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 Apr 2006 Dec 2018 0.95 0.83 0.38 -0.02 0.03% 0.39% 97.5%
iShares Russell 2000 Value ETF IWN Apr 2006 Dec 2018 0.95 0.79 0.49 0.01 -0.06% -0.76% 98.1%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Dec 2018 1.06 1.19 0.72 -0.50 0.04% 0.46% 90.5%
Vanguard Small-Cap Value ETF VBR Apr 2006 Dec 2018 1.01 0.56 0.33 -0.07 0.00% 0.00% 97.7%

iShares S&P Small-Cap 600 Value ETF

Factor regression results for iShares S&P Small-Cap 600 Value ETF
Ticker IJS
Time Period Apr 2006 - Dec 2018
Coefficient of Determination (R2) 97.5%
Adjusted R2 97.5%
Regression F statistic 1,462.81 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.012 with p-value 0.516)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 37.316 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.95 0.019 50.676 0.000 0.918...0.992
Size (SMB) 0.83 0.033 25.251 0.000 0.769...0.900
Value (HML) 0.38 0.030 12.465 0.000 0.320...0.440
Momentum (MOM) -0.02 0.018 -1.307 0.193 -0.058...0.012
Alpha (α) 3.24bps 0.001 0.451 0.653 -0.11%...0.17%
Annualized Alpha (α) 0.39%  

iShares Russell 2000 Value ETF

Factor regression results for iShares Russell 2000 Value ETF
Ticker IWN
Time Period Apr 2006 - Dec 2018
Coefficient of Determination (R2) 98.1%
Adjusted R2 98.0%
Regression F statistic 1,878.75 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.255 with p-value 0.939)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 10.129 with p-value 0.038)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.95 0.017 57.423 0.000 0.917...0.983
Size (SMB) 0.79 0.029 27.158 0.000 0.731...0.845
Value (HML) 0.49 0.027 18.130 0.000 0.432...0.538
Momentum (MOM) 0.01 0.016 0.891 0.374 -0.017...0.045
Alpha (α) -6.36bps 0.001 -1.006 0.316 -0.19%...0.06%
Annualized Alpha (α) -0.76%  

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 - Dec 2018
Coefficient of Determination (R2) 90.5%
Adjusted R2 90.2%
Regression F statistic 351.24 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.029 with p-value 0.557)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 49.958 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.056 18.857 0.000 0.946...1.168
Size (SMB) 1.19 0.098 12.154 0.000 1.001...1.389
Value (HML) 0.72 0.091 7.915 0.000 0.539...0.897
Momentum (MOM) -0.50 0.053 -9.374 0.000 -0.601...-0.392
Alpha (α) 3.82bps 0.002 0.178 0.859 -0.38%...0.46%
Annualized Alpha (α) 0.46%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Apr 2006 - Dec 2018
Coefficient of Determination (R2) 97.7%
Adjusted R2 97.6%
Regression F statistic 1,566.25 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.390 with p-value 0.992)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 10.560 with p-value 0.032)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.018 56.612 0.000 0.971...1.041
Size (SMB) 0.56 0.031 18.119 0.000 0.503...0.626
Value (HML) 0.33 0.029 11.479 0.000 0.273...0.387
Momentum (MOM) -0.07 0.017 -4.156 0.000 -0.103...-0.037
Alpha (α) 0.04bps 0.001 0.005 0.996 -0.13%...0.13%
Annualized Alpha (α) 0.00%  
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) 62.54 0.78 -13.91 3.87  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
iShares S&P Small-Cap 600 Value ETF IJS Apr 2006 Dec 2018 0.39% 59.73 0.65 -5.29 -0.09 58.25 97.5%
iShares Russell 2000 Value ETF IWN Apr 2006 Dec 2018 -0.76% 59.42 0.62 -6.75 0.05 46.98 98.1%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Dec 2018 0.46% 66.11 0.94 -9.99 -1.92 58.95 90.5%
Vanguard Small-Cap Value ETF VBR Apr 2006 Dec 2018 0.00% 62.93 0.44 -4.59 -0.27 58.54 97.7%
Regression residuals
MonthIJSIWNRZVVBR
Apr 2006-0.0076-0.0086-0.0070-0.0119
May 2006-0.00120.0023-0.02550.0003
Jun 2006-0.00060.00670.01980.0097
Jul 2006-0.00550.01020.00350.0034
Aug 20060.00140.0080-0.0315-0.0052
Sep 20060.0009-0.0030-0.0008-0.0068
Oct 20060.00560.0048-0.00140.0000
Nov 2006-0.0048-0.0009-0.01110.0057
Dec 2006-0.0121-0.00760.0015-0.0122
Jan 20070.0029-0.00260.00770.0011
Feb 2007-0.0056-0.0071-0.00650.0019
Mar 2007-0.00010.0044-0.0078-0.0020
Apr 20070.0019-0.00830.0095-0.0070
May 20070.01090.0057-0.00790.0015
Jun 2007-0.0101-0.0092-0.0097-0.0075
Jul 20070.0030-0.01800.0214-0.0163
Aug 20070.00960.0183-0.01820.0114
Sep 2007-0.0038-0.00180.0024-0.0046
Oct 2007-0.00090.00120.00370.0054
Nov 2007-0.0024-0.0043-0.0009-0.0041
Dec 20070.0000-0.00700.0329-0.0019
Jan 20080.01000.01090.05310.0105
Feb 20080.00120.0025-0.01930.0123
Mar 20080.00880.00140.04350.0018
Apr 2008-0.00230.0122-0.04940.0110
May 2008-0.0016-0.0069-0.01640.0095
Jun 2008-0.0040-0.01420.0307-0.0208
Jul 2008-0.00960.0060-0.03360.0101
Aug 2008-0.00560.0016-0.0525-0.0091
Sep 20080.02370.03300.03880.0239
Oct 2008-0.0028-0.01470.0265-0.0188
Nov 20080.00560.01370.02510.0247
Dec 20080.01860.0108-0.05510.0041
Jan 2009-0.0204-0.0059-0.0660-0.0068
Feb 2009-0.0070-0.0091-0.0235-0.0127
Mar 2009-0.0255-0.01220.0249-0.0211
Apr 20090.0221-0.00250.13900.0237
May 2009-0.0260-0.0040-0.0266-0.0090
Jun 20090.0005-0.01320.0888-0.0075
Jul 2009-0.0027-0.00120.0242-0.0041
Aug 2009-0.0214-0.0097-0.05040.0015
Sep 2009-0.0224-0.0146-0.0109-0.0074
Oct 20090.01550.0154-0.05340.0047
Nov 2009-0.0029-0.0055-0.0148-0.0056
Dec 20090.00390.0023-0.01760.0089
Jan 20100.00080.00110.0098-0.0030
Feb 2010-0.0065-0.01170.02800.0011
Mar 2010-0.00180.00360.01250.0059
Apr 2010-0.0047-0.0037-0.01250.0069
May 2010-0.00190.0043-0.01020.0072
Jun 20100.00290.0028-0.0330-0.0018
Jul 20100.00050.00520.00870.0060
Aug 2010-0.00150.0040-0.00820.0045
Sep 2010-0.00280.0010-0.0022-0.0027
Oct 20100.00360.00560.02420.0001
Nov 2010-0.0084-0.00430.01050.0004
Dec 20100.0031-0.0045-0.0197-0.0106
Jan 2011-0.0045-0.0042-0.0248-0.0032
Feb 2011-0.00800.0009-0.00400.0010
Mar 20110.0024-0.00350.00700.0031
Apr 2011-0.00480.0042-0.00470.0046
May 20110.00780.01140.02950.0020
Jun 20110.0035-0.00500.00350.0001
Jul 20110.01000.00760.02740.0020
Aug 20110.01180.00240.01240.0034
Sep 20110.0006-0.00080.0073-0.0073
Oct 20110.01650.01160.00130.0104
Nov 20110.01230.00370.01490.0063
Dec 20110.01250.00450.01230.0003
Jan 20120.01490.0094-0.01210.0049
Feb 2012-0.0112-0.0134-0.0092-0.0096
Mar 20120.00090.0024-0.0076-0.0056
Apr 2012-0.0044-0.00080.00510.0057
May 2012-0.00930.00050.00260.0056
Jun 2012-0.00050.00550.0027-0.0010
Jul 20120.00860.00190.01630.0054
Aug 20120.00690.00150.0187-0.0043
Sep 2012-0.0055-0.00350.0021-0.0082
Oct 2012-0.0081-0.0073-0.03970.0046
Nov 20120.0076-0.00160.04500.0023
Dec 2012-0.00270.0031-0.0338-0.0007
Jan 2013-0.0073-0.0001-0.02110.0019
Feb 20130.00760.00160.01100.0065
Mar 2013-0.0027-0.0017-0.01420.0029
Apr 20130.00400.0022-0.0048-0.0030
May 2013-0.0084-0.02190.0171-0.0163
Jun 20130.0004-0.0017-0.0077-0.0066
Jul 2013-0.0059-0.0053-0.01530.0005
Aug 2013-0.0005-0.00700.0049-0.0069
Sep 20130.01040.00480.02550.0045
Oct 20130.0027-0.0008-0.00210.0019
Nov 20130.0013-0.00230.0225-0.0096
Dec 2013-0.0088-0.0003-0.00550.0030
Jan 2014-0.0026-0.0035-0.00020.0088
Feb 20140.00090.00120.01030.0038
Mar 20140.0047-0.0007-0.02200.0004
Apr 20140.00880.00570.00020.0081
May 20140.00300.00270.00830.0078
Jun 2014-0.0094-0.0005-0.01610.0025
Jul 20140.0038-0.00810.0167-0.0036
Aug 20140.00320.00360.00330.0090
Sep 2014-0.0042-0.01100.0094-0.0095
Oct 20140.01800.02120.00230.0048
Nov 20140.00920.00350.02290.0077
Dec 2014-0.0029-0.0025-0.0219-0.0019
Jan 2015-0.00500.0083-0.00060.0156
Feb 20150.0018-0.00590.0208-0.0039
Mar 2015-0.00210.00660.00170.0108
Apr 2015-0.0082-0.0111-0.0087-0.0134
May 2015-0.0064-0.00580.00690.0038
Jun 2015-0.0014-0.00170.0028-0.0109
Jul 20150.01060.00880.04590.0192
Aug 2015-0.0035-0.0074-0.0065-0.0006
Sep 20150.01260.01260.01830.0121
Oct 20150.0071-0.0014-0.0000-0.0031
Nov 2015-0.0088-0.0015-0.0127-0.0097
Dec 20150.00360.00120.0225-0.0004
Jan 20160.01650.0060-0.00700.0073
Feb 20160.01530.00390.01920.0099
Mar 20160.01440.00540.00190.0070
Apr 2016-0.0075-0.0072-0.0259-0.0073
May 2016-0.00350.0121-0.04950.0048
Jun 20160.00950.00680.02460.0059
Jul 2016-0.00620.0015-0.0126-0.0069
Aug 2016-0.0169-0.0048-0.0482-0.0176
Sep 2016-0.0056-0.00330.0055-0.0066
Oct 20160.00210.00250.00850.0023
Nov 20160.00840.0032-0.0217-0.0081
Dec 2016-0.00030.0071-0.0226-0.0025
Jan 2017-0.0125-0.0050-0.02420.0009
Feb 20170.00190.0051-0.0118-0.0001
Mar 2017-0.0068-0.0035-0.0259-0.0061
Apr 2017-0.0049-0.0031-0.0133-0.0050
May 20170.0023-0.0024-0.0055-0.0074
Jun 2017-0.00190.0032-0.0076-0.0008
Jul 20170.00180.0018-0.01640.0006
Aug 2017-0.0065-0.00260.02990.0023
Sep 20170.0109-0.00290.0005-0.0131
Oct 20170.0006-0.00620.0296-0.0008
Nov 20170.01220.00470.01540.0028
Dec 2017-0.0054-0.0104-0.0167-0.0010
Jan 2018-0.0100-0.01120.0028-0.0136
Feb 2018-0.0039-0.01270.0154-0.0066
Mar 20180.00190.0027-0.01470.0079
Apr 20180.00200.0037-0.0017-0.0081
May 20180.00080.00590.01770.0006
Jun 20180.00040.0016-0.0013-0.0031
Jul 20180.00990.0021-0.01450.0009
Aug 20180.0032-0.00010.0323-0.0017
Sep 2018-0.0081-0.00090.0000-0.0011
Oct 2018-0.00260.00320.0081-0.0012
Nov 2018-0.00750.0036-0.04950.0072
Dec 2018-0.0069-0.00420.00660.0010