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 Bet 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

Vanguard Small Cap Growth Index I

Factor regression results for Vanguard Small Cap Growth Index I
Ticker VSGIX
Time Period Feb 2010 - May 2018
Coefficient of Determination (R2) 97.1%
Adjusted R2 97.0%
Regression F statistic 631.54 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.983 with p-value 0.474)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 8.134 with p-value 0.149)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.05 0.034 30.914 0.000 0.986...1.121
Size (SMB) 0.67 0.038 17.839 0.000 0.598...0.747
Value (HML) -0.18 0.041 -4.227 0.000 -0.258...-0.093
Term Risk (TRM) 0.00 0.034 0.002 0.998 -0.068...0.068
Credit Risk (CDT) 0.07 0.063 1.043 0.299 -0.059...0.190
Alpha (α) -8.91bps 0.001 -0.989 0.325 -0.27%...0.09%
Annualized Alpha (α) -1.07%  
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
  • See methodology section of the FAQ regarding fixed income factor model details.
  • 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
    Bt
    Term risk loading factor
    Bc
    Credit risk loading factor
    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) 117.09 11.69 -11.91 51.86 30.56  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML TRM CDT Total R2
Vanguard Small Cap Growth Index I VSGIX Feb 2010 May 2018 -1.07% 123.36 7.86 2.09 0.00 2.00 126.40 97.1%
Regression residuals
MonthVSGIX
Feb 20100.0100
Mar 20100.0088
Apr 2010-0.0005
May 20100.0060
Jun 2010-0.0071
Jul 2010-0.0065
Aug 20100.0023
Sep 20100.0047
Oct 2010-0.0067
Nov 20100.0066
Dec 20100.0092
Jan 20110.0085
Feb 20110.0158
Mar 20110.0085
Apr 20110.0021
May 2011-0.0041
Jun 20110.0012
Jul 2011-0.0085
Aug 2011-0.0022
Sep 2011-0.0116
Oct 20110.0165
Nov 20110.0017
Dec 2011-0.0058
Jan 20120.0008
Feb 20120.0037
Mar 2012-0.0030
Apr 20120.0033
May 2012-0.0068
Jun 20120.0020
Jul 2012-0.0054
Aug 20120.0132
Sep 2012-0.0030
Oct 20120.0086
Nov 20120.0034
Dec 20120.0125
Jan 20130.0024
Feb 2013-0.0004
Mar 20130.0022
Apr 2013-0.0042
May 20130.0089
Jun 2013-0.0008
Jul 2013-0.0049
Aug 20130.0040
Sep 20130.0010
Oct 2013-0.0070
Nov 2013-0.0165
Dec 2013-0.0020
Jan 20140.0141
Feb 2014-0.0004
Mar 2014-0.0047
Apr 2014-0.0045
May 2014-0.0026
Jun 20140.0094
Jul 2014-0.0009
Aug 20140.0001
Sep 2014-0.0027
Oct 2014-0.0176
Nov 2014-0.0080
Dec 2014-0.0042
Jan 20150.0220
Feb 2015-0.0105
Mar 20150.0033
Apr 2015-0.0034
May 20150.0070
Jun 2015-0.0051
Jul 20150.0112
Aug 2015-0.0032
Sep 2015-0.0036
Oct 2015-0.0220
Nov 2015-0.0065
Dec 20150.0053
Jan 2016-0.0010
Feb 2016-0.0036
Mar 2016-0.0025
Apr 20160.0031
May 20160.0066
Jun 2016-0.0017
Jul 2016-0.0065
Aug 2016-0.0019
Sep 2016-0.0127
Oct 20160.0045
Nov 2016-0.0066
Dec 2016-0.0076
Jan 20170.0094
Feb 20170.0001
Mar 2017-0.0102
Apr 2017-0.0059
May 20170.0022
Jun 2017-0.0004
Jul 20170.0016
Aug 20170.0025
Sep 2017-0.0142
Oct 20170.0125
Nov 20170.0019
Dec 2017-0.0005
Jan 2018-0.0022
Feb 20180.0035
Mar 20180.0135
Apr 2018-0.0067
May 2018-0.0106