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.

Portfolio Assets
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Asset 2
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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
iShares Russell 2000 ETF IWM Dec 2000 May 2018 1.01 0.83 0.20 -0.09% -1.13% 98.2%
Vanguard Small Cap Index Adm VSMAX Dec 2000 May 2018 1.03 0.70 0.21 -0.01% -0.07% 97.6%
DFA US Small Cap I DFSTX Dec 2000 May 2018 1.03 0.86 0.27 -0.02% -0.24% 98.8%

iShares Russell 2000 ETF

Factor regression results for iShares Russell 2000 ETF
Ticker IWM
Time Period Dec 2000 - May 2018
Coefficient of Determination (R2) 98.2%
Adjusted R2 98.2%
Regression F statistic 3,723.89 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.306 with p-value 0.987)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 7.041 with p-value 0.071)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.013 80.773 0.000 0.990...1.039
Size (SMB) 0.83 0.021 39.750 0.000 0.793...0.876
Value (HML) 0.20 0.018 10.913 0.000 0.164...0.236
Alpha (α) -9.44bps 0.001 -1.834 0.068 -0.20%...0.01%
Annualized Alpha (α) -1.13%  

Vanguard Small Cap Index Adm

Factor regression results for Vanguard Small Cap Index Adm
Ticker VSMAX
Time Period Dec 2000 - May 2018
Coefficient of Determination (R2) 97.6%
Adjusted R2 97.6%
Regression F statistic 2,775.68 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.204 with p-value 0.931)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 9.437 with p-value 0.024)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.03 0.014 72.753 0.000 1.006...1.062
Size (SMB) 0.70 0.024 29.554 0.000 0.655...0.749
Value (HML) 0.21 0.021 10.010 0.000 0.167...0.248
Alpha (α) -0.62bps 0.001 -0.106 0.916 -0.12%...0.11%
Annualized Alpha (α) -0.07%  

DFA US Small Cap I

Factor regression results for DFA US Small Cap I
Ticker DFSTX
Time Period Dec 2000 - May 2018
Coefficient of Determination (R2) 98.8%
Adjusted R2 98.8%
Regression F statistic 5,510.70 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.535 with p-value 0.000)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 9.288 with p-value 0.026)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.03 0.011 97.333 0.000 1.008...1.049
Size (SMB) 0.86 0.018 48.655 0.000 0.824...0.894
Value (HML) 0.27 0.015 17.205 0.000 0.235...0.296
Alpha (α) -2.01bps 0.000 -0.465 0.642 -0.11%...0.07%
Annualized Alpha (α) -0.24%  
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) 54.16 32.92 17.54  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML Total R2
iShares Russell 2000 ETF IWM Dec 2000 May 2018 -1.13% 54.96 27.48 3.51 76.50 98.2%
Vanguard Small Cap Index Adm VSMAX Dec 2000 May 2018 -0.07% 56.00 23.11 3.64 82.13 97.6%
DFA US Small Cap I DFSTX Dec 2000 May 2018 -0.24% 55.70 28.29 4.65 86.62 98.8%
Regression residuals
MonthIWMVSMAXDFSTX
Dec 20000.04040.04710.0220
Jan 2001-0.0275-0.02120.0063
Feb 20010.01260.01310.0052
Mar 20010.00830.00600.0052
Apr 20010.0041-0.00230.0005
May 2001-0.0159-0.01030.0059
Jun 20010.00060.01890.0184
Jul 2001-0.0109-0.01500.0040
Aug 20010.01330.00880.0057
Sep 2001-0.0058-0.0025-0.0018
Oct 2001-0.0087-0.0058-0.0044
Nov 2001-0.0015-0.0034-0.0032
Dec 2001-0.00240.00820.0067
Jan 2002-0.0040-0.0123-0.0126
Feb 2002-0.0041-0.0021-0.0014
Mar 2002-0.00560.00360.0011
Apr 20020.00680.0117-0.0066
May 2002-0.0104-0.0113-0.0061
Jun 2002-0.0212-0.0026-0.0150
Jul 20020.0000-0.0226-0.0062
Aug 20020.00350.00300.0089
Sep 20020.00020.01290.0038
Oct 2002-0.0037-0.0186-0.0047
Nov 20020.00260.00910.0055
Dec 2002-0.0035-0.0023-0.0026
Jan 2003-0.0044-0.0097-0.0107
Feb 2003-0.0052-0.0062-0.0068
Mar 2003-0.0122-0.0013-0.0046
Apr 20030.01250.00150.0079
May 20030.0087-0.00040.0097
Jun 2003-0.0181-0.0086-0.0046
Jul 2003-0.0001-0.0058-0.0038
Aug 2003-0.00140.0010-0.0022
Sep 2003-0.0134-0.0098-0.0101
Oct 2003-0.0003-0.0044-0.0034
Nov 20030.00350.0051-0.0002
Dec 2003-0.0051-0.0050-0.0019
Jan 2004-0.0056-0.0072-0.0073
Feb 20040.00660.00810.0047
Mar 20040.00800.01180.0024
Apr 2004-0.0140-0.00960.0019
May 20040.01250.00880.0009
Jun 20040.00190.00230.0009
Jul 2004-0.00310.0001-0.0089
Aug 2004-0.00450.0039-0.0048
Sep 20040.01220.00420.0062
Oct 20040.00450.00560.0025
Nov 20040.0092-0.00390.0012
Dec 2004-0.0124-0.0013-0.0029
Jan 2005-0.0046-0.0023-0.0046
Feb 2005-0.00240.0004-0.0032
Mar 2005-0.00110.0022-0.0027
Apr 20050.00270.0072-0.0023
May 20050.00370.00350.0065
Jun 20050.00650.00320.0003
Jul 20050.00110.00040.0021
Aug 2005-0.0046-0.00320.0002
Sep 2005-0.00270.00160.0016
Oct 2005-0.0109-0.0060-0.0028
Nov 20050.01350.00210.0038
Dec 2005-0.00380.0013-0.0002
Jan 20060.00350.00330.0068
Feb 20060.00740.00130.0019
Mar 20060.0007-0.0026-0.0048
Apr 2006-0.0010-0.0067-0.0040
May 2006-0.0037-0.0006-0.0025
Jun 20060.00130.0023-0.0054
Jul 20060.0044-0.0065-0.0069
Aug 20060.0021-0.0052-0.0001
Sep 2006-0.0041-0.0046-0.0029
Oct 20060.00850.00240.0045
Nov 2006-0.00380.0032-0.0041
Dec 2006-0.0053-0.0114-0.0046
Jan 2007-0.00140.0043-0.0042
Feb 2007-0.00040.00650.0004
Mar 20070.00050.00180.0005
Apr 2007-0.00310.0034-0.0010
May 20070.00750.00650.0005
Jun 2007-0.0017-0.00270.0018
Jul 2007-0.00750.00170.0047
Aug 20070.01420.00530.0076
Sep 20070.00690.00500.0012
Oct 20070.01130.00850.0031
Nov 20070.0020-0.0003-0.0022
Dec 20070.0001-0.00090.0041
Jan 2008-0.00180.0001-0.0077
Feb 20080.00550.00810.0030
Mar 2008-0.0056-0.00330.0040
Apr 20080.01360.0189-0.0008
May 20080.00200.01090.0030
Jun 20080.0039-0.0069-0.0087
Jul 20080.0119-0.00620.0015
Aug 2008-0.0134-0.0144-0.0158
Sep 20080.0125-0.00520.0067
Oct 2008-0.0092-0.0155-0.0014
Nov 2008-0.0020-0.00000.0001
Dec 20080.00200.01300.0012
Jan 20090.00900.00470.0026
Feb 2009-0.0033-0.00080.0011
Mar 2009-0.0187-0.00520.0023
Apr 20090.00010.03250.0250
May 20090.00190.00040.0025
Jun 2009-0.0017-0.00560.0064
Jul 2009-0.0135-0.0081-0.0072
Aug 2009-0.01160.0003-0.0113
Sep 2009-0.00720.0024-0.0030
Oct 20090.0060-0.00110.0049
Nov 2009-0.0031-0.0063-0.0096
Dec 20090.00110.00770.0022
Jan 2010-0.0061-0.00200.0003
Feb 2010-0.0052-0.0005-0.0048
Mar 20100.00300.0012-0.0007
Apr 2010-0.0098-0.0058-0.0028
May 20100.00990.00820.0091
Jun 20100.00540.00500.0063
Jul 2010-0.0030-0.00050.0001
Aug 20100.00380.00840.0039
Sep 20100.00210.00030.0071
Oct 2010-0.0014-0.0017-0.0018
Nov 20100.00040.00020.0064
Dec 2010-0.0014-0.0060-0.0062
Jan 2011-0.00420.0036-0.0005
Feb 20110.00600.00460.0044
Mar 20110.00290.00450.0059
Apr 20110.00590.00740.0038
May 20110.00600.00250.0047
Jun 2011-0.0033-0.00010.0046
Jul 20110.0041-0.00070.0039
Aug 20110.00310.00550.0047
Sep 2011-0.0015-0.00380.0011
Oct 20110.00870.01140.0078
Nov 20110.00210.00100.0020
Dec 20110.0010-0.0041-0.0004
Jan 20120.00540.0051-0.0000
Feb 2012-0.0038-0.0016-0.0017
Mar 2012-0.0025-0.0067-0.0028
Apr 2012-0.00140.00440.0007
May 2012-0.0011-0.00260.0003
Jun 20120.0047-0.0014-0.0054
Jul 2012-0.00010.00260.0069
Aug 20120.00420.00250.0019
Sep 2012-0.0016-0.0075-0.0038
Oct 2012-0.00110.00370.0055
Nov 2012-0.00450.00170.0013
Dec 20120.00560.0009-0.0018
Jan 20130.00170.0012-0.0003
Feb 20130.00160.00340.0007
Mar 20130.00070.00040.0011
Apr 20130.00070.0013-0.0049
May 2013-0.0073-0.00970.0016
Jun 2013-0.0049-0.00560.0014
Jul 20130.0003-0.0058-0.0033
Aug 2013-0.00010.0000-0.0009
Sep 20130.00550.00010.0014
Oct 2013-0.0071-0.0023-0.0003
Nov 2013-0.0020-0.01420.0038
Dec 2013-0.00260.0010-0.0033
Jan 20140.00390.0122-0.0085
Feb 2014-0.00030.0013-0.0036
Mar 2014-0.0053-0.00490.0039
Apr 2014-0.00140.00640.0062
May 20140.00390.00400.0012
Jun 20140.00300.0030-0.0035
Jul 2014-0.00350.0015-0.0024
Aug 20140.00440.00500.0025
Sep 2014-0.0039-0.00330.0027
Oct 20140.0094-0.00730.0018
Nov 2014-0.00040.00450.0034
Dec 20140.0052-0.0089-0.0034
Jan 20150.01130.02190.0048
Feb 2015-0.0022-0.00460.0038
Mar 20150.00580.00340.0047
Apr 2015-0.0096-0.0060-0.0085
May 20150.00500.0031-0.0002
Jun 20150.0023-0.01100.0038
Jul 20150.01710.01880.0182
Aug 2015-0.0102-0.00470.0010
Sep 20150.00390.00430.0149
Oct 2015-0.0049-0.0091-0.0037
Nov 2015-0.0015-0.0121-0.0102
Dec 20150.00120.0057-0.0003
Jan 2016-0.00250.00230.0193
Feb 2016-0.00630.00530.0058
Mar 20160.00080.0032-0.0060
Apr 2016-0.0040-0.0037-0.0145
May 20160.01100.00650.0016
Jun 2016-0.00140.0015-0.0063
Jul 2016-0.0005-0.0066-0.0105
Aug 2016-0.0027-0.0139-0.0088
Sep 2016-0.0048-0.0096-0.0118
Oct 20160.00330.00170.0132
Nov 2016-0.0005-0.02020.0019
Dec 20160.0035-0.00800.0006
Jan 2017-0.00240.0081-0.0042
Feb 20170.00390.0042-0.0032
Mar 2017-0.0044-0.0062-0.0056
Apr 2017-0.0015-0.0045-0.0040
May 2017-0.00140.0030-0.0045
Jun 20170.0055-0.0041-0.0044
Jul 20170.00210.00150.0009
Aug 20170.00440.0046-0.0050
Sep 2017-0.0062-0.0207-0.0026
Oct 20170.00080.00520.0032
Nov 20170.00350.00270.0038
Dec 2017-0.00450.0006-0.0043
Jan 2018-0.0032-0.0061-0.0066
Feb 2018-0.0015-0.0035-0.0075
Mar 20180.00320.0072-0.0014
Apr 2018-0.0038-0.0097-0.0068
May 2018-0.0031-0.0081-0.0129