Fama-French Factor Regression Analysis

This online Fama-French factor regression analysis tool supports regression analysis for individual assets or a portfolio of assets using the capital asset pricing model (CAPM), Fama-French three-factor model, the Carhart four-factor model, or the new Fama-French five-factor model. You can also run market model regression for beta analysis based on selected assets or imported benchmarks. The analysis is based on asset returns for the entered mutual funds and ETFs, and the factor returns published on Kenneth French's web site and AQR's web site. The multiple linear regression indicates how well the returns of the given assets or a portfolio are explained by the Fama-French three-factor model based on market, size and value loading factors. Carhart four-factor model adds momentum as the fourth factor for explaining asset returns, and the Fama-French five-factor model extends the three-factor model with profitability (RMW) and investment (CMA) factors. The tool also supports the use of other factor models including Quality Minus Junk (QMJ) and Betting Against Beta (BAB) factors as described in Asness-Frazzini-Pedersen papers. For bond 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 exposure. 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. You can also view the table of mutual fund and ETF factor regressions.

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Factor Analysis Results

Factor Analysis Summary

Factor regression results
Name Ticker Start Date End Date Rm-Rf SMB HML Alpha Annual Alpha R2
Schwab International Equity ETF SCHF Sep 2013 Dec 2018 0.98 -0.15 -0.10 -0.03% -0.40% 97.2%
Schwab Emerging Markets Equity ETF SCHE Sep 2013 Dec 2018 1.06 0.31 0.12 -0.03% -0.31% 62.0%
Schwab Fundamental Intl Sm Co ETF FNDC Sep 2013 Dec 2018 1.00 0.32 -0.14 0.05% 0.65% 94.6%
Vanguard FTSE All-Wld ex-US SmCp ETF VSS Sep 2013 Dec 2018 1.03 0.48 -0.11 -0.10% -1.21% 93.0%
Schwab International Small-Cap Eq ETF SCHC Sep 2013 Dec 2018 1.05 0.43 -0.16 -0.12% -1.48% 94.7%

Schwab International Equity ETF

Factor regression results for Schwab International Equity ETF
Ticker SCHF
Time Period Sep 2013 - Dec 2018
Coefficient of Determination (R2) 97.2%
Adjusted R2 97.0%
Regression F statistic 688.93 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.755 with p-value 0.999)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.804 with p-value 0.283)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.98 0.022 44.161 0.000 0.939...1.028
Size (SMB) -0.15 0.049 -2.981 0.004 -0.245...-0.048
Value (HML) -0.10 0.045 -2.249 0.028 -0.189...-0.011
Alpha (α) -3.36bps 0.001 -0.463 0.645 -0.18%...0.11%
Annualized Alpha (α) -0.40%  

Schwab Emerging Markets Equity ETF

Factor regression results for Schwab Emerging Markets Equity ETF
Ticker SCHE
Time Period Sep 2013 - Dec 2018
Coefficient of Determination (R2) 62.0%
Adjusted R2 60.1%
Regression F statistic 32.57 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.969 with p-value 0.446)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.993 with p-value 0.574)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.110 9.627 0.000 0.840...1.281
Size (SMB) 0.31 0.243 1.294 0.201 -0.172...0.801
Value (HML) 0.12 0.221 0.565 0.575 -0.317...0.566
Alpha (α) -2.57bps 0.004 -0.072 0.943 -0.74%...0.69%
Annualized Alpha (α) -0.31%  

Schwab Fundamental Intl Sm Co ETF

Factor regression results for Schwab Fundamental Intl Sm Co ETF
Ticker FNDC
Time Period Sep 2013 - Dec 2018
Coefficient of Determination (R2) 94.6%
Adjusted R2 94.3%
Regression F statistic 350.18 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.574 with p-value 0.991)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.445 with p-value 0.695)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.00 0.031 32.238 0.000 0.942...1.066
Size (SMB) 0.32 0.069 4.679 0.000 0.184...0.459
Value (HML) -0.14 0.062 -2.177 0.033 -0.260...-0.011
Alpha (α) 5.45bps 0.001 0.537 0.593 -0.15%...0.26%
Annualized Alpha (α) 0.65%  

Vanguard FTSE All-Wld ex-US SmCp ETF

Factor regression results for Vanguard FTSE All-Wld ex-US SmCp ETF
Ticker VSS
Time Period Sep 2013 - Dec 2018
Coefficient of Determination (R2) 93.0%
Adjusted R2 92.6%
Regression F statistic 264.70 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.609 with p-value 0.994)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 13.383 with p-value 0.004)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.03 0.037 27.923 0.000 0.955...1.102
Size (SMB) 0.48 0.081 5.851 0.000 0.313...0.638
Value (HML) -0.11 0.074 -1.532 0.131 -0.261...0.035
Alpha (α) -10.04bps 0.001 -0.838 0.406 -0.34%...0.14%
Annualized Alpha (α) -1.21%  

Schwab International Small-Cap Eq ETF

Factor regression results for Schwab International Small-Cap Eq ETF
Ticker SCHC
Time Period Sep 2013 - Dec 2018
Coefficient of Determination (R2) 94.7%
Adjusted R2 94.4%
Regression F statistic 356.95 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 3.054 with p-value 1.000)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 2.305 with p-value 0.512)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.05 0.032 32.542 0.000 0.989...1.119
Size (SMB) 0.43 0.071 6.009 0.000 0.287...0.573
Value (HML) -0.16 0.065 -2.487 0.016 -0.291...-0.032
Alpha (α) -12.31bps 0.001 -1.168 0.248 -0.33%...0.09%
Annualized Alpha (α) -1.48%  
Notes on results:
  • Time frame for factor analysis is the full available data range unless a specific date interval is specified.
  • Results are based on multiple linear regression against monthly factor returns.
  • 3-factor model: Ra = Rrf + Bmkt × ( Rmkt - Rrf ) + Bsmb × SMB + Bhml × HML + 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
    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
  • Resources:

Factor Performance Attribution in Basis Points

Factor regression results
Monthly Factor Premiums (BPS) 30.98 14.89 -0.16  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML Total R2
Schwab International Equity ETF SCHF Sep 2013 Dec 2018 -0.40% 30.46 -2.18 0.02 24.94 97.2%
Schwab Emerging Markets Equity ETF SCHE Sep 2013 Dec 2018 -0.31% 32.87 4.69 -0.02 34.96 62.0%
Schwab Fundamental Intl Sm Co ETF FNDC Sep 2013 Dec 2018 0.65% 31.10 4.79 0.02 41.36 94.6%
Vanguard FTSE All-Wld ex-US SmCp ETF VSS Sep 2013 Dec 2018 -1.21% 31.87 7.08 0.02 28.93 93.0%
Schwab International Small-Cap Eq ETF SCHC Sep 2013 Dec 2018 -1.48% 32.66 6.40 0.03 26.77 94.7%
Regression residuals
MonthSCHFSCHEFNDCVSSSCHC
Sep 20130.00600.00610.0099-0.0038-0.0065
Oct 2013-0.00030.00620.00200.01190.0097
Nov 20130.0008-0.0134-0.0037-0.0086-0.0109
Dec 20130.0046-0.02210.00350.00300.0183
Jan 2014-0.0084-0.0692-0.0132-0.0099-0.0142
Feb 2014-0.0053-0.01610.00470.02690.0224
Mar 20140.00360.0494-0.0027-0.00260.0052
Apr 20140.00270.0020-0.00000.01040.0035
May 20140.00170.01250.00650.0021-0.0019
Jun 20140.00280.0145-0.0030-0.00100.0004
Jul 2014-0.00040.0341-0.0044-0.0124-0.0138
Aug 20140.00640.04020.00180.01710.0115
Sep 2014-0.0047-0.0254-0.0061-0.0118-0.0114
Oct 20140.00880.04890.01770.01070.0074
Nov 2014-0.0120-0.0099-0.0215-0.0188-0.0221
Dec 2014-0.0062-0.01710.00800.00130.0041
Jan 20150.00170.00640.0075-0.00050.0024
Feb 20150.0023-0.01370.00950.01330.0084
Mar 20150.0003-0.00990.0005-0.0041-0.0007
Apr 2015-0.00310.0130-0.0201-0.0044-0.0103
May 20150.0034-0.03540.0005-0.00310.0032
Jun 20150.0010-0.00530.0047-0.00500.0014
Jul 2015-0.0063-0.0604-0.0063-0.0256-0.0121
Aug 2015-0.0036-0.02840.01090.00040.0120
Sep 20150.00330.0141-0.00000.01440.0090
Oct 2015-0.0040-0.0106-0.0001-0.0085-0.0119
Nov 20150.0032-0.01230.00830.00790.0042
Dec 2015-0.0095-0.0315-0.0046-0.0116-0.0092
Jan 20160.01000.02140.00850.00480.0040
Feb 2016-0.01670.0035-0.01090.00820.0002
Mar 20160.00510.05000.0092-0.00650.0027
Apr 2016-0.0043-0.0289-0.0101-0.00110.0019
May 20160.0042-0.02270.01760.00240.0050
Jun 20160.01300.08300.00120.0074-0.0068
Jul 2016-0.0066-0.00480.00710.00090.0044
Aug 20160.00740.0053-0.0006-0.0013-0.0034
Sep 20160.0017-0.00140.00710.00270.0012
Oct 2016-0.00020.01360.0084-0.0071-0.0116
Nov 20160.0091-0.02340.01060.00620.0149
Dec 2016-0.0029-0.0308-0.0054-0.0101-0.0068
Jan 20170.00450.01400.00040.0069-0.0001
Feb 20170.00240.01600.00410.0054-0.0024
Mar 2017-0.0010-0.0021-0.0070-0.0007-0.0020
Apr 2017-0.0076-0.00880.00270.00190.0045
May 2017-0.0023-0.0222-0.0126-0.0156-0.0102
Jun 20170.0063-0.00410.00440.00320.0053
Jul 2017-0.00080.01910.00100.00430.0013
Aug 2017-0.00380.0244-0.00040.00460.0026
Sep 20170.0043-0.02850.00380.00000.0036
Oct 20170.00370.00760.00180.0004-0.0040
Nov 2017-0.0001-0.00810.00010.00070.0020
Dec 20170.00030.0134-0.00060.00450.0040
Jan 20180.00190.0424-0.0076-0.0058-0.0022
Feb 2018-0.0101-0.0172-0.0053-0.0070-0.0082
Mar 20180.00570.01200.00740.01510.0099
Apr 2018-0.0046-0.0455-0.0018-0.00240.0031
May 2018-0.0028-0.0107-0.00940.00220.0010
Jun 2018-0.0057-0.0232-0.0056-0.00820.0006
Jul 20180.00410.0276-0.00320.0038-0.0027
Aug 2018-0.0027-0.0182-0.0069-0.00410.0018
Sep 20180.0012-0.0142-0.0024-0.0188-0.0055
Oct 20180.00020.0188-0.0043-0.0045-0.0026
Nov 20180.00370.04980.00040.0101-0.0061
Dec 2018-0.00530.0264-0.01170.01000.0022