via Generalized Cross Validation (GCV), Cross Validation (CV) or Rolling Validation (RV). GCV tunes parameter tau by minimizing the criterium: ⁠||PE(tau)||_2^2 / (1-df(tau)/T)^2⁠ where ⁠PE(tau) = E[R] - beta_{S(tau)} * OTFRP(tau)⁠ are the pricing errors of the model for given tuning parameter tau, with S(tau) being the index set of the nonzero Oracle TFRP computed with tuning parameter tau, and ⁠beta_{S(tau)} = Cov[R, F_{S(tau)}] * (Cov[F_{S(tau)}, R] * V[R]^{-1} * Cov[R, F_{S(tau)}])^{-1}⁠ the regression coefficients of the test assets excess returns on the factor mimicking portfolios, and ⁠df(tau) = |S(tau)|⁠ are the degrees of freedom of the model, given by the number of nonzero Oracle TFRP. CV and RV, instead, choose the value of tau that minimize the criterium: ⁠PE(tau)' * V[PE(tau)]^{-1} PE(tau)⁠ where V[PE(tau)] is the diagonal matrix collecting the marginal variances of pricing errors PE(tau), and each of these components are aggregated over k-fold cross-validated data or over rolling windows of data, respectively. Oracle weights can be based on the correlation between factors and returns (suggested approach), on the regression coefficients of returns on factors or on the first-step tradable risk premia estimator. Optionally computes the corresponding heteroskedasticity and autocorrelation robust standard errors 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 details are found in Quaini-Trojani-Yuan (2023) doi:10.2139/ssrn.4574683.

Usage

OracleTFRP(
  returns,
  factors,
  penalty_parameters,
  weighting_type = "c",
  tuning_type = "g",
  one_stddev_rule = TRUE,
  gcv_scaling_n_assets = FALSE,
  gcv_identification_check = FALSE,
  target_level_kp2006_rank_test = 0.05,
  n_folds = 5,
  n_train_observations = 120,
  n_test_observations = 12,
  roll_shift = 12,
  relaxed = FALSE,
  include_standard_errors = FALSE,
  hac_prewhite = FALSE,
  plot_score = TRUE,
  check_arguments = TRUE
)

Arguments

Value

A list containing the n_factors-dimensional vector of adaptive tradable factor risk premia in "risk_premia"; the optimal penalty parameter value in "penalty_parameter"; the model score for each penalty parameter value in "model_score"; if include_standard_errors = TRUE, then it further includes n_factors-dimensional vector of tradable factor risk premia 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]

penalty_parameters = seq(0., 1., length.out = 100)

# compute optimal adaptive tradable factor risk premia and their standard errors
oracle_tfrp = OracleTFRP(
returns,
factors,
penalty_parameters,
include_standard_errors = TRUE
)

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

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)

Tradable factor risk premia.

Description

Computes tradable factor risk premia from data on factors F and test asset excess returns R: TFRP = Cov[F, R] * Var[R]^{-1} * E[R]; which are by construction the negative covariance of factors F with the SDF projection on asset returns, i.e., the minimum variance SDF. Optionally computes the corresponding heteroskedasticity and autocorrelation robust standard errors 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 details are found in Quaini-Trojani-Yuan (2023) doi:10.2139/ssrn.4574683.

Usage

TFRP(
  returns,
  factors,
  include_standard_errors = FALSE,
  hac_prewhite = FALSE,
  check_arguments = TRUE
)

Arguments

Value

A list containing n_factors-dimensional vector of tradable factor risk premia in "risk_premia"; if include_standard_errors=TRUE, then it further includes n_factors-dimensional vector of tradable factor risk premia 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 tradable factor risk premia and their standard errors
tfrp = TFRP(returns, factors, include_standard_errors = TRUE)

Factors - monthly observations from 07/1963 to 02/2024

Description

Monthly observations from 07/1963 to 02/2024 of the Fama-French 5 factors and the momentum factor.

Usage

factors

Format

factors

A data frame with 624 rows and 7 columns:

Date

Date in yyyymm format

...

Factor observations

Source

https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

Test Asset Excess Returns - monthly observations from 07/1963 to 02/2024

Description

Monthly excess returns on the 25 Size/Book-to-Market double sorted portfolios and the 17 industry portfolios from 07/1963 to 02/2024.

Usage

returns

Format

returns

A data frame with 624 rows and 43 columns:

Date

Date in yyyymm format

...

Asset excess returns

Source

https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

Risk free - monthly observations from 07/1963 to 02/2024

Description

Monthly observations from 07/1963 to 02/2024 of the US risk free asset.

Usage

risk_free

Format

risk_free

A data frame with 624 rows and 2 columns:

Date

Date in yyyymm format

...

risk free observations

Source

https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html