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.

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 Sep 2017 0.96 0.81 0.50 0.01 0.06% 0.68% 95.6%
iShares Russell 2000 Value ETF IWN Aug 2000 Sep 2017 0.93 0.76 0.60 0.04 -0.01% -0.15% 96.8%
Guggenheim S&P SmallCap 600 PureVal ETF RZV Apr 2006 Sep 2017 1.05 1.19 0.73 -0.51 0.02% 0.23% 90.6%
Vanguard Small-Cap Value ETF VBR Feb 2004 Sep 2017 1.01 0.57 0.35 -0.05 0.05% 0.56% 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 - Sep 2017
Coefficient of Determination (R2) 95.6%
Adjusted R2 95.5%
Regression F statistic 1,085.30 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.713 with p-value 0.019)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 16.432 with p-value 0.002)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.022 44.051 0.000 0.913...0.999
Size (SMB) 0.81 0.034 23.744 0.000 0.739...0.873
Value (HML) 0.50 0.028 17.952 0.000 0.442...0.551
Momentum (MOM) 0.01 0.017 0.426 0.670 -0.027...0.042
Alpha (α) 5.68bps 0.001 0.688 0.493 -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 - Sep 2017
Coefficient of Determination (R2) 96.8%
Adjusted R2 96.7%
Regression F statistic 1,506.49 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.157 with p-value 0.870)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 27.411 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.93 0.018 51.761 0.000 0.890...0.961
Size (SMB) 0.76 0.028 27.247 0.000 0.707...0.817
Value (HML) 0.60 0.023 26.352 0.000 0.555...0.645
Momentum (MOM) 0.04 0.014 2.604 0.010 0.009...0.066
Alpha (α) -1.25bps 0.001 -0.183 0.855 -0.15%...0.12%
Annualized Alpha (α) -0.15%  

Guggenheim S&P SmallCap 600 PureVal ETF

Factor regression results for Guggenheim S&P SmallCap 600 PureVal ETF
Ticker RZV
Time Period Apr 2006 - Sep 2017
Coefficient of Determination (R2) 90.6%
Adjusted R2 90.4%
Regression F statistic 321.87 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.023 with p-value 0.539)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 44.741 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.05 0.061 17.147 0.000 0.929...1.171
Size (SMB) 1.19 0.108 10.965 0.000 0.974...1.403
Value (HML) 0.73 0.095 7.657 0.000 0.542...0.920
Momentum (MOM) -0.51 0.055 -9.310 0.000 -0.623...-0.405
Alpha (α) 1.91bps 0.002 0.083 0.934 -0.44%...0.48%
Annualized Alpha (α) 0.23%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Feb 2004 - Sep 2017
Coefficient of Determination (R2) 97.2%
Adjusted R2 97.1%
Regression F statistic 1,384.47 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.245 with p-value 0.939)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 16.629 with p-value 0.002)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.020 51.116 0.000 0.975...1.054
Size (SMB) 0.57 0.033 17.222 0.000 0.504...0.635
Value (HML) 0.35 0.030 11.584 0.000 0.289...0.408
Momentum (MOM) -0.05 0.017 -3.092 0.002 -0.088...-0.019
Alpha (α) 4.68bps 0.001 0.668 0.505 -0.09%...0.18%
Annualized Alpha (α) 0.56%  
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 20000.0131-0.0054
Sep 20000.02470.0157
Oct 20000.01460.0092
Nov 20000.02240.0386
Dec 20000.06700.0252
Jan 20010.0159-0.0166
Feb 2001-0.00940.0118
Mar 2001-0.0202-0.0002
Apr 20010.00750.0022
May 2001-0.0182-0.0232
Jun 2001-0.00830.0100
Jul 20010.0215-0.0098
Aug 20010.01560.0237
Sep 2001-0.0196-0.0000
Oct 2001-0.0019-0.0055
Nov 2001-0.0048-0.0064
Dec 20010.0085-0.0030
Jan 20020.0068-0.0008
Feb 20020.01170.0143
Mar 20020.0053-0.0067
Apr 20020.02000.0149
May 2002-0.0078-0.0069
Jun 2002-0.0146-0.0006
Jul 2002-0.0222-0.0088
Aug 2002-0.0038-0.0021
Sep 2002-0.0100-0.0156
Oct 2002-0.00020.0032
Nov 2002-0.01970.0119
Dec 20020.0141-0.0093
Jan 2003-0.0243-0.0077
Feb 2003-0.0142-0.0030
Mar 2003-0.01040.0032
Apr 2003-0.00100.0089
May 2003-0.00070.0148
Jun 2003-0.0033-0.0197
Jul 2003-0.0113-0.0032
Aug 2003-0.0051-0.0145
Sep 2003-0.0311-0.0068
Oct 20030.0009-0.0059
Nov 20030.00320.0018
Dec 2003-0.00260.0042
Jan 2004-0.0328-0.0204
Feb 20040.01960.01720.0190
Mar 20040.01420.00890.0174
Apr 20040.0068-0.0049-0.0214
May 20040.00690.00910.0111
Jun 20040.00920.00610.0112
Jul 20040.0001-0.00580.0107
Aug 20040.00810.01730.0149
Sep 20040.0063-0.00190.0035
Oct 2004-0.00510.0023-0.0014
Nov 20040.00490.00750.0078
Dec 2004-0.0197-0.0138-0.0102
Jan 2005-0.0060-0.0162-0.0070
Feb 20050.0044-0.00540.0016
Mar 2005-0.0039-0.0041-0.0013
Apr 20050.00510.0030-0.0028
May 20050.00460.00690.0196
Jun 2005-0.00340.00140.0041
Jul 2005-0.00310.0025-0.0030
Aug 2005-0.0097-0.0165-0.0092
Sep 2005-0.0071-0.01440.0018
Oct 2005-0.0094-0.0086-0.0095
Nov 20050.00940.0139-0.0034
Dec 2005-0.0105-0.0104-0.0021
Jan 20060.0049-0.00290.0004
Feb 20060.00610.00870.0063
Mar 2006-0.00140.0030-0.0043
Apr 2006-0.0115-0.0124-0.0070-0.0130
May 2006-0.0041-0.0019-0.02680.0004
Jun 2006-0.00240.00460.02010.0089
Jul 2006-0.00960.00560.00260.0031
Aug 20060.00440.0110-0.0315-0.0050
Sep 20060.0005-0.0032-0.0008-0.0072
Oct 20060.00590.0056-0.0009-0.0008
Nov 2006-0.0045-0.0006-0.01090.0052
Dec 2006-0.0166-0.01210.0014-0.0134
Jan 20070.0027-0.00270.00810.0005
Feb 2007-0.0050-0.0074-0.00650.0017
Mar 2007-0.00090.0037-0.0071-0.0029
Apr 20070.0024-0.00710.0099-0.0074
May 20070.01070.0061-0.00750.0008
Jun 2007-0.0089-0.0088-0.0094-0.0077
Jul 20070.0051-0.01690.0221-0.0162
Aug 20070.01190.0205-0.01770.0113
Sep 2007-0.0040-0.00100.0037-0.0056
Oct 20070.00030.00300.00520.0045
Nov 2007-0.0023-0.0055-0.0009-0.0039
Dec 2007-0.0015-0.00860.0342-0.0032
Jan 20080.00780.00630.05090.0112
Feb 20080.00020.0009-0.01820.0113
Mar 20080.00770.00010.04440.0008
Apr 2008-0.00190.0136-0.04890.0105
May 2008-0.0003-0.0052-0.01500.0085
Jun 2008-0.0048-0.01660.0328-0.0222
Jul 2008-0.01440.0005-0.03490.0093
Aug 2008-0.00540.0015-0.0529-0.0095
Sep 20080.01580.02260.03770.0231
Oct 2008-0.0027-0.01870.0269-0.0185
Nov 20080.00940.01560.02660.0249
Dec 20080.02110.0131-0.05540.0041
Jan 2009-0.00700.0048-0.0655-0.0043
Feb 2009-0.0000-0.0048-0.0227-0.0117
Mar 2009-0.0264-0.01190.0225-0.0212
Apr 20090.02730.00260.13350.0266
May 2009-0.0229-0.0007-0.0283-0.0078
Jun 20090.0025-0.01110.0904-0.0084
Jul 2009-0.0070-0.00420.0234-0.0055
Aug 2009-0.0283-0.0165-0.05250.0008
Sep 2009-0.0216-0.0133-0.0112-0.0077
Oct 20090.01800.0172-0.05310.0049
Nov 2009-0.0038-0.0051-0.0143-0.0064
Dec 20090.00450.0034-0.01620.0075
Jan 20100.00200.00070.0087-0.0025
Feb 2010-0.0111-0.01550.0292-0.0007
Mar 2010-0.00520.00190.01370.0039
Apr 2010-0.0079-0.0064-0.01170.0050
May 20100.00080.0046-0.01030.0079
Jun 20100.00820.0063-0.0334-0.0005
Jul 20100.00010.00650.01000.0048
Aug 2010-0.00030.0038-0.00840.0050
Sep 20100.00120.0071-0.0004-0.0037
Oct 20100.00610.00880.0252-0.0006
Nov 2010-0.0072-0.00320.0117-0.0004
Dec 2010-0.0005-0.0068-0.0201-0.0118
Jan 2011-0.0061-0.0056-0.0246-0.0037
Feb 2011-0.0097-0.0002-0.0034-0.0004
Mar 20110.0036-0.00240.00830.0021
Apr 2011-0.00250.0070-0.00430.0042
May 20110.00980.01280.02930.0021
Jun 20110.0031-0.00610.0037-0.0005
Jul 20110.01090.00760.02760.0020
Aug 20110.01370.00250.01210.0040
Sep 20110.0018-0.00190.0062-0.0064
Oct 20110.01780.01530.00220.0091
Nov 20110.01120.00260.01590.0053
Dec 20110.00950.00160.0126-0.0008
Jan 20120.01880.0137-0.01250.0053
Feb 2012-0.0120-0.0133-0.0089-0.0103
Mar 2012-0.00090.0012-0.0069-0.0066
Apr 2012-0.0053-0.00190.00610.0049
May 2012-0.0108-0.00240.00370.0047
Jun 2012-0.00070.00590.0029-0.0017
Jul 20120.00680.00030.01710.0045
Aug 20120.00620.00110.0190-0.0047
Sep 2012-0.0069-0.00460.0024-0.0089
Oct 2012-0.0131-0.0129-0.04020.0037
Nov 20120.0084-0.00090.04540.0018
Dec 2012-0.0057-0.0001-0.0342-0.0014
Jan 2013-0.00790.0004-0.02060.0012
Feb 20130.00690.00110.01160.0059
Mar 2013-0.0032-0.0014-0.01360.0017
Apr 20130.00260.0011-0.0042-0.0034
May 2013-0.0105-0.02360.0173-0.0171
Jun 20130.0006-0.0020-0.0073-0.0070
Jul 2013-0.0068-0.0049-0.0144-0.0009
Aug 20130.0026-0.00490.0052-0.0067
Sep 20130.01130.00650.02680.0032
Oct 20130.0006-0.0021-0.00190.0009
Nov 20130.0009-0.00200.0231-0.0105
Dec 2013-0.0090-0.0000-0.00520.0024
Jan 2014-0.0008-0.00270.00010.0086
Feb 20140.00040.00170.01100.0026
Mar 2014-0.0011-0.0067-0.0232-0.0004
Apr 20140.00720.0036-0.00080.0083
May 20140.00190.00200.00830.0070
Jun 2014-0.00810.0012-0.01510.0018
Jul 20140.0023-0.01020.0163-0.0037
Aug 20140.00330.00460.00380.0080
Sep 2014-0.0043-0.01180.0092-0.0096
Oct 20140.02090.02440.00340.0043
Nov 20140.01120.00600.02320.0074
Dec 2014-0.0052-0.0051-0.0216-0.0031
Jan 2015-0.00250.01010.00060.0155
Feb 20150.0041-0.00250.0203-0.0044
Mar 2015-0.00220.00620.00210.0097
Apr 2015-0.0091-0.0126-0.0101-0.0129
May 2015-0.0075-0.00640.00720.0019
Jun 2015-0.0006-0.00140.0043-0.0115
Jul 20150.01100.01020.04860.0181
Aug 2015-0.0061-0.0120-0.0076-0.0009
Sep 20150.00940.00870.01880.0110
Oct 20150.00770.00070.0002-0.0033
Nov 2015-0.0082-0.0009-0.0119-0.0107
Dec 20150.00440.00140.0230-0.0007
Jan 20160.01280.0006-0.00680.0070
Feb 20160.01710.00510.01870.0101
Mar 20160.01440.00650.00110.0063
Apr 2016-0.0093-0.0094-0.0268-0.0074
May 2016-0.00240.0135-0.04870.0042
Jun 20160.00990.00710.02560.0050
Jul 2016-0.00340.0048-0.0122-0.0071
Aug 2016-0.0200-0.0083-0.0495-0.0185
Sep 2016-0.0032-0.00130.0061-0.0068
Oct 2016-0.0044-0.00460.00790.0013
Nov 20160.0013-0.0031-0.0225-0.0100
Dec 2016-0.00480.0029-0.0231-0.0038
Jan 2017-0.0097-0.0023-0.02380.0008
Feb 20170.00350.0073-0.0117-0.0003
Mar 2017-0.00290.0001-0.0258-0.0060
Apr 2017-0.0028-0.0010-0.0126-0.0053
May 20170.00510.0004-0.0052-0.0075
Jun 2017-0.00290.0020-0.0072-0.0015
Jul 20170.00110.0015-0.0156-0.0000
Aug 2017-0.0053-0.00140.03140.0021
Sep 20170.0087-0.00490.0005-0.0144