Fama-French Factor Regression Analysis

This factor regression tool supports factor regression analysis of individual assets or a portfolio of assets using the given risk factor model. The multiple linear regression indicates how well the returns of the given assets or a portfolio are explained by the risk factor exposures. The supported equity risk factor models include:

Additional supported equity factors include the short and long-term reversal factors (STREV, LTREV) based on Fama-French factor data, quality (QMJ) factor based on both AQR and Alpha Architect factor data, and bet against beta (BAB) factor based on AQR factor data.

For fixed income 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 exposures. 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.

Portfolio Assets
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Asset 2
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Asset 5
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Factor Analysis Results

Berkshire Hathaway Inc.

Factor regression results for Berkshire Hathaway Inc.
Ticker BRK.A
Time Period May 1985 - Apr 2019
Coefficient of Determination (R2) 30.8%
Adjusted R2 29.8%
Regression F statistic 29.80 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.057 with p-value 0.708)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.882 with p-value 0.693)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.88 0.077 11.415 0.000 0.727...1.029
Size (SMB) -0.34 0.118 -2.896 0.004 -0.573...-0.110
Value (HML-DEV) 0.24 0.123 1.979 0.049 0.002...0.484
Momentum (MOM) 0.02 0.098 0.172 0.864 -0.176...0.210
Quality (QMJ) 0.42 0.164 2.552 0.011 0.096...0.741
Low Beta (BAB) 0.24 0.083 2.892 0.004 0.077...0.405
Alpha (α) 16.22bps 0.003 0.558 0.577 -0.41%...0.73%
Annualized Alpha (α) 1.95%  
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 × MOM + 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
    Bqmj
    Quality loading factor
    QMJ
    Quality Minus Junk factor
    Bbab
    Low Beta loading factor
    BAB
    Betting Against Beta factor
    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) 68.25 -0.44 9.52 59.57 48.35 78.83  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML-DEV MOM QMJ BAB Total R2
Berkshire Hathaway Inc. BRK.A May 1985 Apr 2019 1.95% 59.92 0.15 2.31 1.01 20.23 19.00 118.84 30.8%
Regression residuals
MonthBRK.A
May 1985-0.0567
Jun 19850.1296
Jul 1985-0.0108
Aug 1985-0.0381
Sep 19850.0501
Oct 19850.1829
Nov 1985-0.0702
Dec 1985-0.1133
Jan 1986-0.0912
Feb 19860.1432
Mar 19860.0634
Apr 1986-0.0593
May 1986-0.0800
Jun 19860.0006
Jul 1986-0.0298
Aug 1986-0.0505
Sep 1986-0.0236
Oct 19860.0460
Nov 1986-0.0788
Dec 19860.0494
Jan 1987-0.0267
Feb 19870.0651
Mar 19870.0122
Apr 1987-0.0377
May 1987-0.0044
Jun 1987-0.0344
Jul 19870.0812
Aug 1987-0.0409
Sep 19870.0775
Oct 1987-0.0536
Nov 1987-0.0718
Dec 1987-0.0248
Jan 1988-0.0322
Feb 19880.0088
Mar 19880.1111
Apr 19880.0877
May 19880.0148
Jun 19880.0183
Jul 19880.0494
Aug 1988-0.0018
Sep 19880.0796
Oct 1988-0.0524
Nov 19880.0004
Dec 1988-0.0097
Jan 1989-0.0175
Feb 1989-0.0176
Mar 19890.0258
Apr 19890.2165
May 1989-0.0097
Jun 19890.0109
Jul 19890.0552
Aug 19890.0391
Sep 19890.0857
Oct 1989-0.0118
Nov 1989-0.0560
Dec 19890.0198
Jan 1990-0.0888
Feb 1990-0.0385
Mar 1990-0.0883
Apr 19900.0206
May 1990-0.0095
Jun 19900.0072
Jul 1990-0.0412
Aug 1990-0.0220
Sep 1990-0.0630
Oct 19900.0062
Nov 19900.0178
Dec 19900.0194
Jan 19910.0926
Feb 19910.0382
Mar 1991-0.0183
Apr 1991-0.0069
May 19910.0344
Jun 1991-0.0216
Jul 1991-0.0291
Aug 19910.0052
Sep 19910.0220
Oct 1991-0.0525
Nov 1991-0.0107
Dec 1991-0.0082
Jan 19920.0037
Feb 1992-0.0352
Mar 19920.0257
Apr 1992-0.0317
May 1992-0.0187
Jun 19920.0039
Jul 1992-0.0130
Aug 1992-0.0403
Sep 19920.0158
Oct 19920.0054
Nov 19920.1194
Dec 19920.0789
Jan 19930.0134
Feb 1993-0.0114
Mar 1993-0.0070
Apr 19930.0015
May 19930.1706
Jun 19930.0143
Jul 19930.0310
Aug 19930.0590
Sep 1993-0.0450
Oct 19930.0155
Nov 19930.0085
Dec 1993-0.0757
Jan 1994-0.0389
Feb 1994-0.0238
Mar 19940.0577
Apr 1994-0.0073
May 1994-0.0183
Jun 19940.0081
Jul 19940.1821
Aug 1994-0.0585
Sep 19940.0038
Oct 19940.0430
Nov 19940.0410
Dec 1994-0.0171
Jan 19950.1690
Feb 1995-0.1372
Mar 1995-0.0149
Apr 1995-0.0780
May 19950.0068
Jun 19950.0164
Jul 19950.0283
Aug 19950.0216
Sep 19950.1035
Oct 1995-0.0164
Nov 19950.0201
Dec 19950.0053
Jan 1996-0.0439
Feb 19960.1036
Mar 1996-0.0627
Apr 1996-0.0154
May 1996-0.1128
Jun 1996-0.0211
Jul 19960.0240
Aug 1996-0.0075
Sep 1996-0.0263
Oct 1996-0.0402
Nov 1996-0.0574
Dec 19960.0369
Jan 1997-0.0404
Feb 1997-0.0151
Mar 19970.0360
Apr 1997-0.0174
May 19970.0933
Jun 19970.0446
Jul 1997-0.0798
Aug 1997-0.0718
Sep 19970.0253
Oct 1997-0.0166
Nov 1997-0.0287
Dec 1997-0.0336
Jan 19980.0839
Feb 19980.0449
Mar 19980.1461
Apr 19980.0056
May 19980.0228
Jun 19980.0692
Jul 1998-0.1021
Aug 1998-0.0612
Sep 1998-0.0615
Oct 19980.0283
Nov 19980.0170
Dec 1998-0.0065
Jan 1999-0.0756
Feb 19990.1110
Mar 1999-0.0154
Apr 19990.0246
May 1999-0.0539
Jun 1999-0.0730
Jul 19990.0100
Aug 1999-0.0551
Sep 1999-0.0947
Oct 19990.1009
Nov 1999-0.0626
Dec 1999-0.0286
Jan 2000-0.0244
Feb 2000-0.0209
Mar 20000.1797
Apr 2000-0.0012
May 2000-0.0340
Jun 2000-0.0314
Jul 2000-0.0160
Aug 20000.0076
Sep 20000.1113
Oct 2000-0.0553
Nov 20000.0119
Dec 20000.0354
Jan 2001-0.0080
Feb 20010.0128
Mar 2001-0.0707
Apr 20010.0041
May 2001-0.0028
Jun 20010.0238
Jul 2001-0.0400
Aug 20010.0229
Sep 20010.0416
Oct 20010.0369
Nov 2001-0.0711
Dec 20010.0739
Jan 2002-0.0356
Feb 2002-0.0405
Mar 2002-0.0586
Apr 20020.0425
May 2002-0.0151
Jun 2002-0.0651
Jul 20020.0682
Aug 20020.0403
Sep 20020.0873
Oct 2002-0.0574
Nov 2002-0.0233
Dec 20020.0065
Jan 2003-0.0509
Feb 2003-0.0837
Mar 20030.0216
Apr 20030.0400
May 20030.0032
Jun 20030.0069
Jul 20030.0011
Aug 20030.0369
Sep 2003-0.0030
Oct 2003-0.0055
Nov 20030.0534
Dec 2003-0.0650
Jan 20040.0704
Feb 20040.0215
Mar 2004-0.0168
Apr 2004-0.0086
May 2004-0.0584
Jun 2004-0.0275
Jul 2004-0.0346
Aug 2004-0.0185
Sep 2004-0.0164
Oct 2004-0.0494
Nov 2004-0.0424
Dec 20040.0175
Jan 20050.0211
Feb 2005-0.0346
Mar 2005-0.0429
Apr 2005-0.0289
May 2005-0.0250
Jun 2005-0.0195
Jul 2005-0.0326
Aug 2005-0.0014
Sep 2005-0.0239
Oct 20050.0580
Nov 20050.0065
Dec 2005-0.0103
Jan 2006-0.0032
Feb 2006-0.0308
Mar 20060.0346
Apr 2006-0.0360
May 20060.0445
Jun 2006-0.0157
Jul 2006-0.0221
Aug 20060.0307
Sep 2006-0.0325
Oct 20060.0753
Nov 2006-0.0054
Dec 20060.0043
Jan 2007-0.0199
Feb 2007-0.0217
Mar 20070.0113
Apr 2007-0.0423
May 2007-0.0357
Jun 20070.0101
Jul 20070.0233
Aug 20070.0681
Sep 2007-0.0389
Oct 20070.1035
Nov 20070.0877
Dec 20070.0154
Jan 20080.0032
Feb 20080.0423
Mar 2008-0.0298
Apr 2008-0.0385
May 2008-0.0018
Jun 2008-0.0307
Jul 2008-0.0312
Aug 2008-0.0018
Sep 20080.2076
Oct 20080.0220
Nov 2008-0.0529
Dec 2008-0.0727
Jan 2009-0.0255
Feb 2009-0.0357
Mar 20090.0239
Apr 2009-0.0043
May 2009-0.0875
Jun 2009-0.0385
Jul 20090.0207
Aug 20090.0250
Sep 2009-0.0232
Oct 2009-0.0297
Nov 2009-0.0413
Dec 2009-0.0245
Jan 20100.1823
Feb 20100.0138
Mar 2010-0.0339
Apr 2010-0.0545
May 2010-0.0177
Jun 20100.1618
Jul 2010-0.0839
Aug 20100.0388
Sep 2010-0.0172
Oct 2010-0.0784
Nov 20100.0174
Dec 2010-0.0452
Jan 2011-0.0165
Feb 20110.0448
Mar 2011-0.0472
Apr 2011-0.0361
May 2011-0.0524
Jun 2011-0.0209
Jul 2011-0.0208
Aug 20110.0035
Sep 20110.0100
Oct 20110.0273
Nov 20110.0050
Dec 2011-0.0499
Jan 2012-0.0002
Feb 2012-0.0472
Mar 2012-0.0034
Apr 2012-0.0125
May 20120.0229
Jun 20120.0173
Jul 2012-0.0011
Aug 2012-0.0282
Sep 20120.0261
Oct 2012-0.0207
Nov 20120.0133
Dec 20120.0158
Jan 20130.0351
Feb 20130.0291
Mar 2013-0.0109
Apr 2013-0.0046
May 20130.0647
Jun 2013-0.0120
Jul 2013-0.0146
Aug 2013-0.0192
Sep 2013-0.0016
Oct 2013-0.0428
Nov 2013-0.0210
Dec 2013-0.0012
Jan 2014-0.0074
Feb 2014-0.0118
Mar 20140.0524
Apr 20140.0095
May 2014-0.0333
Jun 2014-0.0194
Jul 2014-0.0125
Aug 20140.0571
Sep 2014-0.0031
Oct 2014-0.0158
Nov 20140.0221
Dec 20140.0173
Jan 2015-0.0152
Feb 2015-0.0198
Mar 2015-0.0020
Apr 2015-0.0325
May 2015-0.0048
Jun 2015-0.0353
Jul 20150.0124
Aug 2015-0.0075
Sep 2015-0.0511
Oct 2015-0.0239
Nov 2015-0.0149
Dec 2015-0.0126
Jan 2016-0.0127
Feb 20160.0286
Mar 2016-0.0082
Apr 20160.0272
May 2016-0.0499
Jun 20160.0116
Jul 2016-0.0334
Aug 20160.0455
Sep 2016-0.0269
Oct 2016-0.0179
Nov 20160.0622
Dec 2016-0.0093
Jan 2017-0.0034
Feb 20170.0030
Mar 2017-0.0294
Apr 2017-0.0261
May 2017-0.0203
Jun 20170.0230
Jul 20170.0106
Aug 20170.0327
Sep 2017-0.0022
Oct 2017-0.0084
Nov 2017-0.0012
Dec 20170.0082
Jan 20180.0330
Feb 2018-0.0025
Mar 2018-0.0171
Apr 2018-0.0302
May 2018-0.0154
Jun 2018-0.0312
Jul 20180.0267
Aug 20180.0298
Sep 20180.0028
Oct 2018-0.0143
Nov 20180.0337
Dec 20180.0102
Jan 2019-0.0425
Feb 2019-0.0457
Mar 2019-0.0195
Apr 20190.0277