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.

Portfolio Assets
Allocation
Asset 1
%
Asset 2
%
Asset 3
%
Asset 4
%
Asset 5
%
Asset 6
%
Asset 7
%
Asset 8
%
Asset 9
%
Asset 10
%
Total
%

Factor Analysis Results

Factor Analysis Summary

Factor regression results
Name Ticker Start Date End Date Rm-Rf SMB HML RMW CMA Alpha Annual Alpha R2
Vanguard Small-Cap Value ETF VBR Jan 2013 Apr 2021 1.00 0.54 0.37 0.09 -0.13 -0.09% -1.05% 97.8%
Vanguard S&P Small-Cap 600 Value ETF VIOV Jan 2013 Apr 2021 0.98 0.85 0.37 0.15 0.05 0.02% 0.20% 98.2%

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Jan 2013 - Apr 2021
Regression Basis 100 monthly samples
Coefficient of Determination (R2) 97.8%
Adjusted R2 97.6%
Regression F statistic 820.95 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.778 with p-value 0.130)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 6.018 with p-value 0.304)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.00 0.023 43.141 0.000 0.950...1.042
Size (SMB) 0.54 0.039 13.733 0.000 0.462...0.618
Value (HML) 0.37 0.036 10.276 0.000 0.297...0.440
Profitability (RMW) 0.09 0.058 1.500 0.137 -0.028...0.201
Investment (CMA) -0.13 0.062 -2.053 0.043 -0.249...-0.004
Alpha (α) -8.72bps 0.001 -0.994 0.323 -0.26%...0.09%
Annualized Alpha (α) -1.05%  

Vanguard S&P Small-Cap 600 Value ETF

Factor regression results for Vanguard S&P Small-Cap 600 Value ETF
Ticker VIOV
Time Period Jan 2013 - Apr 2021
Regression Basis 100 monthly samples
Coefficient of Determination (R2) 98.2%
Adjusted R2 98.1%
Regression F statistic 1,026.82 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.713 with p-value 0.073)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 8.233 with p-value 0.144)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.98 0.023 43.057 0.000 0.937...1.028
Size (SMB) 0.85 0.039 21.940 0.000 0.776...0.930
Value (HML) 0.37 0.035 10.568 0.000 0.304...0.445
Profitability (RMW) 0.15 0.057 2.673 0.009 0.039...0.266
Investment (CMA) 0.05 0.061 0.798 0.427 -0.072...0.169
Alpha (α) 1.67bps 0.001 0.192 0.848 -0.16%...0.19%
Annualized Alpha (α) 0.20%  
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.
  • 5-factor model: Ra = Rrf + Bmkt × ( Rmkt - Rrf ) + Bsmb × SMB + Bhml × HML + Brmw × RMW + Bcma × CMA + α
  • Symbols:
    Ra
    Asset return
    Rrf
    Risk free return
    Bmkt
    Market loading factor (exposure to market risk, different from CAPM beta)
    Rmkt
    Market return
    Bsmb
    Size loading factor (the level of exposure to size risk)
    SMB
    Small Minus Big: The size premium
    Bhml
    Value loading factor (the level of exposure to value risk)
    HML
    High Minus Low: The value premium
    Brmw
    Profitability loading factor
    RMW
    Robust Minus Weak: The profitability premium
    Bcma
    Investment loading factor
    CMA
    Conservative Minus Aggressive: The conservative investment premium
    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) 131.31 1.68 -38.52 10.14 -19.27  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML RMW CMA Total R2
Vanguard Small-Cap Value ETF VBR Jan 2013 Apr 2021 -1.05% 130.79 0.91 -14.20 0.88 2.44 112.09 97.8%
Vanguard S&P Small-Cap 600 Value ETF VIOV Jan 2013 Apr 2021 0.20% 129.02 1.43 -14.43 1.55 -0.94 118.31 98.2%
Regression residuals
MonthVBRVIOV
Jan 20130.67%-0.99%
Feb 20130.68%0.84%
Mar 20130.37%-0.62%
Apr 2013-0.29%0.07%
May 2013-1.55%-0.41%
Jun 2013-0.66%0.06%
Jul 20130.31%-0.92%
Aug 2013-0.71%0.57%
Sep 20130.51%0.87%
Oct 20130.07%-0.28%
Nov 2013-0.93%-0.28%
Dec 20130.41%-0.59%
Jan 20141.21%0.45%
Feb 20140.46%0.70%
Mar 2014-0.19%-0.87%
Apr 20140.79%0.23%
May 20140.61%0.54%
Jun 20140.31%-0.81%
Jul 2014-0.39%0.45%
Aug 20140.94%0.17%
Sep 2014-1.14%-0.37%
Oct 20141.06%1.98%
Nov 20140.90%1.57%
Dec 2014-0.21%-1.15%
Jan 20151.31%-0.43%
Feb 20150.05%0.61%
Mar 20150.94%-0.42%
Apr 2015-0.89%-0.30%
May 20150.14%-0.43%
Jun 2015-1.39%-0.41%
Jul 20151.27%1.01%
Aug 20150.15%0.06%
Sep 20150.70%1.13%
Oct 20150.24%0.52%
Nov 2015-0.70%-0.18%
Dec 2015-0.17%1.18%
Jan 20160.70%0.43%
Feb 20161.32%1.09%
Mar 20161.01%1.08%
Apr 2016-0.08%-0.57%
May 20160.47%0.09%
Jun 20160.64%0.36%
Jul 2016-0.43%-0.51%
Aug 2016-1.71%-1.69%
Sep 2016-0.23%0.13%
Oct 2016-0.19%-0.66%
Nov 2016-0.77%-0.12%
Dec 2016-0.54%-0.53%
Jan 20170.46%-0.80%
Feb 20170.10%0.48%
Mar 2017-0.24%-0.42%
Apr 2017-0.50%-0.41%
May 2017-0.73%0.55%
Jun 20170.01%0.29%
Jul 20170.24%0.30%
Aug 2017-0.15%-0.75%
Sep 2017-0.96%0.92%
Oct 2017-0.87%-0.05%
Nov 2017-0.00%0.21%
Dec 20170.08%-0.76%
Jan 2018-1.48%-0.68%
Feb 2018-1.28%-0.09%
Mar 20181.27%0.08%
Apr 2018-0.29%0.66%
May 20180.42%0.46%
Jun 20180.17%0.19%
Jul 20180.00%0.47%
Aug 2018-0.29%0.56%
Sep 20180.26%-0.71%
Oct 20180.02%-0.38%
Nov 20180.98%-0.50%
Dec 20180.33%-0.00%
Jan 20191.07%1.62%
Feb 20190.35%0.25%
Mar 20190.15%-0.75%
Apr 2019-0.69%0.36%
May 20190.58%-1.28%
Jun 2019-0.17%0.56%
Jul 20190.43%1.44%
Aug 20190.47%1.66%
Sep 20190.11%0.93%
Oct 20190.07%0.18%
Nov 2019-0.95%-0.53%
Dec 2019-1.09%-1.49%
Jan 20201.21%-0.00%
Feb 2020-0.83%-0.43%
Mar 2020-1.85%-0.25%
Apr 2020-1.74%-1.62%
May 2020-0.34%-2.62%
Jun 2020-0.46%0.42%
Jul 2020-0.14%-0.26%
Aug 2020-1.86%-1.05%
Sep 20200.75%-0.48%
Oct 20201.23%0.17%
Nov 20201.03%0.73%
Dec 20200.43%-0.05%
Jan 2021-1.73%-0.26%
Feb 20210.81%1.45%
Mar 20210.01%-0.50%
Apr 20210.57%-0.46%