BayesianFactorZoo.jl

BayesianFactorZoo.jl is a Julia port of the R package 'BayesianFactorZoo' (CRAN link) implementing the econometric methods from the paper:

Bryzgalova, S., Huang, J., & Julliard, C. (2023). Bayesian solutions for the factor zoo: We just ran two quadrillion models. Journal of Finance, 78(1), 487–557. DOI: 10.1111/jofi.13197

If you use this package, please cite the original paper.

For detailed documentation of the original R implementation, see the R package documentation (PDF). Note that function signatures and exposed functions are equivalent to the R version.

Installation

For now this is not in the general registry (I will register it at some point). In the meantime you can install it directly from my repository.

using Pkg
Pkg.add("http://github.com/eohne/BayesianFactorZoo.jl")

For some examples see the "Tutorial" in the documentation
Link to Tutorial

Main Functions

BayesianFM

BayesianFM(f::Matrix{Float64}, R::Matrix{Float64}, sim_length::Int)

Performs Bayesian Fama-MacBeth regression.

Parameters:

• f: t × k matrix of factors (t periods, k factors)
• R: t × N matrix of test asset returns
• sim_length: Length of MCMC chain

Returns:

• lambda_ols_path: MCMC draws of OLS risk premia
• lambda_gls_path: MCMC draws of GLS risk premia
• R2_ols_path: MCMC draws of OLS R²
• R2_gls_path: MCMC draws of GLS R²

BayesianSDF

BayesianSDF(f::Matrix{Float64}, R::Matrix{Float64}, sim_length::Int; kwargs...)

Performs Bayesian estimation of linear stochastic discount factor (SDF). Supports both flat and normal priors for risk prices.

Parameters:

• f: t × k matrix of factors
• R: t × N matrix of test asset returns
• sim_length: Length of MCMC chain
• intercept: Include intercept (default: true)
• type: "OLS" or "GLS" (default: "OLS")
• prior: "Flat" or "Normal" (default: "Flat")
• psi0: Prior hyperparameter (default: 5.0)
• d: Prior hyperparameter (default: 0.5)

Returns:

• lambda_path: MCMC draws of risk prices
• R2_path: MCMC draws of R²

Model Selection and Testing

continuous_ss_sdf

continuous_ss_sdf(f::Matrix{Float64}, R::Matrix{Float64}, sim_length::Int; kwargs...)

Performs SDF model selection using continuous spike-and-slab prior.

Parameters:

• f: t × k matrix of factors
• R: t × N matrix of test asset returns
• sim_length: Length of MCMC chain
• psi0: Prior scale (default: 1.0)
• r: Spike component (default: 0.001)
• aw, bw: Beta prior parameters (default: 1.0)
• type: "OLS" or "GLS" (default: "OLS")
• intercept: Include intercept (default: true)

Returns:

• gamma_path: MCMC draws of model inclusion indicators
• lambda_path: MCMC draws of risk prices
• sdf_path: MCMC draws of SDF values
• bma_sdf: Bayesian Model Averaged SDF

dirac_ss_sdf_pvalue(f::Matrix{Float64}, R::Matrix{Float64}, sim_length::Int, lambda0::Vector{Float64})

Parameters:

• f: t × k matrix of factors
• R: t × N matrix of test asset returns
• sim_length: Length of MCMC chain
• lambda0: Vector of risk prices under null hypothesis
• psi0: Prior scale (default: 1.0)
• max_k: Maximum model size (optional)

Returns:

• gamma_path: MCMC draws of inclusion indicators
• lambda_path: MCMC draws of risk prices
• model_probs: Posterior model probabilities

Example Usage

using BayesianFactorZoo

# Generate example data
t, k, N = 100, 2, 25
f = randn(t, k)    # Factor returns (100 periods × 2 factors)
R = randn(t, N)    # Test asset returns (100 periods × 25 assets)

# Bayesian Fama-MacBeth regression
bfm_result = BayesianFM(f, R, 10000)
println("Mean OLS risk premia: ", mean(bfm_result.lambda_ols_path, dims=1))
println("Mean OLS R²: ", mean(bfm_result.R2_ols_path))

# Bayesian SDF estimation with normal prior
bsdf_result = BayesianSDF(f, R, 10000, 
                         intercept=true, 
                         type="OLS",
                         prior="Normal",
                         psi0=5.0)

# Model selection with continuous spike-and-slab prior
# Set prior Sharpe ratio through psi0
psi_value = psi_to_priorSR(R, f, priorSR=0.1)
css_result = continuous_ss_sdf(f, R, 10000, 
                             psi0=psi_value, 
                             r=0.001)

# Check factor inclusion probabilities
inclusion_probs = mean(css_result.gamma_path, dims=1)
println("Factor inclusion probabilities: ", inclusion_probs)

License

This package is licensed under GPL-3, as required due to being a port of the GPL-3 licensed R package BayesianFactorZoo.

Related Links

• Original Paper
• R Package on CRAN

Speed

The length of monte-carlo simulations was set to 100,000 and the example data of the R package was used. I ran each function 10 times and report the median values. Timings are from a Laptop with a Ryzen 9 6900HS using 8 threads. Multi-threading of the Julia version is indicated by *.

Method	Julia Time (s)	R Time (s)	Speed Improvement
Two Pass	0.0005	0.0025	5.0x
SDF GMM	0.0011	0.0191	17.4x
Bayesian FM*	3.0535	48.6653	15.9x
Bayesian SDF*	3.6099	36.8375	10.2x
Continuous SS SDF	20.3824	50.6916	2.5x
Continuous SS SDF v2	20.9998	57.7819	2.8x
Dirac SS SDF P-value*	2.9513	54.7477	18.6x