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
Northern Small Cap Value NOSGX Jan 2006 Apr 2017 0.92 0.73 0.44 0.04 0.04% 0.51% 96.7%
Fidelity Small Cap Enhanced Index FCPEX Jan 2008 Apr 2017 1.00 0.78 0.17 0.06 -0.02% -0.21% 97.5%
iShares S&P Small-Cap 600 Value ETF IJS Jan 2006 Apr 2017 0.95 0.82 0.38 -0.02 0.05% 0.57% 97.5%

Northern Small Cap Value

Factor regression results for Northern Small Cap Value
Ticker NOSGX
Time Period Jan 2006 - Apr 2017
Coefficient of Determination (R2) 96.7%
Adjusted R2 96.6%
Regression F statistic 974.65 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.121 with p-value 0.750)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 6.834 with p-value 0.145)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.92 0.022 41.027 0.000 0.875...0.964
Size (SMB) 0.73 0.039 18.580 0.000 0.654...0.809
Value (HML) 0.44 0.035 12.430 0.000 0.367...0.506
Momentum (MOM) 0.04 0.020 2.034 0.044 0.001...0.080
Alpha (α) 4.22bps 0.001 0.500 0.618 -0.12%...0.21%
Annualized Alpha (α) 0.51%  

Fidelity Small Cap Enhanced Index

Factor regression results for Fidelity Small Cap Enhanced Index
Ticker FCPEX
Time Period Jan 2008 - Apr 2017
Coefficient of Determination (R2) 97.5%
Adjusted R2 97.4%
Regression F statistic 1,053.90 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.250 with p-value 0.901)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 5.199 with p-value 0.267)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.00 0.022 46.070 0.000 0.960...1.047
Size (SMB) 0.78 0.040 19.401 0.000 0.699...0.858
Value (HML) 0.17 0.034 5.037 0.000 0.105...0.241
Momentum (MOM) 0.06 0.019 3.166 0.002 0.023...0.100
Alpha (α) -1.73bps 0.001 -0.198 0.843 -0.19%...0.16%
Annualized Alpha (α) -0.21%  

iShares S&P Small-Cap 600 Value ETF

Factor regression results for iShares S&P Small-Cap 600 Value ETF
Ticker IJS
Time Period Jan 2006 - Apr 2017
Coefficient of Determination (R2) 97.5%
Adjusted R2 97.4%
Regression F statistic 1,264.02 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.048 with p-value 0.595)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 37.205 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.95 0.021 45.736 0.000 0.911...0.994
Size (SMB) 0.82 0.037 22.459 0.000 0.749...0.894
Value (HML) 0.38 0.033 11.609 0.000 0.314...0.443
Momentum (MOM) -0.02 0.019 -1.199 0.233 -0.059...0.015
Alpha (α) 4.78bps 0.001 0.610 0.543 -0.11%...0.20%
Annualized Alpha (α) 0.57%  
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) 68.33 11.19 -5.31 -7.00  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
Northern Small Cap Value NOSGX Jan 2006 Apr 2017 0.51% 62.82 8.19 -2.32 -0.29 72.62 96.7%
Factor regression results
Monthly Factor Premiums (BPS) 72.88 19.16 -4.18 -21.64  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
Fidelity Small Cap Enhanced Index FCPEX Jan 2008 Apr 2017 -0.21% 73.13 14.92 -0.72 -1.34 84.26 97.5%
Factor regression results
Monthly Factor Premiums (BPS) 68.33 11.19 -5.31 -7.00  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
iShares S&P Small-Cap 600 Value ETF IJS Jan 2006 Apr 2017 0.57% 65.10 9.20 -2.01 0.16 77.22 97.5%
Regression residuals
MonthNOSGXFCPEXIJS
Jan 20060.00410.0064
Feb 20060.00830.0054
Mar 20060.0010-0.0007
Apr 2006-0.0085-0.0079
May 2006-0.0069-0.0018
Jun 20060.0059-0.0008
Jul 20060.0000-0.0061
Aug 20060.00490.0014
Sep 20060.00050.0006
Oct 2006-0.00430.0057
Nov 2006-0.0032-0.0048
Dec 2006-0.0085-0.0123
Jan 2007-0.00660.0028
Feb 2007-0.0140-0.0056
Mar 2007-0.0015-0.0003
Apr 2007-0.00410.0015
May 2007-0.00510.0108
Jun 2007-0.0052-0.0102
Jul 2007-0.01650.0024
Aug 20070.02120.0094
Sep 2007-0.0033-0.0043
Oct 2007-0.0007-0.0011
Nov 20070.0040-0.0030
Dec 2007-0.0104-0.0002
Jan 20080.0195-0.00280.0097
Feb 20080.00180.00360.0009
Mar 20080.0153-0.00730.0087
Apr 2008-0.0004-0.0037-0.0026
May 20080.00640.0060-0.0014
Jun 2008-0.0172-0.0034-0.0043
Jul 20080.00760.0048-0.0094
Aug 2008-0.0039-0.0166-0.0052
Sep 20080.02260.01190.0233
Oct 20080.00510.0077-0.0038
Nov 20080.0162-0.01390.0048
Dec 20080.01870.01130.0190
Jan 2009-0.01910.0045-0.0209
Feb 2009-0.0119-0.0115-0.0075
Mar 2009-0.0074-0.0133-0.0253
Apr 20090.01260.00880.0232
May 2009-0.0181-0.0007-0.0262
Jun 2009-0.0129-0.00780.0006
Jul 20090.0102-0.0101-0.0023
Aug 2009-0.0194-0.0079-0.0214
Sep 2009-0.0115-0.0030-0.0221
Oct 20090.0129-0.00200.0146
Nov 2009-0.0016-0.0004-0.0033
Dec 2009-0.0028-0.00240.0046
Jan 2010-0.0032-0.00600.0007
Feb 2010-0.0130-0.0097-0.0064
Mar 2010-0.0055-0.0057-0.0016
Apr 2010-0.0066-0.0107-0.0042
May 20100.00020.0118-0.0022
Jun 20100.00980.00770.0023
Jul 20100.00980.00370.0005
Aug 20100.00500.0037-0.0022
Sep 20100.0018-0.0094-0.0023
Oct 20100.00670.00280.0036
Nov 2010-0.0043-0.0064-0.0081
Dec 2010-0.00440.00240.0033
Jan 2011-0.0063-0.0010-0.0049
Feb 20110.00280.0115-0.0078
Mar 2011-0.0039-0.00360.0026
Apr 20110.00190.0073-0.0050
May 20110.01170.00410.0075
Jun 20110.00280.00740.0033
Jul 20110.00920.00030.0096
Aug 20110.01380.01520.0110
Sep 20110.0002-0.0104-0.0002
Oct 20110.02160.02580.0171
Nov 20110.0012-0.00470.0121
Dec 20110.0083-0.00400.0123
Jan 20120.00620.01390.0152
Feb 2012-0.0153-0.0022-0.0115
Mar 2012-0.00050.00080.0008
Apr 2012-0.0065-0.0079-0.0047
May 2012-0.0089-0.0125-0.0097
Jun 2012-0.00320.0002-0.0004
Jul 20120.00170.01620.0081
Aug 2012-0.0005-0.00340.0069
Sep 2012-0.0072-0.0037-0.0055
Oct 2012-0.00340.0081-0.0084
Nov 2012-0.00430.00920.0075
Dec 2012-0.00280.0019-0.0025
Jan 20130.00250.0069-0.0072
Feb 20130.0047-0.00150.0074
Mar 20130.0015-0.0054-0.0027
Apr 2013-0.0036-0.00320.0035
May 2013-0.0169-0.0116-0.0083
Jun 2013-0.0015-0.00370.0003
Jul 2013-0.0034-0.0001-0.0057
Aug 2013-0.0108-0.0067-0.0007
Sep 20130.00630.00770.0106
Oct 20130.00490.00080.0025
Nov 20130.00140.00330.0013
Dec 2013-0.0021-0.0058-0.0090
Jan 2014-0.0115-0.0045-0.0028
Feb 20140.0042-0.01130.0009
Mar 20140.00210.00770.0044
Apr 20140.00820.00120.0082
May 20140.00070.00200.0026
Jun 20140.0003-0.0059-0.0092
Jul 2014-0.00720.00370.0030
Aug 20140.00550.00810.0032
Sep 2014-0.0117-0.0041-0.0049
Oct 20140.03240.01390.0184
Nov 20140.0022-0.00460.0088
Dec 20140.0003-0.0016-0.0027
Jan 20150.00980.0170-0.0054
Feb 2015-0.00810.00510.0019
Mar 20150.00600.0121-0.0019
Apr 2015-0.0124-0.0126-0.0086
May 2015-0.00340.0067-0.0065
Jun 20150.0003-0.0093-0.0013
Jul 20150.01320.01470.0098
Aug 2015-0.0094-0.0124-0.0037
Sep 20150.02180.01460.0120
Oct 20150.0002-0.00440.0070
Nov 2015-0.0053-0.0077-0.0085
Dec 2015-0.0030-0.00600.0030
Jan 20160.00880.00500.0158
Feb 20160.00910.01650.0153
Mar 20160.0063-0.01540.0146
Apr 2016-0.0186-0.0197-0.0074
May 20160.01820.0008-0.0037
Jun 20160.0004-0.00210.0094
Jul 2016-0.00920.0020-0.0059
Aug 2016-0.0109-0.0090-0.0168
Sep 2016-0.00820.0005-0.0055
Oct 20160.0029-0.00100.0014
Nov 20160.00580.02140.0092
Dec 20160.00410.0190-0.0004
Jan 2017-0.0082-0.0106-0.0127
Feb 20170.0038-0.00580.0015
Mar 2017-0.0058-0.0085-0.0068
Apr 2017-0.0053-0.0009-0.0049