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

Schwab Fdmtl Intl Sm Co Idx

Factor regression results for Schwab Fdmtl Intl Sm Co Idx
Ticker SFILX
Time Period Feb 2008 - Dec 2018
Coefficient of Determination (R2) 96.4%
Adjusted R2 96.3%
Regression F statistic 669.59 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.138 with p-value 0.768)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 18.842 with p-value 0.002)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.04 0.024 42.489 0.000 0.992...1.089
Size (SMB) 0.42 0.060 7.005 0.000 0.304...0.543
Value (HML) 0.17 0.076 2.271 0.025 0.022...0.321
Profitability (RMW) 0.26 0.109 2.429 0.017 0.049...0.480
Investment (CMA) 0.02 0.080 0.251 0.802 -0.138...0.178
Alpha (α) 2.00bps 0.001 0.196 0.845 -0.18%...0.22%
Annualized Alpha (α) 0.24%  
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.
  • 5-factor model: Ra = Rrf + Bmkt × ( Rmkt - Rrf ) + Bsmb × SMB + Bhml × HML + Brmw × RMW + Bcma × CMA + 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
    Brmw
    Profitability loading factor
    RMW
    Robust Minus Weak: The profitability premium
    Bcma
    Investment loading factor
    CMA
    Conservative Minus Aggressive: The conservative investment 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) 27.74 17.15 4.18 34.20 13.56  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML RMW CMA Total R2
Schwab Fdmtl Intl Sm Co Idx SFILX Feb 2008 Dec 2018 0.24% 28.87 7.26 0.72 9.04 0.27 48.15 96.4%
Regression residuals
MonthSFILX
Feb 2008-0.0261
Mar 20080.0185
Apr 2008-0.0198
May 2008-0.0040
Jun 2008-0.0116
Jul 20080.0078
Aug 20080.0103
Sep 20080.0165
Oct 20080.0015
Nov 20080.0177
Dec 20080.0202
Jan 2009-0.0072
Feb 2009-0.0084
Mar 20090.0188
Apr 20090.0482
May 20090.0125
Jun 2009-0.0029
Jul 2009-0.0072
Aug 20090.0206
Sep 2009-0.0021
Oct 2009-0.0174
Nov 2009-0.0007
Dec 2009-0.0019
Jan 2010-0.0032
Feb 20100.0031
Mar 20100.0003
Apr 2010-0.0005
May 2010-0.0014
Jun 20100.0105
Jul 20100.0014
Aug 2010-0.0020
Sep 20100.0032
Oct 2010-0.0083
Nov 20100.0038
Dec 20100.0073
Jan 2011-0.0112
Feb 2011-0.0102
Mar 20110.0076
Apr 2011-0.0100
May 20110.0004
Jun 20110.0066
Jul 20110.0036
Aug 20110.0093
Sep 2011-0.0105
Oct 2011-0.0095
Nov 20110.0221
Dec 2011-0.0203
Jan 20120.0084
Feb 2012-0.0085
Mar 2012-0.0019
Apr 2012-0.0105
May 20120.0001
Jun 2012-0.0014
Jul 2012-0.0136
Aug 20120.0005
Sep 2012-0.0028
Oct 2012-0.0004
Nov 20120.0015
Dec 20120.0061
Jan 2013-0.0190
Feb 20130.0093
Mar 20130.0106
Apr 2013-0.0012
May 2013-0.0206
Jun 20130.0199
Jul 2013-0.0037
Aug 2013-0.0085
Sep 20130.0075
Oct 2013-0.0070
Nov 2013-0.0031
Dec 20130.0013
Jan 2014-0.0090
Feb 2014-0.0008
Mar 2014-0.0092
Apr 2014-0.0042
May 20140.0034
Jun 2014-0.0020
Jul 2014-0.0024
Aug 20140.0032
Sep 2014-0.0032
Oct 20140.0163
Nov 2014-0.0109
Dec 20140.0096
Jan 20150.0080
Feb 20150.0094
Mar 2015-0.0006
Apr 2015-0.0144
May 20150.0027
Jun 20150.0013
Jul 20150.0024
Aug 20150.0098
Sep 20150.0032
Oct 2015-0.0029
Nov 20150.0070
Dec 2015-0.0044
Jan 20160.0121
Feb 2016-0.0040
Mar 2016-0.0053
Apr 2016-0.0098
May 20160.0168
Jun 2016-0.0002
Jul 2016-0.0002
Aug 2016-0.0064
Sep 20160.0064
Oct 2016-0.0031
Nov 20160.0048
Dec 2016-0.0079
Jan 2017-0.0046
Feb 20170.0023
Mar 2017-0.0078
Apr 20170.0028
May 2017-0.0111
Jun 20170.0007
Jul 2017-0.0029
Aug 2017-0.0026
Sep 20170.0005
Oct 20170.0024
Nov 2017-0.0003
Dec 2017-0.0021
Jan 2018-0.0063
Feb 2018-0.0069
Mar 20180.0083
Apr 2018-0.0019
May 2018-0.0023
Jun 2018-0.0017
Jul 2018-0.0038
Aug 2018-0.0003
Sep 2018-0.0042
Oct 2018-0.0027
Nov 2018-0.0003
Dec 2018-0.0089