Research on the impact of decimal rounding in Fama-French factors on asset pricing test conclusions.

Status: Ongoing research project.

How sensitive are asset pricing tests to small decimal approximations (±0.005) in Fama-French factors? Could researchers reach different conclusions about anomaly significance simply due to rounding differences in factor data?

Fama-Macbeth two-pass regressions are expected to show greater sensitivity due to the errors-in-variables problem:

1. Stage 1: Measurement error in factors → errors in estimated betas
2. Stage 2: Errors in betas (used as regressors) → classic errors-in-variables
   • Causes attenuation bias (coefficients biased toward zero)
   • Inflates standard errors
   • Can flip statistical significance

In contrast, linear regressions test factors directly without this compounding error.

# Install research_data first (provides CRSP, FF factors, Open Asset Pricing)
cd ../research_data
pip install -e .

# Then install this package
cd ../ff_decimals_randomization
pip install -e .

# Install Jupyter for notebooks (optional)
pip install jupyter

# Launch Jupyter
jupyter notebook

# Open notebooks:
# - notebooks/01_linear_regression_tests.ipynb
# - notebooks/02_fama_macbeth_tests.ipynb

from research_data import load_monthly_base
from ff_decimals.data import load_fama_french_factors, load_chen_zimmerman_from_oap
from ff_decimals.analysis import add_decimal_noise

# Load data (research_data gives us CRSP + FF factors merged)
monthly = load_monthly_base()

# Load FF factors separately
ff = load_fama_french_factors(specification="5-factor")

# Load Chen-Zimmerman predictors from Open Asset Pricing
predictors = load_chen_zimmerman_from_oap()

# Add decimal noise to factors
ff_noisy = add_decimal_noise(ff, noise_type='truncnorm', seed=42)

# Run your tests with noisy factors...

ff_decimals_randomization/
├── src/ff_decimals/              # Thin wrappers around research_data
│   ├── data/                     # Data loaders
│   │   ├── factors.py            # Load FF factors
│   │   ├── predictors.py         # Load Chen-Zimmerman from OAP
│   │   └── crsp.py               # Load CRSP returns
│   ├── analysis/
│   │   └── randomization.py      # Core: Add decimal noise to factors
│   └── utils/
│       └── stats.py              # Sensitivity analysis helpers
├── notebooks/                    # Analysis notebooks
│   ├── 01_linear_regression_tests.ipynb
│   └── 02_fama_macbeth_tests.ipynb
├── results/                      # Outputs
│   ├── figures/
│   ├── tables/
│   └── simulations/
├── data/                         # Legacy data files (optional)
│   ├── chen_predictors.csv
│   └── signal_doc.csv
├── archive/                      # Old notebook versions
└── README.md

The default noise range of ±0.005 represents the maximum rounding error when rounding to 2 decimal places:

• True value: 0.0234 → Rounded: 0.02 → Error: -0.0034
• True value: 0.0267 → Rounded: 0.03 → Error: +0.0033
• Maximum error: ±0.005

We simulate this by adding random noise drawn from a truncated normal distribution on [-0.005, 0.005] to each factor return.

For each predictor/anomaly:

predictor_return_t = α + β₁·Mkt-RF_t + β₂·SMB_t + β₃·HML_t + ε_t

The t-statistic on α tests whether the predictor has significant abnormal returns. We measure how this changes across 100+ simulations with randomized factors.

Uses research_data.methods.fama_macbeth() for the implementation.

Stage 1 (Time-series): Estimate factor loadings:

R_it = α_i + β_i·Factors_t + ε_it

Stage 2 (Cross-sectional): Estimate risk premia:

R_it = γ₀ + γ·β̂_i + u_it

If factors have measurement error in Stage 1, the estimated β̂_i will have errors, creating an errors-in-variables problem in Stage 2.

• Fama-French Factors: WRDS ff.fivefactors_monthly
• Chen-Zimmerman Predictors: Open Asset Pricing (200+ anomalies)
• CRSP Returns: WRDS crsp.msf

All data access is handled through the research_data package.

from ff_decimals.data import (
    load_fama_french_factors,      # FF factors from research_data
    load_fama_french_with_rf,      # FF factors + risk-free rate
    load_chen_zimmerman_from_oap,  # Chen-Zimmerman from OAP
    load_crsp_monthly_returns,     # CRSP from research_data
)

from ff_decimals.analysis import add_decimal_noise

# Add noise to factors
ff_noisy = add_decimal_noise(
    factors=ff,
    noise_type='truncnorm',  # or 'uniform'
    lower=-0.005,
    upper=0.005,
    seed=42,
)

from research_data.methods import fama_macbeth, portfolio_sorts, rolling_ols

• t_range: Range of t-statistics (max - min) across simulations
• t_std: Standard deviation of t-statistics
• cv: Coefficient of variation (relative dispersion)

Predictors are "fragile" if decimal rounding can:

1. Flip significance status (cross the |t| > 1.96 threshold)
2. Change the sign of the coefficient

Fama, E. F., & MacBeth, J. D. (1973). Risk, return, and equilibrium: Empirical tests. Journal of Political Economy, 81(3), 607-636.

Fama, E. F., & French, K. R. (1992). The cross‐section of expected stock returns. The Journal of Finance, 47(2), 427-465.

Chen, A. Y., & Zimmermann, T. (2021). Open source cross-sectional asset pricing. Critical Finance Review, Forthcoming.

Akey, P., Robertson, A., & Simutin, M. (2022). Noisy factors. Rotman School of Management Working Paper, Forthcoming.

Shanken, J. (1992). On the estimation of beta-pricing models. The Review of Financial Studies, 5(1), 1-33.

Kim, D. (1995). The errors in the variables problem in the cross‐section of expected stock returns. The Journal of Finance, 50(5), 1605-1634.

Kan, R., Robotti, C., & Shanken, J. (2013). Pricing model performance and the two‐pass cross‐sectional regression methodology. The Journal of Finance, 68(6), 2617-2649.

Research code - academic use only.