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

The package is registered in the General registry and so can be installed at the REPL with ] add BayesianFactorZoo or by running:

    using Pkg 
    Pkg.add("BayesianFactorZoo")

Alternatively you can install the latest dev version directly from this repository.

using Pkg
Pkg.add(url="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; seed::Union{Nothing,Integer}=nothing)

Performs Bayesian Fama-MacBeth regression.

Parameters:

• f: t x k matrix of factors (t periods, k factors)
• R: t x N matrix of test asset returns
• sim_length: Length of MCMC chain
• seed: Random seed for reproducibility. nothing (default) uses fresh non-reproducible randomness; an integer gives reproducible results

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 R^2
• R2_gls_path: MCMC draws of GLS R^2

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 x k matrix of factors
• R: t x 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)
• seed: Random seed for reproducibility. nothing (default) uses fresh non-reproducible randomness; an integer gives reproducible results

Returns:

• lambda_path: MCMC draws of risk prices
• R2_path: MCMC draws of R^2

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 x k matrix of factors
• R: t x 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)
• seed: Random seed for reproducibility. nothing (default) uses fresh non-reproducible randomness; an integer gives a reproducible chain

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

continuous_ss_sdf_v2

continuous_ss_sdf_v2(f1::Matrix{Float64}, f2::Matrix{Float64}, R::Matrix{Float64}, sim_length::Int; kwargs...)

Performs SDF model selection using continuous spike-and-slab prior while treating tradable factors as test assets.

Parameters:

• f1: t x k1 matrix of nontradable factors
• f2: t x k2 matrix of tradable factors
• R: t x N matrix of test asset returns, excluding f2
• 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)
• seed: Random seed for reproducibility. nothing (default) uses fresh non-reproducible randomness; an integer gives a reproducible chain

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

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

Parameters:

• f: t x k matrix of factors
• R: t x 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)
• seed: Random seed for reproducibility. nothing (default) uses fresh non-reproducible randomness; an integer gives reproducible results

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 x 2 factors)
R = randn(t, N)    # Test asset returns (100 periods x 25 assets)

# Bayesian Fama-MacBeth regression
bfm_result = BayesianFM(f, R, 10000; seed=1234)
println("Mean OLS risk premia: ", mean(bfm_result.lambda_ols_path, dims=1))
println("Mean OLS R^2: ", 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,
    seed=1234,
)

# 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,
    seed=1234,
)

# 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 an Intel Ultra 9 185H using 18 threads. Multi-threading of the Julia version is indicated by *.

Method	Julia Time (s)	R Time (s)	Speed Improvement
SDF GMM	0.0008	0.0050	6.4x
Bayesian FM*	2.30	41.69	18.1x
Bayesian SDF*	2.69	29.54	11.0x
Continuous SS SDF	8.13	42.82	5.3x
Continuous SS SDF v2	10.51	44.17	4.2x
Dirac SS SDF P-value*	2.09	41.64	19.9x