Fama-French Factor Regression Analysis

This factor regression tool supports factor regression analysis of individual assets or a portfolio of assets using the given risk factor model. The multiple linear regression indicates how well the returns of the given assets or a portfolio are explained by the risk factor exposures. The supported equity risk factor models include:

Additional supported equity factors include the short and long-term reversal factors (STREV, LTREV) based on Fama-French factor data, quality (QMJ) factor based on both AQR and Alpha Architect factor data, and bet against beta (BAB) factor based on AQR factor data.

For fixed income 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 exposures. 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.

Portfolio Assets
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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 Mar 2019 0.96 0.82 0.49 0.01 0.06% 0.67% 95.8%
iShares Russell 2000 Value ETF IWN Aug 2000 Mar 2019 0.93 0.77 0.60 0.04 -0.01% -0.13% 96.9%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Mar 2019 1.06 1.19 0.72 -0.50 0.04% 0.47% 90.7%
Vanguard Small-Cap Value ETF VBR Feb 2004 Mar 2019 1.01 0.58 0.35 -0.06 0.04% 0.49% 97.4%

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 - Mar 2019
Coefficient of Determination (R2) 95.8%
Adjusted R2 95.7%
Regression F statistic 1,240.31 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.695 with p-value 0.011)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 18.180 with p-value 0.001)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.020 47.488 0.000 0.921...1.000
Size (SMB) 0.82 0.032 25.865 0.000 0.757...0.882
Value (HML) 0.49 0.026 18.732 0.000 0.443...0.547
Momentum (MOM) 0.01 0.017 0.379 0.705 -0.026...0.039
Alpha (α) 5.55bps 0.001 0.720 0.472 -0.10%...0.21%
Annualized Alpha (α) 0.67%  

iShares Russell 2000 Value ETF

Factor regression results for iShares Russell 2000 Value ETF
Ticker IWN
Time Period Aug 2000 - Mar 2019
Coefficient of Determination (R2) 96.9%
Adjusted R2 96.8%
Regression F statistic 1,688.13 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.096 with p-value 0.762)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 28.979 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.93 0.017 55.377 0.000 0.896...0.962
Size (SMB) 0.77 0.026 29.437 0.000 0.721...0.825
Value (HML) 0.60 0.022 27.179 0.000 0.552...0.638
Momentum (MOM) 0.04 0.014 2.629 0.009 0.009...0.063
Alpha (α) -1.08bps 0.001 -0.169 0.866 -0.14%...0.12%
Annualized Alpha (α) -0.13%  

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 - Mar 2019
Coefficient of Determination (R2) 90.7%
Adjusted R2 90.5%
Regression F statistic 368.78 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.028 with p-value 0.555)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 48.849 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.055 19.201 0.000 0.949...1.167
Size (SMB) 1.19 0.096 12.338 0.000 0.999...1.380
Value (HML) 0.72 0.088 8.099 0.000 0.541...0.890
Momentum (MOM) -0.50 0.052 -9.551 0.000 -0.599...-0.393
Alpha (α) 3.88bps 0.002 0.184 0.854 -0.38%...0.46%
Annualized Alpha (α) 0.47%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Feb 2004 - Mar 2019
Coefficient of Determination (R2) 97.4%
Adjusted R2 97.3%
Regression F statistic 1,631.53 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.244 with p-value 0.948)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 12.611 with p-value 0.013)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.018 56.484 0.000 0.974...1.045
Size (SMB) 0.58 0.030 19.524 0.000 0.521...0.638
Value (HML) 0.35 0.028 12.450 0.000 0.292...0.402
Momentum (MOM) -0.06 0.016 -3.652 0.000 -0.092...-0.027
Alpha (α) 4.09bps 0.001 0.636 0.526 -0.09%...0.17%
Annualized Alpha (α) 0.49%  
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 × MOM + 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) 47.49 23.13 20.69 13.44  
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 Mar 2019 0.67% 45.61 18.95 10.23 0.08 80.43 95.8%
Factor regression results
Monthly Factor Premiums (BPS) 47.49 23.13 20.69 13.44  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
iShares Russell 2000 Value ETF IWN Aug 2000 Mar 2019 -0.13% 44.11 17.88 12.31 0.49 73.71 96.9%
Factor regression results
Monthly Factor Premiums (BPS) 69.62 1.97 -18.36 0.20  
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 Mar 2019 0.47% 73.63 2.35 -13.14 -0.10 66.63 90.7%
Factor regression results
Monthly Factor Premiums (BPS) 68.35 6.98 -7.93 7.76  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
Vanguard Small-Cap Value ETF VBR Feb 2004 Mar 2019 0.49% 69.00 4.04 -2.75 -0.46 73.92 97.4%
Regression residuals
MonthIJSIWNRZVVBR
Aug 20000.0130-0.0055
Sep 20000.02520.0164
Oct 20000.01530.0099
Nov 20000.02340.0398
Dec 20000.06700.0255
Jan 20010.0146-0.0180
Feb 2001-0.00850.0130
Mar 2001-0.01970.0005
Apr 20010.00690.0015
May 2001-0.0185-0.0233
Jun 2001-0.00900.0094
Jul 20010.0223-0.0089
Aug 20010.01570.0238
Sep 2001-0.01830.0012
Oct 2001-0.0033-0.0070
Nov 2001-0.0051-0.0066
Dec 20010.0079-0.0035
Jan 20020.0069-0.0007
Feb 20020.01210.0147
Mar 20020.0046-0.0073
Apr 20020.01960.0147
May 2002-0.0073-0.0064
Jun 2002-0.0147-0.0007
Jul 2002-0.0212-0.0081
Aug 2002-0.0034-0.0017
Sep 2002-0.0097-0.0154
Oct 2002-0.00030.0029
Nov 2002-0.02050.0112
Dec 20020.0145-0.0089
Jan 2003-0.0243-0.0078
Feb 2003-0.0140-0.0029
Mar 2003-0.01060.0030
Apr 2003-0.00150.0085
May 2003-0.00170.0140
Jun 2003-0.0035-0.0199
Jul 2003-0.0120-0.0039
Aug 2003-0.0054-0.0148
Sep 2003-0.0311-0.0069
Oct 20030.0003-0.0063
Nov 20030.00300.0016
Dec 2003-0.00240.0045
Jan 2004-0.0331-0.0206
Feb 20040.01980.01730.0192
Mar 20040.01410.00880.0173
Apr 20040.0070-0.0049-0.0215
May 20040.00690.00910.0113
Jun 20040.00890.00590.0113
Jul 20040.0009-0.00500.0109
Aug 20040.00830.01750.0150
Sep 20040.0060-0.00220.0037
Oct 2004-0.00530.0022-0.0014
Nov 20040.00440.00710.0080
Dec 2004-0.0199-0.0140-0.0102
Jan 2005-0.0057-0.0160-0.0068
Feb 20050.0046-0.00520.0021
Mar 2005-0.0038-0.0040-0.0013
Apr 20050.00560.0033-0.0027
May 20050.00390.00630.0195
Jun 2005-0.00370.00120.0041
Jul 2005-0.00370.0020-0.0030
Aug 2005-0.0094-0.0163-0.0089
Sep 2005-0.0070-0.01430.0022
Oct 2005-0.0091-0.0084-0.0095
Nov 20050.00910.0136-0.0032
Dec 2005-0.0104-0.0103-0.0019
Jan 20060.0041-0.00350.0003
Feb 20060.00610.00870.0063
Mar 2006-0.00190.0026-0.0044
Apr 2006-0.0113-0.0122-0.0070-0.0127
May 2006-0.0036-0.0014-0.02560.0004
Jun 2006-0.00230.00470.01980.0090
Jul 2006-0.00900.00620.00330.0034
Aug 20060.00410.0107-0.0315-0.0051
Sep 20060.0006-0.0032-0.0009-0.0070
Oct 20060.00560.0053-0.0014-0.0007
Nov 2006-0.0047-0.0008-0.01100.0052
Dec 2006-0.0164-0.01180.0015-0.0131
Jan 20070.0027-0.00270.00770.0007
Feb 2007-0.0050-0.0075-0.00640.0015
Mar 2007-0.00090.0037-0.0078-0.0026
Apr 20070.0025-0.00710.0093-0.0070
May 20070.01060.0059-0.00790.0010
Jun 2007-0.0089-0.0089-0.0097-0.0078
Jul 20070.0056-0.01670.0212-0.0159
Aug 20070.01180.0204-0.01830.0113
Sep 2007-0.0038-0.00100.0022-0.0049
Oct 20070.00030.00280.00360.0048
Nov 2007-0.0017-0.0051-0.0010-0.0038
Dec 2007-0.0015-0.00860.0329-0.0028
Jan 20080.00820.00660.05320.0107
Feb 20080.00040.0010-0.01940.0115
Mar 20080.00770.00000.04350.0010
Apr 2008-0.00190.0136-0.04960.0109
May 2008-0.0008-0.0057-0.01630.0085
Jun 2008-0.0045-0.01650.0307-0.0220
Jul 2008-0.01460.0004-0.03330.0089
Aug 2008-0.00600.0011-0.0523-0.0099
Sep 20080.01640.02330.03890.0229
Oct 2008-0.0015-0.01780.0264-0.0186
Nov 20080.01010.01600.02480.0252
Dec 20080.02060.0125-0.05490.0036
Jan 2009-0.00690.0044-0.0662-0.0049
Feb 20090.0004-0.0047-0.0236-0.0120
Mar 2009-0.0269-0.01220.0250-0.0212
Apr 20090.02600.00160.13940.0248
May 2009-0.0230-0.0008-0.0267-0.0080
Jun 20090.0021-0.01150.0888-0.0083
Jul 2009-0.0075-0.00440.0244-0.0054
Aug 2009-0.0283-0.0162-0.05030.0007
Sep 2009-0.0221-0.0138-0.0107-0.0079
Oct 20090.01870.0177-0.05380.0055
Nov 2009-0.0037-0.0051-0.0150-0.0058
Dec 20090.00360.0026-0.01730.0072
Jan 20100.00210.00070.0098-0.0029
Feb 2010-0.0114-0.01560.0281-0.0004
Mar 2010-0.00560.00160.01260.0044
Apr 2010-0.0085-0.0068-0.01220.0049
May 20100.00110.0047-0.01020.0075
Jun 20100.00870.0064-0.0332-0.0007
Jul 2010-0.00030.00610.00860.0052
Aug 20100.00030.0042-0.00840.0051
Sep 20100.00030.0062-0.0021-0.0036
Oct 20100.00580.00850.0242-0.0003
Nov 2010-0.0078-0.00370.0107-0.0006
Dec 2010-0.0008-0.0069-0.0196-0.0116
Jan 2011-0.0061-0.0055-0.0249-0.0034
Feb 2011-0.0100-0.0003-0.0039-0.0001
Mar 20110.0033-0.00260.00710.0022
Apr 2011-0.00240.0070-0.00480.0045
May 20110.01010.01290.02940.0022
Jun 20110.0032-0.00600.0035-0.0004
Jul 20110.01110.00770.02730.0020
Aug 20110.01430.00290.01220.0041
Sep 20110.0026-0.00130.0071-0.0065
Oct 20110.01680.01450.00140.0093
Nov 20110.01130.00260.01490.0056
Dec 20110.00950.00170.0122-0.0005
Jan 20120.01830.0133-0.01200.0050
Feb 2012-0.0120-0.0133-0.0093-0.0099
Mar 2012-0.00100.0011-0.0076-0.0063
Apr 2012-0.0053-0.00190.00500.0051
May 2012-0.0105-0.00220.00260.0048
Jun 2012-0.00100.00570.0027-0.0016
Jul 20120.00730.00070.01620.0051
Aug 20120.00580.00070.0187-0.0049
Sep 2012-0.0072-0.00480.0022-0.0089
Oct 2012-0.0128-0.0126-0.03970.0038
Nov 20120.0084-0.00090.04500.0019
Dec 2012-0.0059-0.0003-0.0337-0.0016
Jan 2013-0.0083-0.0000-0.02110.0012
Feb 20130.00680.00100.01090.0060
Mar 2013-0.0033-0.0014-0.01420.0021
Apr 20130.00250.0009-0.0049-0.0032
May 2013-0.0110-0.02400.0172-0.0173
Jun 20130.0004-0.0022-0.0076-0.0071
Jul 2013-0.0073-0.0053-0.0152-0.0007
Aug 20130.0026-0.00500.0049-0.0068
Sep 20130.01090.00620.02560.0034
Oct 20130.0007-0.0020-0.00220.0014
Nov 20130.0007-0.00230.0226-0.0104
Dec 2013-0.0090-0.0000-0.00560.0027
Jan 2014-0.0006-0.0027-0.00020.0086
Feb 20140.00030.00170.01020.0031
Mar 2014-0.0007-0.0063-0.0220-0.0003
Apr 20140.00780.0041-0.00000.0086
May 20140.00230.00240.00810.0075
Jun 2014-0.00870.0007-0.01590.0016
Jul 20140.0031-0.00970.0164-0.0033
Aug 20140.00320.00450.00330.0084
Sep 2014-0.0036-0.01130.0092-0.0091
Oct 20140.02020.02370.00250.0040
Nov 20140.01160.00620.02270.0080
Dec 2014-0.0054-0.0052-0.0217-0.0031
Jan 2015-0.00230.0100-0.00070.0156
Feb 20150.0042-0.00240.0207-0.0040
Mar 2015-0.00220.00620.00180.0098
Apr 2015-0.0089-0.0123-0.0088-0.0130
May 2015-0.0068-0.00570.00690.0029
Jun 2015-0.0011-0.00190.0029-0.0119
Jul 20150.01130.01020.04550.0190
Aug 2015-0.0058-0.0116-0.0064-0.0012
Sep 20150.01000.00920.01810.0115
Oct 20150.00750.0004-0.0002-0.0030
Nov 2015-0.0086-0.0013-0.0126-0.0108
Dec 20150.00500.00180.0223-0.0002
Jan 20160.01330.0011-0.00720.0071
Feb 20160.01700.00490.01920.0098
Mar 20160.01420.00640.00190.0065
Apr 2016-0.0095-0.0096-0.0257-0.0078
May 2016-0.00240.0134-0.04960.0045
Jun 20160.00980.00700.02450.0053
Jul 2016-0.00420.0040-0.0127-0.0074
Aug 2016-0.0198-0.0080-0.0482-0.0184
Sep 2016-0.0035-0.00160.0059-0.0069
Oct 2016-0.0037-0.00390.00830.0018
Nov 20160.0001-0.0041-0.0218-0.0108
Dec 2016-0.00430.0036-0.0221-0.0033
Jan 2017-0.0097-0.0022-0.02460.0010
Feb 20170.00360.0073-0.01200.0000
Mar 2017-0.0031-0.0002-0.0259-0.0061
Apr 2017-0.0032-0.0015-0.0136-0.0054
May 20170.00540.0006-0.0060-0.0070
Jun 2017-0.00330.0016-0.0076-0.0018
Jul 20170.00100.0014-0.01650.0002
Aug 2017-0.0055-0.00170.02950.0022
Sep 20170.0083-0.00510.0009-0.0146
Oct 2017-0.0012-0.00740.0294-0.0014
Nov 20170.01200.00500.01530.0025
Dec 2017-0.0056-0.0107-0.0169-0.0011
Jan 2018-0.0106-0.01040.0025-0.0139
Feb 2018-0.0037-0.01350.0154-0.0071
Mar 20180.00290.0027-0.01460.0072
Apr 20180.00120.0027-0.0016-0.0088
May 20180.00380.00940.0179-0.0005
Jun 20180.00380.0045-0.0012-0.0030
Jul 20180.00930.0019-0.01450.0009
Aug 20180.00590.00330.0317-0.0025
Sep 2018-0.0072-0.0004-0.0002-0.0010
Oct 2018-0.0064-0.00290.0081-0.0010
Nov 2018-0.00740.0037-0.04910.0072
Dec 2018-0.0061-0.00610.00610.0012
Jan 20190.01790.0124-0.00190.0036
Feb 20190.00380.0067-0.00460.0021
Mar 2019-0.00630.00750.01030.0012