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

Factor Analysis Summary

Factor regression results
Name Ticker Start Date End Date Rm-Rf SMB HML MOM Alpha Annual Alpha R2
iShares S&P Small-Cap 600 Value ETF IJS Aug 2000 Apr 2018 0.95 0.81 0.50 0.01 0.05% 0.64% 95.6%
iShares Russell 2000 Value ETF IWN Aug 2000 Apr 2018 0.92 0.77 0.60 0.03 -0.03% -0.35% 96.7%
Invesco S&P Smallcap 600 Pure Value ETF RZV Apr 2006 Apr 2018 1.06 1.17 0.73 -0.50 0.04% 0.44% 90.5%
Vanguard Small-Cap Value ETF VBR Feb 2004 Apr 2018 1.01 0.58 0.35 -0.06 0.04% 0.44% 97.2%

iShares S&P Small-Cap 600 Value ETF

Factor regression results for iShares S&P Small-Cap 600 Value ETF
Ticker IJS
Time Period Aug 2000 - Apr 2018
Coefficient of Determination (R2) 95.6%
Adjusted R2 95.5%
Regression F statistic 1,117.73 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.713 with p-value 0.017)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 16.711 with p-value 0.002)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.95 0.021 45.355 0.000 0.912...0.995
Size (SMB) 0.81 0.033 24.610 0.000 0.745...0.874
Value (HML) 0.50 0.027 18.219 0.000 0.443...0.551
Momentum (MOM) 0.01 0.017 0.305 0.761 -0.029...0.039
Alpha (α) 5.30bps 0.001 0.659 0.510 -0.11%...0.21%
Annualized Alpha (α) 0.64%  

iShares Russell 2000 Value ETF

Factor regression results for iShares Russell 2000 Value ETF
Ticker IWN
Time Period Aug 2000 - Apr 2018
Coefficient of Determination (R2) 96.7%
Adjusted R2 96.6%
Regression F statistic 1,528.41 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.131 with p-value 0.829)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 26.533 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.92 0.017 52.826 0.000 0.888...0.957
Size (SMB) 0.77 0.027 28.083 0.000 0.713...0.821
Value (HML) 0.60 0.023 26.560 0.000 0.557...0.647
Momentum (MOM) 0.03 0.014 2.427 0.016 0.006...0.063
Alpha (α) -2.93bps 0.001 -0.440 0.661 -0.16%...0.10%
Annualized Alpha (α) -0.35%  

Invesco S&P Smallcap 600 Pure Value ETF

Factor regression results for Invesco S&P Smallcap 600 Pure Value ETF
Ticker RZV
Time Period Apr 2006 - Apr 2018
Coefficient of Determination (R2) 90.5%
Adjusted R2 90.2%
Regression F statistic 333.20 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.020 with p-value 0.534)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 46.758 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.058 18.129 0.000 0.944...1.175
Size (SMB) 1.17 0.103 11.348 0.000 0.965...1.372
Value (HML) 0.73 0.094 7.828 0.000 0.549...0.920
Momentum (MOM) -0.50 0.054 -9.367 0.000 -0.609...-0.397
Alpha (α) 3.68bps 0.002 0.166 0.868 -0.40%...0.48%
Annualized Alpha (α) 0.44%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Feb 2004 - Apr 2018
Coefficient of Determination (R2) 97.2%
Adjusted R2 97.1%
Regression F statistic 1,416.61 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.244 with p-value 0.942)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 13.345 with p-value 0.010)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.019 52.813 0.000 0.971...1.046
Size (SMB) 0.58 0.032 18.295 0.000 0.518...0.643
Value (HML) 0.35 0.030 11.698 0.000 0.290...0.408
Momentum (MOM) -0.06 0.017 -3.403 0.001 -0.092...-0.024
Alpha (α) 3.64bps 0.001 0.534 0.594 -0.10%...0.17%
Annualized Alpha (α) 0.44%  
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.
  • 4-factor model: Ra = Rrf + Bmkt × ( Rmkt - Rrf ) + Bsmb × SMB + Bhml × HML + Bmom × UMD + 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
    Bmom
    Momentum loading factor (the level of exposure to momentum)
    MOM
    Up Minus Down: The momentum 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) 46.57 25.92 29.47 15.06  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
iShares S&P Small-Cap 600 Value ETF IJS Aug 2000 Apr 2018 0.64% 44.41 20.98 14.66 0.08 85.43 95.6%
Factor regression results
Monthly Factor Premiums (BPS) 46.57 25.92 29.47 15.06  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
iShares Russell 2000 Value ETF IWN Aug 2000 Apr 2018 -0.35% 42.96 19.89 17.74 0.52 78.17 96.7%
Factor regression results
Monthly Factor Premiums (BPS) 69.94 4.28 -8.70 1.50  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
Invesco S&P Smallcap 600 Pure Value ETF RZV Apr 2006 Apr 2018 0.44% 74.11 5.00 -6.39 -0.75 75.65 90.5%
Factor regression results
Monthly Factor Premiums (BPS) 68.54 9.23 0.92 9.37  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
Vanguard Small-Cap Value ETF VBR Feb 2004 Apr 2018 0.44% 69.12 5.36 0.32 -0.55 77.90 97.2%
Regression residuals
MonthIJSIWNRZVVBR
Aug 20000.0134-0.0049
Sep 20000.02460.0157
Oct 20000.01460.0093
Nov 20000.02210.0384
Dec 20000.06710.0255
Jan 20010.0153-0.0172
Feb 2001-0.00940.0119
Mar 2001-0.0202-0.0001
Apr 20010.00760.0024
May 2001-0.0182-0.0231
Jun 2001-0.00850.0099
Jul 20010.0217-0.0094
Aug 20010.01540.0236
Sep 2001-0.01950.0004
Oct 2001-0.0022-0.0058
Nov 2001-0.0047-0.0062
Dec 20010.0085-0.0030
Jan 20020.0070-0.0006
Feb 20020.01190.0146
Mar 20020.0052-0.0067
Apr 20020.01980.0148
May 2002-0.0077-0.0066
Jun 2002-0.0148-0.0007
Jul 2002-0.0221-0.0085
Aug 2002-0.0037-0.0018
Sep 2002-0.0101-0.0156
Oct 20020.00000.0037
Nov 2002-0.02000.0116
Dec 20020.0142-0.0091
Jan 2003-0.0242-0.0076
Feb 2003-0.0141-0.0028
Mar 2003-0.01030.0034
Apr 2003-0.00100.0090
May 2003-0.00090.0146
Jun 2003-0.0033-0.0196
Jul 2003-0.0125-0.0044
Aug 2003-0.0061-0.0155
Sep 2003-0.0308-0.0065
Oct 2003-0.0009-0.0076
Nov 20030.00160.0002
Dec 2003-0.00190.0051
Jan 2004-0.0322-0.0198
Feb 20040.01970.01740.0193
Mar 20040.01400.00880.0171
Apr 20040.0072-0.0043-0.0210
May 20040.00660.00900.0111
Jun 20040.00970.00680.0116
Jul 20040.0001-0.00570.0108
Aug 20040.00800.01740.0150
Sep 20040.0063-0.00170.0036
Oct 2004-0.00520.0024-0.0014
Nov 20040.00510.00770.0079
Dec 2004-0.0197-0.0137-0.0101
Jan 2005-0.0059-0.0160-0.0068
Feb 20050.0045-0.00520.0020
Mar 2005-0.0039-0.0039-0.0012
Apr 20050.00520.0033-0.0025
May 20050.00460.00710.0196
Jun 2005-0.00340.00150.0041
Jul 2005-0.00310.0027-0.0030
Aug 2005-0.0096-0.0163-0.0090
Sep 2005-0.0069-0.01410.0022
Oct 2005-0.0094-0.0085-0.0094
Nov 20050.00950.0141-0.0031
Dec 2005-0.0104-0.0102-0.0019
Jan 20060.0049-0.00280.0002
Feb 20060.00610.00880.0064
Mar 2006-0.00140.0031-0.0044
Apr 2006-0.0114-0.0122-0.0077-0.0127
May 2006-0.0042-0.0019-0.02690.0005
Jun 2006-0.00230.00480.01970.0090
Jul 2006-0.00950.00580.00180.0035
Aug 20060.00440.0111-0.0313-0.0050
Sep 20060.0006-0.0030-0.0013-0.0069
Oct 20060.00600.0058-0.0010-0.0007
Nov 2006-0.0045-0.0005-0.01100.0053
Dec 2006-0.0165-0.01180.0008-0.0131
Jan 20070.0028-0.00250.00780.0007
Feb 2007-0.0050-0.0073-0.00610.0015
Mar 2007-0.00080.0040-0.0076-0.0026
Apr 20070.0026-0.00670.0090-0.0068
May 20070.01080.0063-0.00800.0011
Jun 2007-0.0089-0.0087-0.0092-0.0078
Jul 20070.0052-0.01660.0217-0.0159
Aug 20070.01200.0208-0.01790.0114
Sep 2007-0.0037-0.00050.0023-0.0049
Oct 20070.00050.00340.00450.0049
Nov 2007-0.0022-0.0053-0.0011-0.0038
Dec 2007-0.0014-0.00830.0335-0.0029
Jan 20080.00750.00600.05190.0107
Feb 20080.00030.0011-0.01870.0115
Mar 20080.00780.00030.04410.0009
Apr 2008-0.00170.0140-0.04980.0110
May 2008-0.0002-0.0050-0.01500.0085
Jun 2008-0.0047-0.01630.0325-0.0222
Jul 2008-0.01460.0002-0.03420.0089
Aug 2008-0.00560.0014-0.0522-0.0099
Sep 20080.01560.02240.03790.0228
Oct 2008-0.0028-0.01870.0273-0.0188
Nov 20080.00950.01600.02600.0252
Dec 20080.02100.0130-0.05440.0037
Jan 2009-0.00720.0049-0.0643-0.0047
Feb 2009-0.0001-0.0047-0.0220-0.0120
Mar 2009-0.0265-0.01180.0225-0.0211
Apr 20090.02660.00170.13670.0253
May 2009-0.0230-0.0006-0.0281-0.0076
Jun 20090.0026-0.01080.0903-0.0084
Jul 2009-0.0070-0.00410.0232-0.0054
Aug 2009-0.0284-0.0166-0.05260.0008
Sep 2009-0.0216-0.0133-0.0108-0.0078
Oct 20090.01820.0177-0.05390.0055
Nov 2009-0.0036-0.0047-0.0156-0.0057
Dec 20090.00450.0034-0.01580.0072
Jan 20100.00180.00060.0095-0.0028
Feb 2010-0.0109-0.01520.0284-0.0004
Mar 2010-0.00490.00220.01270.0044
Apr 2010-0.0079-0.0063-0.01160.0048
May 20100.00060.0046-0.00960.0075
Jun 20100.00810.0063-0.0330-0.0006
Jul 20100.00040.00690.00900.0053
Aug 2010-0.00030.0040-0.00860.0051
Sep 20100.00140.0075-0.0008-0.0034
Oct 20100.00620.00920.0248-0.0003
Nov 2010-0.0072-0.00310.0119-0.0006
Dec 2010-0.0004-0.0066-0.0206-0.0116
Jan 2011-0.0060-0.0052-0.0254-0.0032
Feb 2011-0.00960.0001-0.0039-0.0001
Mar 20110.0036-0.00220.00820.0021
Apr 2011-0.00230.0073-0.00470.0045
May 20110.00990.01300.02920.0021
Jun 20110.0031-0.00590.0034-0.0004
Jul 20110.01100.00780.02750.0021
Aug 20110.01360.00270.01200.0041
Sep 20110.0017-0.00180.0064-0.0065
Oct 20110.01800.01560.00170.0094
Nov 20110.01130.00290.01530.0056
Dec 20110.00960.00180.0119-0.0005
Jan 20120.01870.0137-0.01190.0051
Feb 2012-0.0118-0.0129-0.0098-0.0098
Mar 2012-0.00070.0015-0.0077-0.0062
Apr 2012-0.0052-0.00160.00550.0051
May 2012-0.0108-0.00220.00350.0047
Jun 2012-0.00060.00610.0026-0.0015
Jul 20120.00700.00070.01600.0051
Aug 20120.00630.00120.0188-0.0046
Sep 2012-0.0069-0.00440.0022-0.0088
Oct 2012-0.0131-0.0128-0.04070.0038
Nov 20120.0084-0.00070.04520.0019
Dec 2012-0.0058-0.0001-0.0340-0.0016
Jan 2013-0.00780.0006-0.02110.0015
Feb 20130.00700.00140.01110.0062
Mar 2013-0.0031-0.0011-0.01420.0020
Apr 20130.00270.0014-0.0051-0.0029
May 2013-0.0105-0.02350.0172-0.0171
Jun 20130.0005-0.0019-0.0071-0.0071
Jul 2013-0.0067-0.0046-0.0150-0.0006
Aug 20130.0026-0.00480.0055-0.0068
Sep 20130.01140.00670.02650.0034
Oct 20130.0008-0.0017-0.00290.0014
Nov 20130.0010-0.00180.0228-0.0103
Dec 2013-0.00890.0003-0.00570.0027
Jan 2014-0.0008-0.00260.00030.0085
Feb 20140.00060.00210.01020.0030
Mar 2014-0.0011-0.0066-0.0237-0.0003
Apr 20140.00730.0038-0.00150.0087
May 20140.00210.00240.00750.0074
Jun 2014-0.00810.0014-0.01490.0017
Jul 20140.0024-0.00990.0155-0.0033
Aug 20140.00350.00490.00320.0084
Sep 2014-0.0042-0.01150.0084-0.0092
Oct 20140.02090.02450.00390.0041
Nov 20140.01140.00640.02240.0079
Dec 2014-0.0053-0.0050-0.0214-0.0032
Jan 2015-0.00240.01030.00030.0157
Feb 20150.0042-0.00220.0200-0.0041
Mar 2015-0.00220.00620.00230.0095
Apr 2015-0.0092-0.0125-0.0102-0.0128
May 2015-0.0073-0.00600.00650.0023
Jun 2015-0.0006-0.00130.0046-0.0117
Jul 20150.01140.01090.04650.0192
Aug 2015-0.0063-0.0121-0.0070-0.0013
Sep 20150.00960.00910.01780.0114
Oct 20150.00790.0011-0.0007-0.0027
Nov 2015-0.0082-0.0008-0.0117-0.0109
Dec 20150.00460.00180.0222-0.0003
Jan 20160.01280.0008-0.00740.0072
Feb 20160.01700.00510.01920.0099
Mar 20160.01440.00670.00090.0065
Apr 2016-0.0094-0.0095-0.0264-0.0076
May 2016-0.00220.0138-0.04940.0045
Jun 20160.01000.00740.02530.0053
Jul 2016-0.00340.0049-0.0119-0.0071
Aug 2016-0.0201-0.0083-0.0493-0.0186
Sep 2016-0.0033-0.00120.0065-0.0069
Oct 2016-0.0043-0.00430.00680.0018
Nov 20160.0012-0.0034-0.0219-0.0105
Dec 2016-0.00470.0031-0.0236-0.0036
Jan 2017-0.0096-0.0020-0.02420.0011
Feb 20170.00360.0077-0.01240.0002
Mar 2017-0.00290.0003-0.0256-0.0060
Apr 2017-0.0027-0.0008-0.0128-0.0051
May 20170.00530.0009-0.0060-0.0070
Jun 2017-0.00290.0021-0.0070-0.0016
Jul 20170.00120.0018-0.01640.0004
Aug 2017-0.0053-0.00110.03040.0024
Sep 20170.0088-0.00480.0013-0.0146
Oct 2017-0.0010-0.00690.0295-0.0013
Nov 20170.01160.00470.01420.0022
Dec 2017-0.0054-0.0103-0.0168-0.0008
Jan 2018-0.0100-0.00950.0033-0.0134
Feb 2018-0.0038-0.01330.0162-0.0071
Mar 20180.00290.0026-0.01410.0069
Apr 20180.00160.0032-0.0013-0.0086