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 MOM Alpha Annual Alpha R2
iShares S&P Small-Cap 600 Value ETF IJS Apr 2006 Feb 2019 0.96 0.84 0.37 -0.03 0.04% 0.47% 97.6%
iShares Russell 2000 Value ETF IWN Apr 2006 Feb 2019 0.95 0.79 0.48 0.01 -0.06% -0.71% 98.1%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Feb 2019 1.06 1.19 0.72 -0.50 0.03% 0.40% 90.7%
Vanguard Small-Cap Value ETF VBR Apr 2006 Feb 2019 1.01 0.57 0.33 -0.07 0.00% 0.04% 97.7%

iShares S&P Small-Cap 600 Value ETF

Factor regression results for iShares S&P Small-Cap 600 Value ETF
Ticker IJS
Time Period Apr 2006 - Feb 2019
Coefficient of Determination (R2) 97.6%
Adjusted R2 97.5%
Regression F statistic 1,500.44 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.017 with p-value 0.529)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 34.508 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.019 50.955 0.000 0.921...0.995
Size (SMB) 0.84 0.033 25.374 0.000 0.773...0.903
Value (HML) 0.37 0.030 12.380 0.000 0.315...0.435
Momentum (MOM) -0.03 0.018 -1.554 0.122 -0.062...0.007
Alpha (α) 3.92bps 0.001 0.545 0.587 -0.10%...0.18%
Annualized Alpha (α) 0.47%  

iShares Russell 2000 Value ETF

Factor regression results for iShares Russell 2000 Value ETF
Ticker IWN
Time Period Apr 2006 - Feb 2019
Coefficient of Determination (R2) 98.1%
Adjusted R2 98.0%
Regression F statistic 1,935.02 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.248 with p-value 0.936)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 10.265 with p-value 0.036)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.95 0.016 57.953 0.000 0.919...0.984
Size (SMB) 0.79 0.029 27.389 0.000 0.733...0.847
Value (HML) 0.48 0.026 18.213 0.000 0.429...0.534
Momentum (MOM) 0.01 0.015 0.756 0.451 -0.019...0.042
Alpha (α) -5.88bps 0.001 -0.935 0.351 -0.18%...0.07%
Annualized Alpha (α) -0.71%  

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 - Feb 2019
Coefficient of Determination (R2) 90.7%
Adjusted R2 90.4%
Regression F statistic 365.34 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.029 with p-value 0.558)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 48.293 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.055 19.066 0.000 0.947...1.165
Size (SMB) 1.19 0.097 12.266 0.000 1.001...1.386
Value (HML) 0.72 0.089 8.072 0.000 0.544...0.896
Momentum (MOM) -0.50 0.052 -9.524 0.000 -0.599...-0.393
Alpha (α) 3.36bps 0.002 0.159 0.874 -0.39%...0.45%
Annualized Alpha (α) 0.40%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Apr 2006 - Feb 2019
Coefficient of Determination (R2) 97.7%
Adjusted R2 97.7%
Regression F statistic 1,626.32 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.382 with p-value 0.991)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 10.791 with p-value 0.029)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.018 57.264 0.000 0.972...1.042
Size (SMB) 0.57 0.031 18.320 0.000 0.505...0.627
Value (HML) 0.33 0.028 11.582 0.000 0.272...0.384
Momentum (MOM) -0.07 0.017 -4.285 0.000 -0.104...-0.038
Alpha (α) 0.29bps 0.001 0.044 0.965 -0.13%...0.14%
Annualized Alpha (α) 0.04%  
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) 69.35 4.03 -15.83 -1.28  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
iShares S&P Small-Cap 600 Value ETF IJS Apr 2006 Feb 2019 0.47% 66.42 3.38 -5.93 0.04 67.82 97.6%
iShares Russell 2000 Value ETF IWN Apr 2006 Feb 2019 -0.71% 66.01 3.19 -7.63 -0.01 55.68 98.1%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Feb 2019 0.40% 73.23 4.81 -11.40 0.63 70.65 90.7%
Vanguard Small-Cap Value ETF VBR Apr 2006 Feb 2019 0.04% 69.84 2.28 -5.19 0.09 67.31 97.7%
Regression residuals
MonthIJSIWNRZVVBR
Apr 2006-0.0075-0.0086-0.0070-0.0119
May 2006-0.00110.0024-0.02560.0004
Jun 2006-0.00050.00670.01990.0097
Jul 2006-0.00530.01030.00340.0035
Aug 20060.00100.0077-0.0314-0.0053
Sep 20060.0008-0.0030-0.0008-0.0068
Oct 20060.00540.0046-0.0013-0.0001
Nov 2006-0.0049-0.0010-0.01100.0057
Dec 2006-0.0120-0.00750.0015-0.0121
Jan 20070.0028-0.00270.00780.0011
Feb 2007-0.0057-0.0072-0.00640.0018
Mar 2007-0.00010.0044-0.0077-0.0020
Apr 20070.0017-0.00840.0096-0.0070
May 20070.01070.0055-0.00780.0014
Jun 2007-0.0101-0.0093-0.0096-0.0075
Jul 20070.0031-0.01800.0215-0.0163
Aug 20070.00940.0182-0.01810.0113
Sep 2007-0.0038-0.00180.0025-0.0046
Oct 2007-0.00100.00110.00380.0054
Nov 2007-0.0023-0.0042-0.0009-0.0040
Dec 20070.0002-0.00690.0329-0.0018
Jan 20080.01000.01090.05300.0106
Feb 20080.00140.0027-0.01930.0123
Mar 20080.00890.00140.04350.0019
Apr 2008-0.00250.0121-0.04930.0110
May 2008-0.0018-0.0070-0.01630.0094
Jun 2008-0.0035-0.01390.0306-0.0207
Jul 2008-0.00970.0060-0.03360.0101
Aug 2008-0.00590.0014-0.0524-0.0092
Sep 20080.02430.03340.03860.0242
Oct 2008-0.0022-0.01440.0264-0.0186
Nov 20080.00590.01380.02510.0247
Dec 20080.01810.0105-0.05500.0039
Jan 2009-0.0209-0.0063-0.0658-0.0070
Feb 2009-0.0070-0.0092-0.0234-0.0127
Mar 2009-0.0261-0.01260.0250-0.0213
Apr 20090.0204-0.00340.13920.0233
May 2009-0.0267-0.0044-0.0264-0.0092
Jun 20090.0004-0.01330.0889-0.0075
Jul 2009-0.0030-0.00140.0243-0.0042
Aug 2009-0.0215-0.0097-0.05050.0016
Sep 2009-0.0228-0.0148-0.0108-0.0075
Oct 20090.01550.0154-0.05340.0047
Nov 2009-0.0030-0.0056-0.0147-0.0057
Dec 20090.00370.0022-0.01750.0088
Jan 20100.00060.00100.0098-0.0031
Feb 2010-0.0064-0.01170.02810.0012
Mar 2010-0.00180.00360.01260.0059
Apr 2010-0.0047-0.0037-0.01240.0069
May 2010-0.00190.0043-0.01020.0072
Jun 20100.00260.0027-0.0330-0.0019
Jul 20100.00030.00510.00880.0059
Aug 2010-0.00150.0040-0.00820.0045
Sep 2010-0.00330.0006-0.0020-0.0029
Oct 20100.00330.00540.02430.0000
Nov 2010-0.0085-0.00440.01060.0004
Dec 20100.0029-0.0046-0.0197-0.0106
Jan 2011-0.0045-0.0042-0.0248-0.0032
Feb 2011-0.00800.0008-0.00390.0010
Mar 20110.0023-0.00360.00710.0030
Apr 2011-0.00510.0040-0.00450.0045
May 20110.00770.01130.02950.0020
Jun 20110.0036-0.00500.00360.0001
Jul 20110.01000.00750.02740.0019
Aug 20110.01180.00240.01240.0034
Sep 20110.0006-0.00070.0072-0.0073
Oct 20110.01600.01130.00150.0102
Nov 20110.01240.00380.01490.0063
Dec 20110.01260.00450.01230.0003
Jan 20120.01420.0090-0.01190.0047
Feb 2012-0.0113-0.0135-0.0091-0.0096
Mar 20120.00090.0023-0.0075-0.0056
Apr 2012-0.0043-0.00070.00510.0057
May 2012-0.00900.00070.00260.0057
Jun 2012-0.00070.00540.0028-0.0011
Jul 20120.00870.00190.01640.0055
Aug 20120.00670.00140.0188-0.0044
Sep 2012-0.0056-0.00360.0022-0.0083
Oct 2012-0.0079-0.0072-0.03980.0047
Nov 20120.0074-0.00170.04510.0022
Dec 2012-0.00280.0030-0.0338-0.0007
Jan 2013-0.0076-0.0003-0.02100.0018
Feb 20130.00760.00160.01100.0065
Mar 2013-0.0028-0.0018-0.01410.0029
Apr 20130.00400.0023-0.0048-0.0030
May 2013-0.0086-0.02200.0171-0.0163
Jun 20130.0003-0.0017-0.0076-0.0066
Jul 2013-0.0061-0.0054-0.01520.0004
Aug 2013-0.0007-0.00710.0050-0.0070
Sep 20130.01020.00470.02560.0044
Oct 20130.0027-0.0009-0.00210.0019
Nov 20130.0011-0.00240.0226-0.0096
Dec 2013-0.0090-0.0004-0.00540.0030
Jan 2014-0.0026-0.0035-0.00010.0088
Feb 20140.00080.00110.01040.0038
Mar 20140.0048-0.0006-0.02200.0005
Apr 20140.00880.00570.00020.0081
May 20140.00290.00270.00830.0078
Jun 2014-0.0097-0.0006-0.01600.0024
Jul 20140.0039-0.00800.0166-0.0036
Aug 20140.00300.00350.00340.0089
Sep 2014-0.0041-0.01100.0094-0.0095
Oct 20140.01760.02100.00250.0047
Nov 20140.00900.00330.02300.0077
Dec 2014-0.0029-0.0025-0.0218-0.0019
Jan 2015-0.00500.0083-0.00050.0156
Feb 20150.0014-0.00620.0209-0.0040
Mar 2015-0.00210.00660.00170.0108
Apr 2015-0.0084-0.0112-0.0087-0.0135
May 2015-0.0064-0.00580.00700.0038
Jun 2015-0.0015-0.00170.0028-0.0110
Jul 20150.01080.00890.04600.0192
Aug 2015-0.0033-0.0073-0.0065-0.0006
Sep 20150.01300.01280.01820.0122
Oct 20150.0068-0.00160.0001-0.0032
Nov 2015-0.0090-0.0016-0.0126-0.0098
Dec 20150.00370.00120.0225-0.0004
Jan 20160.01690.0062-0.00710.0074
Feb 20160.01500.00370.01920.0098
Mar 20160.01400.00520.00200.0068
Apr 2016-0.0077-0.0073-0.0258-0.0073
May 2016-0.00360.0120-0.04940.0048
Jun 20160.00950.00670.02460.0059
Jul 2016-0.00680.0011-0.0127-0.0071
Aug 2016-0.0169-0.0048-0.0483-0.0176
Sep 2016-0.0057-0.00330.0059-0.0066
Oct 20160.00240.00270.00840.0024
Nov 20160.00790.0028-0.0223-0.0084
Dec 20160.00010.0076-0.0222-0.0022
Jan 2017-0.0129-0.0054-0.02440.0006
Feb 20170.00150.0049-0.0118-0.0003
Mar 2017-0.0072-0.0038-0.0257-0.0062
Apr 2017-0.0052-0.0034-0.0135-0.0052
May 20170.0021-0.0026-0.0056-0.0075
Jun 2017-0.00200.0030-0.0077-0.0009
Jul 20170.00170.0017-0.01630.0006
Aug 2017-0.0065-0.00260.02970.0023
Sep 20170.0109-0.00290.0007-0.0131
Oct 20170.0008-0.00610.0296-0.0008
Nov 20170.01200.00460.01550.0028
Dec 2017-0.0055-0.0105-0.0168-0.0010
Jan 2018-0.0100-0.01130.0029-0.0136
Feb 2018-0.0037-0.01260.0155-0.0066
Mar 20180.00170.0026-0.01480.0078
Apr 20180.00190.0036-0.0016-0.0081
May 20180.00050.00570.01790.0004
Jun 20180.00010.0014-0.0011-0.0032
Jul 20180.00980.0021-0.01430.0010
Aug 20180.0027-0.00070.0318-0.0021
Sep 2018-0.0083-0.00110.0000-0.0012
Oct 2018-0.00210.00350.0081-0.0010
Nov 2018-0.00730.0038-0.04900.0074
Dec 2018-0.0069-0.00430.00610.0009
Jan 20190.01410.0076-0.00180.0035
Feb 20190.00050.0029-0.00470.0024