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 Apr 2021 1.02 0.37 0.42 -0.06 0.15 -0.24% -2.87% 98.7%
Vanguard US Multifactor ETF VFMF Mar 2018 Apr 2021 0.95 0.38 0.36 0.08 0.13 -0.21% -2.58% 98.5%

Vident Core US Equity

Factor regression results for Vident Core US Equity
Ticker VUSE
Time Period Mar 2018 - Apr 2021
Regression Basis 38 monthly samples
Coefficient of Determination (R2) 98.7%
Adjusted R2 98.5%
Regression F statistic 474.32 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.484 with p-value 0.923)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 11.095 with p-value 0.050)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
FF-MKT-RF Market 1.02 0.036 28.423 0.000 0.946...1.092
FF-SMB Size 0.37 0.073 5.013 0.000 0.217...0.515
FF-HML Value 0.42 0.051 8.192 0.000 0.315...0.523
FF-MOM Momentum -0.06 0.046 -1.232 0.227 -0.152...0.037
FF-RMW Profitability 0.15 0.111 1.311 0.199 -0.081...0.372
Alpha Alpha -23.88bps 0.002 -1.514 0.140 -0.56%...0.08%
Annualized Alpha Annualized Alpha -2.87%  

Vanguard US Multifactor ETF

Factor regression results for Vanguard US Multifactor ETF
Ticker VFMF
Time Period Mar 2018 - Apr 2021
Regression Basis 38 monthly samples
Coefficient of Determination (R2) 98.5%
Adjusted R2 98.3%
Regression F statistic 432.07 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.170 with p-value 0.665)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 10.459 with p-value 0.063)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
FF-MKT-RF Market 0.95 0.033 28.835 0.000 0.879...1.013
FF-SMB Size 0.38 0.067 5.681 0.000 0.244...0.516
FF-HML Value 0.36 0.047 7.674 0.000 0.264...0.455
FF-MOM Momentum 0.08 0.043 1.868 0.071 -0.007...0.166
FF-RMW Profitability 0.13 0.102 1.303 0.202 -0.075...0.339
Alpha Alpha -21.50bps 0.001 -1.490 0.146 -0.51%...0.08%
Annualized Alpha Annualized Alpha -2.58%  
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) 140.61 33.76 -91.42 -20.32 10.76  
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 Apr 2021 -2.87% 143.27 12.36 -38.31 1.16 1.57 96.17 98.7%
Vanguard US Multifactor ETF VFMF Mar 2018 Apr 2021 -2.58% 133.04 12.83 -32.85 -1.61 1.42 91.33 98.5%
Regression residuals
MonthVUSEVFMF
Mar 20180.24%1.12%
Apr 20180.12%-0.30%
May 20180.03%0.23%
Jun 2018-0.47%-0.04%
Jul 2018-0.86%0.09%
Aug 20181.30%0.53%
Sep 2018-0.90%0.14%
Oct 20180.04%-0.13%
Nov 2018-1.04%-0.90%
Dec 2018-0.24%-0.21%
Jan 20190.39%0.64%
Feb 2019-0.31%1.00%
Mar 20190.18%-0.13%
Apr 2019-0.43%-1.01%
May 20190.18%-0.38%
Jun 20190.12%0.91%
Jul 20190.52%0.68%
Aug 2019-0.22%0.37%
Sep 2019-0.11%-0.19%
Oct 20191.26%0.44%
Nov 2019-0.23%0.62%
Dec 2019-1.81%-0.77%
Jan 20200.70%-0.20%
Feb 20200.47%-1.66%
Mar 20200.16%0.48%
Apr 20200.80%-0.65%
May 20200.69%0.72%
Jun 2020-1.27%-0.63%
Jul 20200.13%-0.12%
Aug 2020-1.49%-1.73%
Sep 20201.16%1.02%
Oct 2020-1.35%-0.95%
Nov 20200.23%-0.44%
Dec 2020-0.05%0.18%
Jan 2021-0.10%-0.48%
Feb 20211.34%1.22%
Mar 20211.76%1.23%
Apr 2021-0.92%-0.69%