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-SMB FF-HML FF-MOM FF-RMW Alpha Annual Alpha R2
Vident Core US Equity VUSE Mar 2018 Oct 2020 1.05 0.33 0.37 -0.04 -0.04 -0.40% -4.79% 98.9%
Vanguard US Multifactor ETF VFMF Mar 2018 Oct 2020 0.98 0.36 0.33 0.09 -0.06 -0.30% -3.61% 98.8%

Vident Core US Equity

Factor regression results for Vident Core US Equity
Ticker VUSE
Time Period Mar 2018 - Oct 2020
Regression Basis 32 monthly samples
Coefficient of Determination (R2) 98.9%
Adjusted R2 98.7%
Regression F statistic 478.12 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.465 with p-value 0.908)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 2.989 with p-value 0.702)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
FF-MKT-RF Market 1.05 0.035 29.779 0.000 0.980...1.125
FF-SMB Size 0.33 0.073 4.523 0.000 0.180...0.479
FF-HML Value 0.37 0.052 7.044 0.000 0.261...0.477
FF-MOM Momentum -0.04 0.050 -0.847 0.405 -0.146...0.061
FF-RMW Profitability -0.04 0.136 -0.276 0.784 -0.318...0.242
Alpha Alpha -39.95bps 0.002 -2.494 0.019 -0.73%...-0.07%
Annualized Alpha Annualized Alpha -4.79%  

Vanguard US Multifactor ETF

Factor regression results for Vanguard US Multifactor ETF
Ticker VFMF
Time Period Mar 2018 - Oct 2020
Regression Basis 32 monthly samples
Coefficient of Determination (R2) 98.8%
Adjusted R2 98.5%
Regression F statistic 414.59 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.854 with p-value 0.319)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 5.325 with p-value 0.377)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
FF-MKT-RF Market 0.98 0.034 28.902 0.000 0.911...1.050
FF-SMB Size 0.36 0.070 5.093 0.000 0.212...0.500
FF-HML Value 0.33 0.050 6.527 0.000 0.225...0.431
FF-MOM Momentum 0.09 0.048 1.786 0.086 -0.013...0.186
FF-RMW Profitability -0.06 0.131 -0.494 0.625 -0.333...0.204
Alpha Alpha -30.05bps 0.002 -1.955 0.061 -0.62%...0.02%
Annualized Alpha Annualized Alpha -3.61%  
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 monthly 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
Monthly Factor Premiums (BPS) 79.88 -4.88 -163.47 47.06 11.06  
Name Ticker Start Date End Date Annual Alpha FF-MKT-RF FF-SMB FF-HML FF-MOM FF-RMW Total R2
Vident Core US Equity VUSE Mar 2018 Oct 2020 -4.79% 84.09 -1.61 -60.32 -2.01 -0.42 -20.20 98.9%
Vanguard US Multifactor ETF VFMF Mar 2018 Oct 2020 -3.61% 78.33 -1.74 -53.64 4.07 -0.71 -3.74 98.8%
Regression residuals
MonthVUSEVFMF
Mar 20180.00560.0130
Apr 2018-0.0009-0.0063
May 2018-0.0028-0.0017
Jun 2018-0.00220.0016
Jul 2018-0.00560.0034
Aug 20180.01090.0035
Sep 2018-0.00790.0025
Oct 20180.00630.0039
Nov 2018-0.0100-0.0095
Dec 20180.00030.0008
Jan 20190.00370.0044
Feb 2019-0.00310.0096
Mar 20190.0012-0.0013
Apr 2019-0.0002-0.0069
May 20190.0019-0.0033
Jun 20190.00250.0097
Jul 20190.00520.0064
Aug 2019-0.00290.0040
Sep 20190.00740.0045
Oct 20190.01370.0051
Nov 2019-0.00570.0020
Dec 2019-0.0160-0.0070
Jan 20200.0012-0.0067
Feb 20200.0048-0.0169
Mar 2020-0.00400.0021
Apr 20200.0106-0.0050
May 20200.00590.0063
Jun 2020-0.0124-0.0067
Jul 2020-0.0009-0.0030
Aug 2020-0.0096-0.0116
Sep 20200.01080.0092
Oct 2020-0.0077-0.0060