Factor Regression Analysis

This factor regression tool supports factor regression analysis of individual assets or a portfolio of assets using the given risk factor model. The multiple linear regression indicates how well the returns of the given assets or a portfolio are explained by the risk factor exposures. The supported equity risk factor models include:

Additional supported equity factors include the short and long-term reversal factors (STREV, LTREV) based on Fama-French factor data, quality (QMJ) factor based on both AQR and Alpha Architect factor data, and bet against beta (BAB) factor based on AQR factor data.

For fixed income funds and balanced funds you can include the fixed income factor model to explain returns based on term risk (interest rate risk) and credit risk exposures. The fixed income factors can be further adjusted to account for the yield curve and to add high yield credit risk as an additional factor.

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Factor Analysis Results

Factor Analysis Summary

Factor regression results
Name Ticker Start Date End Date FF-MKT-RF FF-SMB5 FF-HML FF-MOM FF-RMW FF-CMA Alpha Annual Alpha R2
Avantis U.S. Equity ETF AVUS 09/26/2019 05/28/2021 0.98 0.13 0.14 0.02 0.10 -0.03 0.00% 0.16% 99.2%
Avantis U.S. Small Cap Value ETF AVUV 09/26/2019 05/28/2021 1.01 0.91 0.47 -0.05 0.30 -0.17 0.00% 0.89% 98.7%
Vanguard Total Stock Market ETF VTI 09/26/2019 05/28/2021 0.98 -0.02 0.04 -0.00 0.01 0.01 -0.00% -0.33% 99.7%

Avantis U.S. Equity ETF

Factor regression results for Avantis U.S. Equity ETF
Ticker AVUS
Time Period 09/26/2019 - 05/28/2021
Regression Basis 422 daily samples
Coefficient of Determination (R2) 99.2%
Adjusted R2 99.2%
Regression F statistic 8,531.50 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.579 with p-value 1.000)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 11.460 with p-value 0.075)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
FF-MKT-RF Market 0.98 0.005 199.932 0.000 0.970...0.990
FF-SMB5 Size 0.13 0.011 12.240 0.000 0.109...0.151
FF-HML Value 0.14 0.012 11.337 0.000 0.113...0.161
FF-MOM Momentum 0.02 0.008 2.530 0.012 0.004...0.036
FF-RMW Profitability 0.10 0.018 5.668 0.000 0.067...0.138
FF-CMA Investment -0.03 0.021 -1.621 0.106 -0.076...0.007
Alpha Alpha 0.06bps 0.000 0.078 0.938 -0.02%...0.02%
Annualized Alpha Annualized Alpha 0.16%  

Avantis U.S. Small Cap Value ETF

Factor regression results for Avantis U.S. Small Cap Value ETF
Ticker AVUV
Time Period 09/26/2019 - 05/28/2021
Regression Basis 422 daily samples
Coefficient of Determination (R2) 98.7%
Adjusted R2 98.7%
Regression F statistic 5,385.14 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.210 with p-value 0.985)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 9.660 with p-value 0.140)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
FF-MKT-RF Market 1.01 0.009 116.738 0.000 0.989...1.023
FF-SMB5 Size 0.91 0.019 48.550 0.000 0.871...0.944
FF-HML Value 0.47 0.021 21.900 0.000 0.424...0.508
FF-MOM Momentum -0.05 0.014 -3.954 0.000 -0.082...-0.028
FF-RMW Profitability 0.30 0.032 9.373 0.000 0.236...0.362
FF-CMA Investment -0.17 0.037 -4.627 0.000 -0.246...-0.099
Alpha Alpha 0.36bps 0.000 0.249 0.803 -0.02%...0.03%
Annualized Alpha Annualized Alpha 0.89%  

Vanguard Total Stock Market ETF

Factor regression results for Vanguard Total Stock Market ETF
Ticker VTI
Time Period 09/26/2019 - 05/28/2021
Regression Basis 422 daily samples
Coefficient of Determination (R2) 99.7%
Adjusted R2 99.7%
Regression F statistic 26,011.72 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.445 with p-value 1.000)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 5.569 with p-value 0.473)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
FF-MKT-RF Market 0.98 0.003 365.025 0.000 0.980...0.990
FF-SMB5 Size -0.02 0.006 -3.448 0.001 -0.032...-0.009
FF-HML Value 0.04 0.007 6.018 0.000 0.027...0.053
FF-MOM Momentum -0.00 0.004 -0.747 0.455 -0.012...0.005
FF-RMW Profitability 0.01 0.010 0.639 0.523 -0.013...0.026
FF-CMA Investment 0.01 0.012 0.713 0.476 -0.015...0.031
Alpha Alpha -0.13bps 0.000 -0.290 0.772 -0.01%...0.01%
Annualized Alpha Annualized Alpha -0.33%  
Notes on results:
  • Past performance is no guarantee of future results, which may vary. All use is subject to terms of service.
  • Investing involves risk, including possible loss of principal. The value of the investments and the income derived from them may fluctuate over time.
  • The results are based on information from a variety of sources we consider reliable, but we do not represent that the information is accurate or complete.
  • The results do not constitute investment advice or recommendation, are provided solely for informational purposes, and are not an offer to buy or sell any securities.
  • The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
  • Refer to the FAQ section regarding the list of factor data sources and methodology descriptions
  • Results are based on multiple linear regression against daily factor returns.
  • Symbols:
    MKT-RF
    Market factor (excess return over the risk free rate)
    SMB
    Size factor (Small Minus Big)
    HML
    Value factor (High Minus Low)
    MOM
    Momentum factor (Up Minus Down)
    RMW
    Profitability factor (Robust Minus Weak)
    CMA
    Conservative investment factor (Conservative Minus Aggressive)
    ST-REV
    Short-term reversal factor
    LT-REV
    Long-term reversal factor
    QMJ
    Quality factor (Quality Minus Junk)
    BAB
    Bet Against Beta factor
    TRM
    Term factor (fixed income)
    CDT
    Credit factor (fixed income)
    Alpha
    Excess return over the benchmark
    t-stat
    t-statistic is a ratio of the departure of an estimated parameter from its notional value and its standard error
    p-value
    p-value measures the statistical significance of the estimated parameter
    R2
    Coefficient of determination

Factor Performance Attribution in Basis Points

Factor regression results
Daily Factor Premiums (BPS) 11.04 3.48 -2.87 -4.71 0.96 -0.69  
Name Ticker Start Date End Date Annual Alpha FF-MKT-RF FF-SMB5 FF-HML FF-MOM FF-RMW FF-CMA Total R2
Avantis U.S. Equity ETF AVUS 09/26/2019 05/28/2021 0.16% 10.82 0.45 -0.39 -0.09 0.10 0.02 10.97 99.2%
Avantis U.S. Small Cap Value ETF AVUV 09/26/2019 05/28/2021 0.89% 11.11 3.16 -1.34 0.26 0.29 0.12 13.95 98.7%
Vanguard Total Stock Market ETF VTI 09/26/2019 05/28/2021 -0.33% 10.87 -0.07 -0.11 0.02 0.01 -0.01 10.57 99.7%