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 Aug 2000 Oct 2018 0.96 0.81 0.49 0.01 0.06% 0.69% 95.6%
iShares Russell 2000 Value ETF IWN Aug 2000 Oct 2018 0.92 0.77 0.60 0.04 -0.02% -0.24% 96.8%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Oct 2018 1.06 1.19 0.72 -0.50 0.06% 0.76% 90.5%
Vanguard Small-Cap Value ETF VBR Feb 2004 Oct 2018 1.01 0.58 0.35 -0.06 0.03% 0.40% 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 - Oct 2018
Coefficient of Determination (R2) 95.6%
Adjusted R2 95.5%
Regression F statistic 1,168.62 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.700 with p-value 0.013)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 17.567 with p-value 0.001)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.021 46.460 0.000 0.917...0.998
Size (SMB) 0.81 0.032 25.450 0.000 0.751...0.877
Value (HML) 0.49 0.027 18.485 0.000 0.441...0.546
Momentum (MOM) 0.01 0.017 0.463 0.644 -0.025...0.041
Alpha (α) 5.76bps 0.001 0.734 0.464 -0.10%...0.21%
Annualized Alpha (α) 0.69%  

iShares Russell 2000 Value ETF

Factor regression results for iShares Russell 2000 Value ETF
Ticker IWN
Time Period Aug 2000 - Oct 2018
Coefficient of Determination (R2) 96.8%
Adjusted R2 96.7%
Regression F statistic 1,596.00 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.111 with p-value 0.792)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 27.708 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.92 0.017 54.091 0.000 0.891...0.958
Size (SMB) 0.77 0.027 29.142 0.000 0.721...0.826
Value (HML) 0.60 0.022 26.976 0.000 0.554...0.641
Momentum (MOM) 0.04 0.014 2.636 0.009 0.009...0.064
Alpha (α) -2.03bps 0.001 -0.312 0.755 -0.15%...0.11%
Annualized Alpha (α) -0.24%  

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 - Oct 2018
Coefficient of Determination (R2) 90.5%
Adjusted R2 90.2%
Regression F statistic 347.31 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.018 with p-value 0.528)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 49.336 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.057 18.763 0.000 0.950...1.174
Size (SMB) 1.19 0.098 12.153 0.000 0.996...1.383
Value (HML) 0.72 0.090 7.958 0.000 0.539...0.896
Momentum (MOM) -0.50 0.053 -9.449 0.000 -0.602...-0.394
Alpha (α) 6.29bps 0.002 0.293 0.770 -0.36%...0.49%
Annualized Alpha (α) 0.76%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Feb 2004 - Oct 2018
Coefficient of Determination (R2) 97.2%
Adjusted R2 97.2%
Regression F statistic 1,502.47 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.250 with p-value 0.949)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 13.010 with p-value 0.011)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.018 54.576 0.000 0.972...1.045
Size (SMB) 0.58 0.030 19.134 0.000 0.520...0.640
Value (HML) 0.35 0.029 12.202 0.000 0.293...0.406
Momentum (MOM) -0.06 0.017 -3.489 0.001 -0.091...-0.025
Alpha (α) 3.30bps 0.001 0.500 0.618 -0.10%...0.16%
Annualized Alpha (α) 0.40%  
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) 46.27 24.34 25.12 16.15  
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 Oct 2018 0.69% 44.29 19.82 12.40 0.13 82.40 95.6%
Factor regression results
Monthly Factor Premiums (BPS) 46.27 24.34 25.12 16.15  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
iShares Russell 2000 Value ETF IWN Aug 2000 Oct 2018 -0.24% 42.78 18.82 15.02 0.59 75.18 96.8%
Factor regression results
Monthly Factor Premiums (BPS) 68.58 3.03 -13.23 3.68  
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 Oct 2018 0.76% 72.85 3.60 -9.49 -1.83 71.41 90.5%
Factor regression results
Monthly Factor Premiums (BPS) 67.44 8.02 -3.25 10.94  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
Vanguard Small-Cap Value ETF VBR Feb 2004 Oct 2018 0.40% 68.02 4.65 -1.14 -0.64 74.19 97.2%
Regression residuals
MonthIJSIWNRZVVBR
Aug 20000.0131-0.0051
Sep 20000.02500.0161
Oct 20000.01510.0098
Nov 20000.02300.0392
Dec 20000.06710.0254
Jan 20010.0153-0.0175
Feb 2001-0.00900.0123
Mar 2001-0.02000.0000
Apr 20010.00730.0021
May 2001-0.0184-0.0233
Jun 2001-0.00880.0094
Jul 20010.0220-0.0090
Aug 20010.01550.0235
Sep 2001-0.01900.0008
Oct 2001-0.0028-0.0066
Nov 2001-0.0048-0.0062
Dec 20010.0082-0.0034
Jan 20020.0068-0.0008
Feb 20020.01190.0146
Mar 20020.0049-0.0071
Apr 20020.01960.0145
May 2002-0.0075-0.0064
Jun 2002-0.0149-0.0010
Jul 2002-0.0218-0.0083
Aug 2002-0.0036-0.0016
Sep 2002-0.0101-0.0158
Oct 2002-0.00020.0035
Nov 2002-0.02000.0116
Dec 20020.0142-0.0092
Jan 2003-0.0244-0.0078
Feb 2003-0.0141-0.0029
Mar 2003-0.01050.0032
Apr 2003-0.00110.0090
May 2003-0.00110.0144
Jun 2003-0.0034-0.0198
Jul 2003-0.0117-0.0037
Aug 2003-0.0052-0.0146
Sep 2003-0.0311-0.0069
Oct 20030.0006-0.0060
Nov 20030.00310.0017
Dec 2003-0.00230.0047
Jan 2004-0.0329-0.0205
Feb 20040.01970.01750.0194
Mar 20040.01410.00880.0173
Apr 20040.0069-0.0047-0.0213
May 20040.00690.00920.0114
Jun 20040.00900.00600.0113
Jul 20040.0007-0.00510.0109
Aug 20040.00830.01760.0151
Sep 20040.0061-0.00200.0037
Oct 2004-0.00520.0024-0.0013
Nov 20040.00470.00730.0080
Dec 2004-0.0197-0.0137-0.0100
Jan 2005-0.0060-0.0161-0.0069
Feb 20050.0046-0.00510.0022
Mar 2005-0.0040-0.0041-0.0013
Apr 20050.00530.0033-0.0026
May 20050.00410.00650.0196
Jun 2005-0.00360.00130.0041
Jul 2005-0.00340.0023-0.0029
Aug 2005-0.0096-0.0163-0.0089
Sep 2005-0.0070-0.01420.0022
Oct 2005-0.0092-0.0084-0.0094
Nov 20050.00930.0139-0.0031
Dec 2005-0.0104-0.0103-0.0019
Jan 20060.0045-0.00330.0003
Feb 20060.00610.00880.0064
Mar 2006-0.00170.0027-0.0044
Apr 2006-0.0113-0.0121-0.0073-0.0126
May 2006-0.0038-0.0015-0.02580.0005
Jun 2006-0.00240.00480.01960.0091
Jul 2006-0.00920.00620.00300.0035
Aug 20060.00430.0109-0.0319-0.0050
Sep 20060.0005-0.0030-0.0013-0.0069
Oct 20060.00570.0055-0.0017-0.0006
Nov 2006-0.0046-0.0006-0.01140.0053
Dec 2006-0.0165-0.01180.0012-0.0130
Jan 20070.0027-0.00260.00740.0008
Feb 2007-0.0050-0.0075-0.00650.0016
Mar 2007-0.00090.0038-0.0080-0.0026
Apr 20070.0025-0.00680.0089-0.0068
May 20070.01070.0062-0.00830.0011
Jun 2007-0.0089-0.0089-0.0098-0.0077
Jul 20070.0052-0.01670.0213-0.0158
Aug 20070.01180.0206-0.01850.0115
Sep 2007-0.0039-0.00070.0019-0.0048
Oct 20070.00020.00300.00340.0049
Nov 2007-0.0021-0.0052-0.0010-0.0037
Dec 2007-0.0016-0.00850.0328-0.0029
Jan 20080.00800.00640.05300.0107
Feb 20080.00020.0009-0.01930.0115
Mar 20080.00760.00010.04340.0010
Apr 2008-0.00190.0139-0.05000.0110
May 2008-0.0007-0.0055-0.01650.0085
Jun 2008-0.0049-0.01670.0311-0.0221
Jul 2008-0.01440.0004-0.03370.0089
Aug 2008-0.00570.0012-0.0527-0.0098
Sep 20080.01610.02290.03900.0228
Oct 2008-0.0023-0.01840.0271-0.0187
Nov 20080.00950.01590.02510.0253
Dec 20080.02090.0127-0.05530.0038
Jan 2009-0.00730.0045-0.0659-0.0046
Feb 2009-0.0001-0.0049-0.0232-0.0119
Mar 2009-0.0264-0.01180.0240-0.0210
Apr 20090.02710.00210.13800.0253
May 2009-0.0228-0.0004-0.0274-0.0076
Jun 20090.0022-0.01130.0887-0.0083
Jul 2009-0.0070-0.00410.0236-0.0054
Aug 2009-0.0280-0.0162-0.05100.0008
Sep 2009-0.0218-0.0135-0.0113-0.0078
Oct 20090.01840.0178-0.05380.0056
Nov 2009-0.0037-0.0047-0.0155-0.0057
Dec 20090.00400.0028-0.01760.0073
Jan 20100.00200.00070.0096-0.0028
Feb 2010-0.0113-0.01550.0278-0.0005
Mar 2010-0.00540.00180.01210.0044
Apr 2010-0.0082-0.0067-0.01250.0049
May 20100.00080.0045-0.01000.0076
Jun 20100.00840.0064-0.0332-0.0005
Jul 2010-0.00010.00650.00810.0053
Aug 2010-0.00000.0041-0.00840.0052
Sep 20100.00070.0068-0.0027-0.0034
Oct 20100.00590.00890.0238-0.0002
Nov 2010-0.0076-0.00360.0105-0.0006
Dec 2010-0.0005-0.0066-0.0203-0.0115
Jan 2011-0.0061-0.0054-0.0253-0.0033
Feb 2011-0.0098-0.0001-0.0043-0.0001
Mar 20110.0034-0.00250.00690.0022
Apr 2011-0.00240.0073-0.00510.0047
May 20110.01000.01300.02920.0023
Jun 20110.0031-0.00600.0034-0.0003
Jul 20110.01090.00770.02720.0021
Aug 20110.01390.00280.01220.0042
Sep 20110.0022-0.00150.0072-0.0064
Oct 20110.01740.01510.00060.0095
Nov 20110.01120.00270.01470.0056
Dec 20110.00950.00170.0120-0.0005
Jan 20120.01870.0136-0.01260.0052
Feb 2012-0.0119-0.0130-0.0097-0.0097
Mar 2012-0.00100.0013-0.0080-0.0062
Apr 2012-0.0054-0.00190.00490.0051
May 2012-0.0108-0.00240.00280.0048
Jun 2012-0.00080.00600.0022-0.0015
Jul 20120.00710.00090.01590.0052
Aug 20120.00590.00080.0183-0.0048
Sep 2012-0.0071-0.00470.0018-0.0089
Oct 2012-0.0129-0.0127-0.03990.0038
Nov 20120.0084-0.00080.04470.0020
Dec 2012-0.0058-0.0002-0.0341-0.0016
Jan 2013-0.00810.0003-0.02160.0014
Feb 20130.00680.00110.01070.0061
Mar 2013-0.0031-0.0011-0.01460.0022
Apr 20130.00240.0011-0.0053-0.0031
May 2013-0.0108-0.02390.0168-0.0172
Jun 20130.0004-0.0021-0.0078-0.0071
Jul 2013-0.0071-0.0050-0.0157-0.0006
Aug 20130.0025-0.00500.0048-0.0067
Sep 20130.01110.00640.02520.0035
Oct 20130.0007-0.0017-0.00270.0015
Nov 20130.0008-0.00210.0222-0.0103
Dec 2013-0.00890.0002-0.00590.0028
Jan 2014-0.0008-0.0027-0.00020.0086
Feb 20140.00040.00200.00980.0032
Mar 2014-0.0007-0.0063-0.0224-0.0002
Apr 20140.00760.0041-0.00030.0087
May 20140.00220.00260.00780.0076
Jun 2014-0.00850.0009-0.01630.0017
Jul 20140.0028-0.00960.0163-0.0032
Aug 20140.00330.00480.00290.0085
Sep 2014-0.0039-0.01120.0090-0.0090
Oct 20140.02050.02390.00220.0041
Nov 20140.01150.00650.02240.0081
Dec 2014-0.0053-0.0051-0.0219-0.0031
Jan 2015-0.00260.0100-0.00060.0157
Feb 20150.0045-0.00200.0202-0.0037
Mar 2015-0.00210.00620.00170.0098
Apr 2015-0.0089-0.0122-0.0092-0.0128
May 2015-0.0068-0.00560.00670.0029
Jun 2015-0.0011-0.00190.0028-0.0119
Jul 20150.01090.01050.04550.0191
Aug 2015-0.0059-0.0119-0.0064-0.0012
Sep 20150.00970.00920.01810.0115
Oct 20150.00760.0009-0.0009-0.0028
Nov 2015-0.0085-0.0012-0.0128-0.0108
Dec 20150.00470.00190.0223-0.0002
Jan 20160.01290.0009-0.00720.0070
Feb 20160.01710.00500.01890.0100
Mar 20160.01450.00680.00130.0067
Apr 2016-0.0094-0.0095-0.0262-0.0077
May 2016-0.00240.0136-0.04990.0046
Jun 20160.00980.00710.02440.0053
Jul 2016-0.00380.0045-0.0129-0.0071
Aug 2016-0.0197-0.0079-0.0484-0.0183
Sep 2016-0.0036-0.00160.0054-0.0069
Oct 2016-0.0040-0.00400.00820.0018
Nov 20160.0010-0.0035-0.0219-0.0105
Dec 2016-0.00460.0032-0.0230-0.0035
Jan 2017-0.0095-0.0018-0.02470.0013
Feb 20170.00370.0077-0.01230.0003
Mar 2017-0.00290.0001-0.0261-0.0059
Apr 2017-0.0030-0.0011-0.0136-0.0051
May 20170.00540.0010-0.0060-0.0068
Jun 2017-0.00310.0018-0.0078-0.0017
Jul 20170.00100.0016-0.01680.0003
Aug 2017-0.0057-0.00150.02960.0023
Sep 20170.0084-0.00520.0004-0.0146
Oct 2017-0.0013-0.00720.0292-0.0013
Nov 20170.01200.00520.01490.0026
Dec 2017-0.0056-0.0106-0.0171-0.0010
Jan 2018-0.0107-0.01010.0021-0.0138
Feb 2018-0.0039-0.01360.0155-0.0071
Mar 20180.00310.0026-0.01470.0072
Apr 20180.00130.0028-0.0019-0.0087
May 20180.00400.00960.0176-0.0005
Jun 20180.00390.0047-0.0016-0.0029
Jul 20180.00910.0021-0.01500.0010
Aug 20180.00620.00390.0320-0.0021
Sep 2018-0.0072-0.0002-0.0004-0.0008
Oct 2018-0.0072-0.00360.0075-0.0013