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 SmallCap 600 Value ETF IJS Aug 2000 Jul 2017 0.96 0.80 0.49 0.01 0.06% 0.68% 95.5%
iShares Russell 2000 Value ETF IWN Aug 2000 Jul 2017 0.93 0.76 0.60 0.04 -0.01% -0.12% 96.7%
Guggenheim S&P Smallcap 600 Pure Value ETF RZV Apr 2006 Jul 2017 1.05 1.20 0.74 -0.52 -0.00% -0.03% 90.6%
Vanguard Small-Cap Value ETF VBR Feb 2004 Jul 2017 1.01 0.58 0.35 -0.05 0.05% 0.66% 97.2%

iShares S&P SmallCap 600 Value ETF

Factor regression results for iShares S&P SmallCap 600 Value ETF
Ticker IJS
Time Period Aug 2000 - Jul 2017
Coefficient of Determination (R2) 95.5%
Adjusted R2 95.5%
Regression F statistic 1,065.92 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.712 with p-value 0.019)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 16.404 with p-value 0.003)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.022 43.916 0.000 0.914...0.999
Size (SMB) 0.80 0.034 23.372 0.000 0.735...0.870
Value (HML) 0.49 0.028 17.754 0.000 0.439...0.549
Momentum (MOM) 0.01 0.018 0.444 0.657 -0.027...0.042
Alpha (α) 5.68bps 0.001 0.682 0.496 -0.11%...0.22%
Annualized Alpha (α) 0.68%  

iShares Russell 2000 Value ETF

Factor regression results for iShares Russell 2000 Value ETF
Ticker IWN
Time Period Aug 2000 - Jul 2017
Coefficient of Determination (R2) 96.7%
Adjusted R2 96.7%
Regression F statistic 1,480.44 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.157 with p-value 0.869)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 27.150 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.93 0.018 51.524 0.000 0.890...0.961
Size (SMB) 0.76 0.028 26.966 0.000 0.708...0.820
Value (HML) 0.60 0.023 26.165 0.000 0.556...0.646
Momentum (MOM) 0.04 0.014 2.596 0.010 0.009...0.066
Alpha (α) -0.98bps 0.001 -0.143 0.886 -0.15%...0.13%
Annualized Alpha (α) -0.12%  

Guggenheim S&P Smallcap 600 Pure Value ETF

Factor regression results for Guggenheim S&P Smallcap 600 Pure Value ETF
Ticker RZV
Time Period Apr 2006 - Jul 2017
Coefficient of Determination (R2) 90.6%
Adjusted R2 90.3%
Regression F statistic 316.86 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.013 with p-value 0.517)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 43.953 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.05 0.061 17.034 0.000 0.925...1.169
Size (SMB) 1.20 0.110 10.845 0.000 0.978...1.415
Value (HML) 0.74 0.096 7.654 0.000 0.545...0.926
Momentum (MOM) -0.52 0.055 -9.333 0.000 -0.626...-0.407
Alpha (α) -0.21bps 0.002 -0.009 0.993 -0.46%...0.46%
Annualized Alpha (α) -0.03%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Feb 2004 - Jul 2017
Coefficient of Determination (R2) 97.2%
Adjusted R2 97.2%
Regression F statistic 1,385.96 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.257 with p-value 0.946)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 15.038 with p-value 0.005)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.020 51.098 0.000 0.974...1.052
Size (SMB) 0.58 0.033 17.309 0.000 0.512...0.644
Value (HML) 0.35 0.030 11.712 0.000 0.293...0.412
Momentum (MOM) -0.05 0.017 -3.096 0.002 -0.088...-0.020
Alpha (α) 5.47bps 0.001 0.779 0.437 -0.08%...0.19%
Annualized Alpha (α) 0.66%  
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:
Regression residuals
MonthIJSIWNRZVVBR
Aug 20000.0130-0.0054
Sep 20000.02480.0157
Oct 20000.01460.0092
Nov 20000.02260.0386
Dec 20000.06720.0251
Jan 20010.0161-0.0167
Feb 2001-0.00920.0117
Mar 2001-0.0200-0.0002
Apr 20010.00740.0022
May 2001-0.0181-0.0233
Jun 2001-0.00810.0099
Jul 20010.0215-0.0098
Aug 20010.01570.0236
Sep 2001-0.01980.0000
Oct 2001-0.0018-0.0056
Nov 2001-0.0048-0.0064
Dec 20010.0087-0.0031
Jan 20020.0069-0.0009
Feb 20020.01170.0143
Mar 20020.0055-0.0068
Apr 20020.02030.0148
May 2002-0.0079-0.0069
Jun 2002-0.0144-0.0006
Jul 2002-0.0225-0.0087
Aug 2002-0.0038-0.0021
Sep 2002-0.0099-0.0156
Oct 2002-0.00040.0033
Nov 2002-0.01960.0119
Dec 20020.0142-0.0093
Jan 2003-0.0242-0.0078
Feb 2003-0.0142-0.0030
Mar 2003-0.01040.0032
Apr 2003-0.00100.0089
May 2003-0.00050.0148
Jun 2003-0.0032-0.0197
Jul 2003-0.0111-0.0033
Aug 2003-0.0049-0.0146
Sep 2003-0.0310-0.0069
Oct 20030.0010-0.0060
Nov 20030.00330.0017
Dec 2003-0.00270.0042
Jan 2004-0.0326-0.0205
Feb 20040.01960.01720.0191
Mar 20040.01430.00890.0172
Apr 20040.0067-0.0049-0.0212
May 20040.00690.00910.0111
Jun 20040.00930.00610.0109
Jul 20040.0001-0.00580.0107
Aug 20040.00810.01730.0149
Sep 20040.0064-0.00200.0032
Oct 2004-0.00510.0023-0.0015
Nov 20040.00510.00740.0074
Dec 2004-0.0197-0.0138-0.0102
Jan 2005-0.0060-0.0163-0.0071
Feb 20050.0044-0.00550.0016
Mar 2005-0.0039-0.0041-0.0014
Apr 20050.00500.0030-0.0026
May 20050.00460.00690.0194
Jun 2005-0.00330.00130.0037
Jul 2005-0.00300.0025-0.0032
Aug 2005-0.0097-0.0165-0.0092
Sep 2005-0.0071-0.01440.0018
Oct 2005-0.0094-0.0086-0.0095
Nov 20050.00940.0138-0.0034
Dec 2005-0.0105-0.0104-0.0021
Jan 20060.0051-0.0030-0.0001
Feb 20060.00610.00870.0063
Mar 2006-0.00130.0029-0.0047
Apr 2006-0.0115-0.0125-0.0068-0.0130
May 2006-0.0042-0.0019-0.02660.0004
Jun 2006-0.00240.00460.02040.0088
Jul 2006-0.00970.00560.00290.0032
Aug 20060.00440.0110-0.0313-0.0050
Sep 20060.0004-0.0032-0.0004-0.0071
Oct 20060.00600.0056-0.0008-0.0009
Nov 2006-0.0045-0.0006-0.01070.0051
Dec 2006-0.0166-0.01210.0016-0.0135
Jan 20070.0027-0.00270.00830.0005
Feb 2007-0.0049-0.0074-0.00650.0015
Mar 2007-0.00090.0037-0.0068-0.0029
Apr 20070.0023-0.00710.0104-0.0072
May 20070.01070.0060-0.00720.0008
Jun 2007-0.0089-0.0088-0.0092-0.0078
Jul 20070.0050-0.01690.0227-0.0159
Aug 20070.01180.0205-0.01730.0113
Sep 2007-0.0042-0.00110.0043-0.0054
Oct 20070.00030.00290.00570.0045
Nov 2007-0.0024-0.0055-0.0005-0.0038
Dec 2007-0.0016-0.00870.0346-0.0033
Jan 20080.00790.00620.05060.0110
Feb 20080.00010.0008-0.01790.0112
Mar 20080.00780.00010.04460.0006
Apr 2008-0.00200.0136-0.04840.0107
May 2008-0.0002-0.0052-0.01490.0082
Jun 2008-0.0048-0.01660.0332-0.0224
Jul 2008-0.01410.0004-0.03530.0088
Aug 2008-0.00530.0014-0.0531-0.0099
Sep 20080.01590.02250.03740.0227
Oct 2008-0.0027-0.01860.0272-0.0185
Nov 20080.00910.01570.02730.0253
Dec 20080.02130.0130-0.05550.0038
Jan 2009-0.00720.0048-0.0651-0.0041
Feb 2009-0.0002-0.0048-0.0224-0.0117
Mar 2009-0.0263-0.01180.0225-0.0212
Apr 20090.02770.00250.13230.0261
May 2009-0.0230-0.0007-0.0281-0.0075
Jun 20090.0025-0.01110.0907-0.0086
Jul 2009-0.0068-0.00430.0232-0.0058
Aug 2009-0.0281-0.0166-0.05280.0006
Sep 2009-0.0215-0.0134-0.0113-0.0079
Oct 20090.01770.0173-0.05230.0053
Nov 2009-0.0038-0.0051-0.0136-0.0061
Dec 20090.00470.0032-0.01640.0069
Jan 20100.00210.00070.0086-0.0026
Feb 2010-0.0110-0.01550.0293-0.0010
Mar 2010-0.00510.00180.01400.0038
Apr 2010-0.0076-0.0065-0.01190.0044
May 20100.00080.0046-0.01020.0078
Jun 20100.00810.0063-0.0331-0.0003
Jul 20100.00010.00640.01050.0048
Aug 2010-0.00040.0038-0.00800.0052
Sep 20100.00120.0071-0.0001-0.0039
Oct 20100.00600.00880.0256-0.0006
Nov 2010-0.0071-0.00330.0117-0.0008
Dec 2010-0.0004-0.0068-0.0200-0.0120
Jan 2011-0.0062-0.0056-0.0242-0.0036
Feb 2011-0.0097-0.0002-0.0032-0.0006
Mar 20110.0036-0.00250.00850.0019
Apr 2011-0.00250.0070-0.00380.0043
May 20110.00980.01290.02970.0021
Jun 20110.0031-0.00610.0039-0.0006
Jul 20110.01090.00760.02790.0021
Aug 20110.01350.00250.01250.0042
Sep 20110.0017-0.00180.0065-0.0062
Oct 20110.01790.01520.00240.0089
Nov 20110.01120.00260.01620.0052
Dec 20110.00950.00150.0129-0.0009
Jan 20120.01890.0137-0.01260.0052
Feb 2012-0.0121-0.0133-0.0084-0.0102
Mar 2012-0.00090.0011-0.0065-0.0066
Apr 2012-0.0053-0.00190.00640.0048
May 2012-0.0108-0.00240.00400.0045
Jun 2012-0.00070.00590.0031-0.0018
Jul 20120.00670.00030.01770.0047
Aug 20120.00630.00100.0191-0.0048
Sep 2012-0.0069-0.00460.0026-0.0091
Oct 2012-0.0130-0.0130-0.04010.0035
Nov 20120.0084-0.00090.04560.0017
Dec 2012-0.0056-0.0002-0.0344-0.0018
Jan 2013-0.00790.0003-0.02030.0011
Feb 20130.00690.00110.01200.0059
Mar 2013-0.0032-0.0015-0.01320.0016
Apr 20130.00250.0011-0.0038-0.0032
May 2013-0.0103-0.02360.0172-0.0174
Jun 20130.0006-0.0021-0.0071-0.0072
Jul 2013-0.0068-0.0050-0.0141-0.0011
Aug 20130.0025-0.00490.0054-0.0067
Sep 20130.01130.00640.02700.0030
Oct 20130.0005-0.0021-0.00150.0010
Nov 20130.0010-0.00210.0233-0.0106
Dec 2013-0.0090-0.0000-0.00480.0024
Jan 2014-0.0008-0.00280.00030.0085
Feb 20140.00040.00170.01140.0026
Mar 2014-0.0010-0.0068-0.0232-0.0006
Apr 20140.00710.0036-0.00050.0085
May 20140.00180.00200.00880.0071
Jun 2014-0.00800.0012-0.01500.0015
Jul 20140.0022-0.01020.0168-0.0034
Aug 20140.00330.00450.00410.0080
Sep 2014-0.0045-0.01180.0097-0.0093
Oct 20140.02100.02430.00340.0040
Nov 20140.01110.00600.02390.0076
Dec 2014-0.0051-0.0051-0.0216-0.0035
Jan 2015-0.00260.01010.00100.0156
Feb 20150.0041-0.00250.0207-0.0044
Mar 2015-0.00210.00610.00210.0094
Apr 2015-0.0092-0.0125-0.0099-0.0128
May 2015-0.0075-0.00640.00760.0019
Jun 2015-0.0005-0.00140.0044-0.0119
Jul 20150.01070.01020.04970.0185
Aug 2015-0.0060-0.0121-0.0078-0.0012
Sep 20150.00930.00870.01930.0111
Oct 20150.00760.00070.0007-0.0031
Nov 2015-0.0081-0.0010-0.0119-0.0111
Dec 20150.00430.00150.0236-0.0005
Jan 20160.01270.0007-0.00660.0071
Feb 20160.01720.00510.01880.0100
Mar 20160.01440.00650.00120.0062
Apr 2016-0.0092-0.0095-0.0270-0.0076
May 2016-0.00250.0135-0.04830.0043
Jun 20160.00990.00710.02590.0050
Jul 2016-0.00330.0047-0.0122-0.0073
Aug 2016-0.0199-0.0083-0.0496-0.0188
Sep 2016-0.0032-0.00130.0063-0.0070
Oct 2016-0.0045-0.00460.00820.0014
Nov 20160.0017-0.0033-0.0231-0.0109
Dec 2016-0.00470.0029-0.0230-0.0040
Jan 2017-0.0098-0.0023-0.02340.0010
Feb 20170.00340.0073-0.0112-0.0001
Mar 2017-0.00290.0001-0.0256-0.0060
Apr 2017-0.0028-0.0011-0.0123-0.0053
May 20170.00490.0005-0.0046-0.0072
Jun 2017-0.00280.0019-0.0072-0.0019
Jul 20170.00110.0015-0.01490.0002