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 Small-Cap 600 Value ETF IJS Aug 2000 Feb 2018 0.95 0.81 0.50 0.01 0.05% 0.61% 95.6%
iShares Russell 2000 Value ETF IWN Aug 2000 Feb 2018 0.92 0.77 0.60 0.03 -0.03% -0.38% 96.7%
Guggenheim S&P SmallCap 600 PureVal ETF RZV Apr 2006 Feb 2018 1.06 1.18 0.73 -0.50 0.05% 0.60% 90.5%
Vanguard Small-Cap Value ETF VBR Feb 2004 Feb 2018 1.01 0.58 0.35 -0.06 0.04% 0.44% 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 - Feb 2018
Coefficient of Determination (R2) 95.6%
Adjusted R2 95.5%
Regression F statistic 1,107.39 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.712 with p-value 0.018)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 16.649 with p-value 0.002)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.95 0.021 44.993 0.000 0.912...0.996
Size (SMB) 0.81 0.033 24.282 0.000 0.743...0.874
Value (HML) 0.50 0.027 18.136 0.000 0.443...0.551
Momentum (MOM) 0.01 0.017 0.314 0.754 -0.029...0.039
Alpha (α) 5.09bps 0.001 0.627 0.531 -0.11%...0.21%
Annualized Alpha (α) 0.61%  

iShares Russell 2000 Value ETF

Factor regression results for iShares Russell 2000 Value ETF
Ticker IWN
Time Period Aug 2000 - Feb 2018
Coefficient of Determination (R2) 96.7%
Adjusted R2 96.6%
Regression F statistic 1,515.00 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.120 with p-value 0.807)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 26.784 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.92 0.018 52.417 0.000 0.888...0.958
Size (SMB) 0.77 0.028 27.714 0.000 0.711...0.820
Value (HML) 0.60 0.023 26.444 0.000 0.557...0.647
Momentum (MOM) 0.03 0.014 2.426 0.016 0.006...0.063
Alpha (α) -3.20bps 0.001 -0.476 0.635 -0.16%...0.10%
Annualized Alpha (α) -0.38%  

Guggenheim S&P SmallCap 600 PureVal ETF

Factor regression results for Guggenheim S&P SmallCap 600 PureVal ETF
Ticker RZV
Time Period Apr 2006 - Feb 2018
Coefficient of Determination (R2) 90.5%
Adjusted R2 90.2%
Regression F statistic 329.21 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.012 with p-value 0.515)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 46.827 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.059 17.822 0.000 0.939...1.173
Size (SMB) 1.18 0.105 11.194 0.000 0.970...1.387
Value (HML) 0.73 0.094 7.773 0.000 0.547...0.921
Momentum (MOM) -0.50 0.054 -9.324 0.000 -0.611...-0.397
Alpha (α) 5.04bps 0.002 0.224 0.823 -0.39%...0.50%
Annualized Alpha (α) 0.60%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Feb 2004 - Feb 2018
Coefficient of Determination (R2) 97.2%
Adjusted R2 97.1%
Regression F statistic 1,413.92 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.231 with p-value 0.930)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 13.715 with p-value 0.008)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.019 52.438 0.000 0.972...1.048
Size (SMB) 0.58 0.032 17.916 0.000 0.514...0.641
Value (HML) 0.35 0.030 11.711 0.000 0.291...0.409
Momentum (MOM) -0.06 0.017 -3.347 0.001 -0.091...-0.024
Alpha (α) 3.65bps 0.001 0.531 0.596 -0.10%...0.17%
Annualized Alpha (α) 0.44%  
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) 47.98 23.79 29.55 15.69  
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 Feb 2018 0.61% 45.78 19.23 14.69 0.08 84.88 95.6%
Factor regression results
Monthly Factor Premiums (BPS) 47.98 23.79 29.55 15.69  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
iShares Russell 2000 Value ETF IWN Aug 2000 Feb 2018 -0.38% 44.28 18.22 17.79 0.54 77.63 96.7%
Factor regression results
Monthly Factor Premiums (BPS) 72.35 0.83 -9.13 2.24  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
Guggenheim S&P SmallCap 600 PureVal ETF RZV Apr 2006 Feb 2018 0.60% 76.39 0.97 -6.71 -1.13 74.57 90.5%
Factor regression results
Monthly Factor Premiums (BPS) 70.57 6.37 0.67 10.09  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
Vanguard Small-Cap Value ETF VBR Feb 2004 Feb 2018 0.44% 71.27 3.68 0.24 -0.58 78.25 97.2%
Regression residuals
MonthIJSIWNRZVVBR
Aug 20000.0134-0.0049
Sep 20000.02460.0158
Oct 20000.01460.0093
Nov 20000.02220.0384
Dec 20000.06710.0255
Jan 20010.0155-0.0171
Feb 2001-0.00940.0119
Mar 2001-0.0202-0.0001
Apr 20010.00760.0024
May 2001-0.0182-0.0231
Jun 2001-0.00840.0100
Jul 20010.0217-0.0094
Aug 20010.01550.0237
Sep 2001-0.01950.0004
Oct 2001-0.0020-0.0057
Nov 2001-0.0047-0.0062
Dec 20010.0085-0.0030
Jan 20020.0070-0.0005
Feb 20020.01190.0146
Mar 20020.0053-0.0067
Apr 20020.01990.0149
May 2002-0.0077-0.0066
Jun 2002-0.0147-0.0006
Jul 2002-0.0221-0.0085
Aug 2002-0.0037-0.0018
Sep 2002-0.0100-0.0155
Oct 2002-0.00000.0037
Nov 2002-0.02000.0116
Dec 20020.0143-0.0090
Jan 2003-0.0242-0.0075
Feb 2003-0.0141-0.0027
Mar 2003-0.01030.0035
Apr 2003-0.00100.0090
May 2003-0.00080.0147
Jun 2003-0.0033-0.0196
Jul 2003-0.0124-0.0043
Aug 2003-0.0061-0.0155
Sep 2003-0.0308-0.0064
Oct 2003-0.0009-0.0076
Nov 20030.00160.0003
Dec 2003-0.00190.0051
Jan 2004-0.0322-0.0197
Feb 20040.01970.01740.0192
Mar 20040.01410.00880.0172
Apr 20040.0072-0.0043-0.0210
May 20040.00660.00900.0111
Jun 20040.00970.00680.0116
Jul 20040.0001-0.00570.0108
Aug 20040.00800.01750.0150
Sep 20040.0064-0.00170.0036
Oct 2004-0.00510.0025-0.0014
Nov 20040.00510.00770.0079
Dec 2004-0.0197-0.0136-0.0101
Jan 2005-0.0059-0.0160-0.0069
Feb 20050.0045-0.00520.0019
Mar 2005-0.0039-0.0039-0.0012
Apr 20050.00520.0032-0.0026
May 20050.00460.00710.0197
Jun 2005-0.00330.00160.0041
Jul 2005-0.00300.0027-0.0029
Aug 2005-0.0096-0.0163-0.0090
Sep 2005-0.0069-0.01410.0021
Oct 2005-0.0093-0.0085-0.0094
Nov 20050.00950.0141-0.0031
Dec 2005-0.0104-0.0102-0.0019
Jan 20060.0050-0.00280.0003
Feb 20060.00610.00880.0064
Mar 2006-0.00140.0031-0.0044
Apr 2006-0.0114-0.0122-0.0077-0.0127
May 2006-0.0042-0.0018-0.02690.0004
Jun 2006-0.00230.00480.01960.0090
Jul 2006-0.00950.00580.00200.0033
Aug 20060.00440.0111-0.0315-0.0049
Sep 20060.0006-0.0029-0.0013-0.0069
Oct 20060.00600.0058-0.0012-0.0006
Nov 2006-0.0045-0.0004-0.01110.0053
Dec 2006-0.0165-0.01180.0008-0.0131
Jan 20070.0028-0.00240.00770.0007
Feb 2007-0.0050-0.0073-0.00650.0016
Mar 2007-0.00080.0040-0.0077-0.0027
Apr 20070.0026-0.00670.0092-0.0069
May 20070.01080.0063-0.00800.0010
Jun 2007-0.0088-0.0087-0.0095-0.0077
Jul 20070.0052-0.01660.0216-0.0159
Aug 20070.01200.0208-0.01800.0114
Sep 2007-0.0037-0.00050.0026-0.0050
Oct 20070.00060.00340.00440.0048
Nov 2007-0.0022-0.0053-0.0012-0.0038
Dec 2007-0.0014-0.00830.0334-0.0029
Jan 20080.00750.00600.05150.0108
Feb 20080.00030.0012-0.01890.0115
Mar 20080.00780.00040.04390.0009
Apr 2008-0.00170.0140-0.04960.0109
May 2008-0.0002-0.0049-0.01540.0086
Jun 2008-0.0047-0.01630.0321-0.0221
Jul 2008-0.01450.0003-0.03460.0089
Aug 2008-0.00550.0015-0.0526-0.0097
Sep 20080.01560.02250.03760.0228
Oct 2008-0.0027-0.01860.0268-0.0187
Nov 20080.00950.01600.02590.0253
Dec 20080.02110.0130-0.05490.0039
Jan 2009-0.00710.0049-0.0648-0.0045
Feb 2009-0.0000-0.0046-0.0226-0.0119
Mar 2009-0.0265-0.01180.0226-0.0211
Apr 20090.02670.00180.13610.0255
May 2009-0.0230-0.0006-0.0280-0.0077
Jun 20090.0026-0.01080.0899-0.0083
Jul 2009-0.0069-0.00410.0231-0.0054
Aug 2009-0.0284-0.0166-0.05260.0008
Sep 2009-0.0216-0.0133-0.0111-0.0078
Oct 20090.01820.0177-0.05370.0054
Nov 2009-0.0036-0.0047-0.0152-0.0059
Dec 20090.00450.0035-0.01640.0073
Jan 20100.00190.00070.0091-0.0027
Feb 2010-0.0109-0.01520.0283-0.0004
Mar 2010-0.00500.00220.01270.0043
Apr 2010-0.0078-0.0063-0.01210.0049
May 20100.00070.0046-0.01010.0076
Jun 20100.00820.0064-0.0332-0.0005
Jul 20100.00030.00690.00910.0052
Aug 2010-0.00030.0040-0.00860.0051
Sep 20100.00140.0075-0.0010-0.0034
Oct 20100.00620.00920.0247-0.0003
Nov 2010-0.0072-0.00300.0115-0.0005
Dec 2010-0.0004-0.0066-0.0206-0.0117
Jan 2011-0.0060-0.0053-0.0252-0.0033
Feb 2011-0.00960.0001-0.0040-0.0002
Mar 20110.0037-0.00220.00790.0022
Apr 2011-0.00230.0073-0.00470.0045
May 20110.00990.01300.02910.0022
Jun 20110.0031-0.00590.0033-0.0004
Jul 20110.01100.00780.02740.0021
Aug 20110.01370.00270.01190.0041
Sep 20110.0017-0.00180.0063-0.0064
Oct 20110.01800.01560.00170.0094
Nov 20110.01140.00290.01520.0055
Dec 20110.00960.00180.0119-0.0006
Jan 20120.01880.0137-0.01220.0052
Feb 2012-0.0118-0.0129-0.0096-0.0099
Mar 2012-0.00070.0015-0.0076-0.0063
Apr 2012-0.0052-0.00160.00540.0051
May 2012-0.0107-0.00220.00320.0048
Jun 2012-0.00060.00620.0025-0.0016
Jul 20120.00700.00070.01620.0050
Aug 20120.00630.00120.0187-0.0046
Sep 2012-0.0068-0.00440.0021-0.0088
Oct 2012-0.0131-0.0128-0.04070.0037
Nov 20120.0085-0.00060.04510.0019
Dec 2012-0.0057-0.0001-0.0343-0.0015
Jan 2013-0.00780.0006-0.02100.0014
Feb 20130.00710.00140.01110.0061
Mar 2013-0.0031-0.0011-0.01420.0020
Apr 20130.00270.0014-0.0049-0.0030
May 2013-0.0104-0.02350.0170-0.0171
Jun 20130.0006-0.0019-0.0074-0.0070
Jul 2013-0.0067-0.0046-0.0150-0.0006
Aug 20130.0026-0.00480.0052-0.0067
Sep 20130.01140.00680.02630.0034
Oct 20130.0008-0.0017-0.00270.0013
Nov 20130.0010-0.00180.0227-0.0103
Dec 2013-0.00890.0003-0.00570.0027
Jan 2014-0.0008-0.0026-0.00000.0086
Feb 20140.00060.00210.01020.0030
Mar 2014-0.0011-0.0066-0.0236-0.0004
Apr 20140.00730.0038-0.00120.0086
May 20140.00210.00240.00760.0073
Jun 2014-0.00800.0014-0.01530.0018
Jul 20140.0024-0.00990.0157-0.0034
Aug 20140.00350.00490.00320.0083
Sep 2014-0.0042-0.01150.0086-0.0093
Oct 20140.02100.02450.00340.0042
Nov 20140.01140.00640.02260.0078
Dec 2014-0.0052-0.0050-0.0218-0.0032
Jan 2015-0.00230.01040.00010.0157
Feb 20150.0042-0.00220.0200-0.0042
Mar 2015-0.00210.00630.00190.0096
Apr 2015-0.0092-0.0125-0.0101-0.0128
May 2015-0.0073-0.00600.00640.0023
Jun 2015-0.0006-0.00120.0041-0.0116
Jul 20150.01140.01090.04690.0190
Aug 2015-0.0063-0.0121-0.0074-0.0012
Sep 20150.00960.00910.01790.0113
Oct 20150.00790.0010-0.0004-0.0029
Nov 2015-0.0081-0.0008-0.0121-0.0108
Dec 20150.00460.00180.0223-0.0004
Jan 20160.01280.0008-0.00730.0072
Feb 20160.01710.00520.01890.0100
Mar 20160.01440.00670.00090.0064
Apr 2016-0.0094-0.0095-0.0267-0.0076
May 2016-0.00220.0138-0.04950.0045
Jun 20160.01000.00750.02510.0053
Jul 2016-0.00340.0049-0.0122-0.0071
Aug 2016-0.0201-0.0082-0.0496-0.0186
Sep 2016-0.0032-0.00120.0061-0.0068
Oct 2016-0.0043-0.00430.00700.0017
Nov 20160.0013-0.0033-0.0224-0.0104
Dec 2016-0.00470.0031-0.0236-0.0037
Jan 2017-0.0096-0.0020-0.02420.0011
Feb 20170.00360.0076-0.01220.0001
Mar 2017-0.00280.0003-0.0258-0.0060
Apr 2017-0.0027-0.0008-0.0129-0.0051
May 20170.00530.0009-0.0059-0.0071
Jun 2017-0.00290.0021-0.0074-0.0016
Jul 20170.00120.0018-0.01630.0003
Aug 2017-0.0053-0.00110.03050.0024
Sep 20170.0089-0.00470.0008-0.0145
Oct 2017-0.0010-0.00690.0297-0.0014
Nov 20170.01160.00470.01430.0021
Dec 2017-0.0054-0.0103-0.0168-0.0009
Jan 2018-0.0099-0.00940.0039-0.0135
Feb 2018-0.0037-0.01330.0159-0.0071