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 Jan 2017 0.95 0.80 0.49 0.01 0.05% 0.58% 95.5%
iShares Russell 2000 Value ETF IWN Aug 2000 Jan 2017 0.92 0.76 0.60 0.04 -0.02% -0.29% 96.8%
Guggenheim S&P Smallcap 600 Pure Value ETF RZV Apr 2006 Jan 2017 1.05 1.19 0.72 -0.52 0.04% 0.45% 90.7%
Vanguard Small-Cap Value ETF VBR Feb 2004 Jan 2017 1.01 0.58 0.34 -0.06 0.06% 0.76% 97.3%

iShares S&P SmallCap 600 Value ETF

Factor regression results for iShares S&P SmallCap 600 Value ETF
Ticker IJS
Time Period Aug 2000 - Jan 2017
Coefficient of Determination (R2) 95.5%
Adjusted R2 95.4%
Regression F statistic 1,023.15 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.716 with p-value 0.022)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 15.400 with p-value 0.004)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.95 0.022 42.801 0.000 0.911...0.999
Size (SMB) 0.80 0.035 22.706 0.000 0.733...0.872
Value (HML) 0.49 0.029 17.218 0.000 0.437...0.551
Momentum (MOM) 0.01 0.018 0.427 0.670 -0.028...0.043
Alpha (α) 4.79bps 0.001 0.555 0.579 -0.12%...0.22%
Annualized Alpha (α) 0.58%  

iShares Russell 2000 Value ETF

Factor regression results for iShares Russell 2000 Value ETF
Ticker IWN
Time Period Aug 2000 - Jan 2017
Coefficient of Determination (R2) 96.8%
Adjusted R2 96.7%
Regression F statistic 1,436.73 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.163 with p-value 0.874)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 25.845 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.92 0.018 50.507 0.000 0.888...0.960
Size (SMB) 0.76 0.029 26.344 0.000 0.706...0.820
Value (HML) 0.60 0.024 25.557 0.000 0.555...0.648
Momentum (MOM) 0.04 0.015 2.569 0.011 0.009...0.066
Alpha (α) -2.41bps 0.001 -0.341 0.734 -0.16%...0.12%
Annualized Alpha (α) -0.29%  

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 - Jan 2017
Coefficient of Determination (R2) 90.7%
Adjusted R2 90.4%
Regression F statistic 305.70 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.038 with p-value 0.572)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 43.633 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.05 0.063 16.709 0.000 0.927...1.177
Size (SMB) 1.19 0.114 10.421 0.000 0.962...1.413
Value (HML) 0.72 0.099 7.242 0.000 0.522...0.915
Momentum (MOM) -0.52 0.056 -9.258 0.000 -0.633...-0.410
Alpha (α) 3.73bps 0.002 0.155 0.877 -0.44%...0.51%
Annualized Alpha (α) 0.45%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Feb 2004 - Jan 2017
Coefficient of Determination (R2) 97.3%
Adjusted R2 97.2%
Regression F statistic 1,337.39 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.292 with p-value 0.964)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 15.754 with p-value 0.003)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.020 49.864 0.000 0.974...1.054
Size (SMB) 0.58 0.035 16.713 0.000 0.509...0.645
Value (HML) 0.34 0.031 11.051 0.000 0.283...0.406
Momentum (MOM) -0.06 0.018 -3.151 0.002 -0.091...-0.021
Alpha (α) 6.37bps 0.001 0.880 0.380 -0.08%...0.21%
Annualized Alpha (α) 0.76%  
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 20000.0131-0.0052
Sep 20000.02490.0159
Oct 20000.01460.0092
Nov 20000.02240.0384
Dec 20000.06750.0255
Jan 20010.0162-0.0164
Feb 2001-0.00940.0114
Mar 2001-0.0206-0.0009
Apr 20010.00780.0027
May 2001-0.0179-0.0231
Jun 2001-0.00770.0104
Jul 20010.0214-0.0099
Aug 20010.01540.0232
Sep 2001-0.01980.0000
Oct 2001-0.0015-0.0054
Nov 2001-0.0047-0.0062
Dec 20010.0090-0.0027
Jan 20020.0069-0.0009
Feb 20020.01210.0146
Mar 20020.0054-0.0068
Apr 20020.02040.0149
May 2002-0.0078-0.0068
Jun 2002-0.0144-0.0005
Jul 2002-0.0214-0.0076
Aug 2002-0.0040-0.0022
Sep 2002-0.0095-0.0153
Oct 2002-0.00090.0030
Nov 2002-0.02130.0102
Dec 20020.0144-0.0091
Jan 2003-0.0251-0.0086
Feb 2003-0.0140-0.0027
Mar 2003-0.01200.0016
Apr 2003-0.00150.0084
May 2003-0.00240.0128
Jun 2003-0.0021-0.0185
Jul 2003-0.0123-0.0046
Aug 2003-0.0055-0.0152
Sep 2003-0.0311-0.0068
Oct 2003-0.0007-0.0078
Nov 20030.00180.0002
Dec 2003-0.00190.0052
Jan 2004-0.0319-0.0197
Feb 20040.01980.01750.0190
Mar 20040.01400.00860.0169
Apr 20040.0072-0.0043-0.0212
May 20040.00660.00880.0107
Jun 20040.00980.00670.0112
Jul 20040.0002-0.00560.0110
Aug 20040.00820.01750.0149
Sep 20040.0064-0.00190.0031
Oct 2004-0.00550.0020-0.0020
Nov 20040.00530.00770.0075
Dec 2004-0.0200-0.0141-0.0107
Jan 2005-0.0058-0.0160-0.0069
Feb 20050.0044-0.00540.0016
Mar 2005-0.0036-0.0038-0.0012
Apr 20050.00500.0031-0.0027
May 20050.00480.00710.0192
Jun 2005-0.00330.00130.0038
Jul 2005-0.00240.0032-0.0030
Aug 2005-0.0095-0.0163-0.0091
Sep 2005-0.0070-0.01420.0018
Oct 2005-0.0094-0.0086-0.0097
Nov 20050.00980.0142-0.0034
Dec 2005-0.0099-0.0098-0.0019
Jan 20060.0052-0.0029-0.0001
Feb 20060.00610.00880.0061
Mar 2006-0.00030.0040-0.0041
Apr 2006-0.0115-0.0125-0.0068-0.0130
May 2006-0.0043-0.0020-0.02740.0003
Jun 2006-0.00200.00500.02060.0090
Jul 2006-0.00960.00570.00270.0033
Aug 20060.00440.0110-0.0324-0.0055
Sep 20060.0005-0.0030-0.0010-0.0073
Oct 20060.00600.0057-0.0015-0.0011
Nov 2006-0.0042-0.0003-0.01100.0051
Dec 2006-0.0165-0.01190.0017-0.0133
Jan 20070.0029-0.00240.00820.0005
Feb 2007-0.0048-0.0072-0.00660.0015
Mar 2007-0.00080.0039-0.0070-0.0030
Apr 20070.0025-0.00680.0096-0.0074
May 20070.01130.0067-0.00720.0009
Jun 2007-0.0091-0.0090-0.0104-0.0082
Jul 20070.0049-0.01690.0216-0.0163
Aug 20070.01170.0205-0.01850.0109
Sep 2007-0.0039-0.00070.0040-0.0055
Oct 20070.00050.00330.00480.0043
Nov 2007-0.0025-0.0056-0.0014-0.0041
Dec 2007-0.0018-0.00890.0341-0.0035
Jan 20080.00750.00580.05060.0109
Feb 2008-0.00030.0004-0.01880.0108
Mar 20080.00820.00060.04500.0009
Apr 2008-0.00160.0141-0.04900.0106
May 20080.0010-0.0039-0.01360.0089
Jun 2008-0.0051-0.01670.0327-0.0225
Jul 2008-0.01420.0003-0.03520.0090
Aug 2008-0.00520.0016-0.0533-0.0099
Sep 20080.01600.02280.03840.0234
Oct 2008-0.0043-0.02040.0255-0.0195
Nov 20080.00880.01520.02640.0247
Dec 20080.02100.0128-0.05650.0033
Jan 2009-0.00750.0049-0.0674-0.0052
Feb 20090.0000-0.0045-0.0227-0.0120
Mar 2009-0.0265-0.01210.0212-0.0216
Apr 20090.02880.00370.13140.0262
May 2009-0.0230-0.0007-0.0293-0.0081
Jun 20090.0024-0.01120.0902-0.0089
Jul 2009-0.0061-0.00340.0237-0.0054
Aug 2009-0.0292-0.0176-0.05460.0000
Sep 2009-0.0219-0.0137-0.0129-0.0085
Oct 20090.01880.0184-0.05190.0056
Nov 2009-0.0041-0.0053-0.0150-0.0066
Dec 20090.00490.0035-0.01610.0070
Jan 20100.00220.00090.0086-0.0026
Feb 2010-0.0109-0.01540.0294-0.0008
Mar 2010-0.00570.00120.01290.0033
Apr 2010-0.0077-0.0065-0.01150.0046
May 20100.00130.0052-0.01010.0079
Jun 20100.00840.0067-0.0336-0.0005
Jul 2010-0.00040.00590.00900.0042
Aug 2010-0.00050.0038-0.00860.0049
Sep 20100.00150.0074-0.0010-0.0043
Oct 20100.00600.00880.0224-0.0013
Nov 2010-0.0068-0.00290.0118-0.0007
Dec 20100.0001-0.0062-0.0197-0.0117
Jan 2011-0.0061-0.0054-0.0247-0.0036
Feb 2011-0.0097-0.0002-0.0033-0.0006
Mar 20110.0040-0.00200.00860.0019
Apr 2011-0.00260.0071-0.00500.0039
May 20110.01010.01330.02930.0021
Jun 20110.0034-0.00570.0041-0.0004
Jul 20110.01080.00750.02690.0018
Aug 20110.01300.00210.01120.0037
Sep 20110.0017-0.00190.0058-0.0064
Oct 20110.01810.01570.00160.0087
Nov 20110.01170.00320.01650.0055
Dec 20110.00940.00160.0122-0.0010
Jan 20120.01910.0140-0.01360.0049
Feb 2012-0.0123-0.0135-0.0095-0.0106
Mar 2012-0.00070.0014-0.0069-0.0066
Apr 2012-0.0051-0.00170.00640.0049
May 2012-0.0112-0.00290.00370.0044
Jun 2012-0.00050.00610.0026-0.0020
Jul 20120.00700.00060.01700.0047
Aug 20120.00630.00100.0187-0.0049
Sep 2012-0.0068-0.00450.0021-0.0091
Oct 2012-0.0126-0.0124-0.03930.0040
Nov 20120.0081-0.00120.04440.0013
Dec 2012-0.0055-0.0000-0.0341-0.0016
Jan 2013-0.00820.0000-0.02200.0006
Feb 20130.00630.00040.01080.0053
Mar 2013-0.0035-0.0016-0.01430.0012
Apr 20130.00260.0013-0.0041-0.0033
May 2013-0.0101-0.02320.0168-0.0173
Jun 20130.0008-0.0019-0.0071-0.0072
Jul 2013-0.0071-0.0052-0.0149-0.0014
Aug 20130.0029-0.00450.0054-0.0067
Sep 20130.01160.00680.02660.0029
Oct 20130.0012-0.0014-0.00140.0013
Nov 20130.0009-0.00210.0229-0.0108
Dec 2013-0.00900.0001-0.00570.0022
Jan 2014-0.0005-0.0023-0.00000.0084
Feb 20140.00040.00170.01070.0023
Mar 2014-0.0009-0.0066-0.0228-0.0003
Apr 20140.00690.0035-0.00180.0082
May 20140.00260.00300.00850.0073
Jun 2014-0.00790.0013-0.01530.0014
Jul 20140.0023-0.01000.0161-0.0035
Aug 20140.00310.00440.00270.0075
Sep 2014-0.0048-0.01200.0083-0.0098
Oct 20140.02070.02410.00240.0034
Nov 20140.01100.00610.02240.0072
Dec 2014-0.0056-0.0057-0.0226-0.0038
Jan 2015-0.00300.0097-0.00090.0149
Feb 20150.0042-0.00240.0194-0.0048
Mar 2015-0.00210.00610.00210.0093
Apr 2015-0.0087-0.0120-0.0103-0.0127
May 2015-0.0071-0.00600.00750.0019
Jun 2015-0.0008-0.00160.0036-0.0122
Jul 20150.01050.01020.04790.0180
Aug 2015-0.0064-0.0123-0.0085-0.0013
Sep 20150.00890.00830.01810.0108
Oct 20150.00750.0007-0.0007-0.0036
Nov 2015-0.0075-0.0003-0.0111-0.0108
Dec 20150.00380.00090.0218-0.0012
Jan 20160.0117-0.0005-0.00830.0065
Feb 20160.01680.00480.01740.0095
Mar 20160.01500.00710.00160.0064
Apr 2016-0.0091-0.0094-0.0269-0.0076
May 2016-0.00230.0137-0.04920.0040
Jun 20160.01030.00750.02650.0051
Jul 2016-0.00600.0021-0.0176-0.0096
Aug 2016-0.0171-0.0054-0.0458-0.0168
Sep 2016-0.0038-0.00200.0050-0.0076
Oct 2016-0.0040-0.00400.00860.0019
Nov 2016-0.0005-0.0056-0.0254-0.0121
Dec 2016-0.00310.0046-0.0203-0.0027
Jan 2017-0.0101-0.0024-0.02530.0003