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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Factor Analysis Results

Berkshire Hathaway Inc.

Factor regression results for Berkshire Hathaway Inc.
Ticker BRK.A
Time Period May 1985 - Jun 2019
Coefficient of Determination (R2) 31.3%
Adjusted R2 30.3%
Regression F statistic 30.65 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.060 with p-value 0.720)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.845 with p-value 0.698)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.89 0.076 11.667 0.000 0.736...1.035
Size (SMB) -0.34 0.117 -2.854 0.005 -0.566...-0.104
Value (HML-DEV) 0.25 0.122 2.024 0.044 0.007...0.488
Momentum (MOM) 0.02 0.098 0.154 0.877 -0.178...0.208
Quality (QMJ) 0.44 0.162 2.686 0.008 0.117...0.754
Bet Against Beta (BAB) 0.24 0.083 2.866 0.004 0.075...0.402
Alpha (α) 14.43bps 0.003 0.500 0.617 -0.42%...0.71%
Annualized Alpha (α) 1.73%  
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
    Bet Against 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) 67.98 -0.86 8.47 61.01 48.08 79.49  
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 Jun 2019 1.73% 60.21 0.29 2.10 0.92 20.93 18.93 117.81 31.3%
Regression residuals
MonthBRK.A
May 1985-0.0566
Jun 19850.1298
Jul 1985-0.0110
Aug 1985-0.0378
Sep 19850.0502
Oct 19850.1829
Nov 1985-0.0706
Dec 1985-0.1135
Jan 1986-0.0906
Feb 19860.1429
Mar 19860.0633
Apr 1986-0.0593
May 1986-0.0801
Jun 19860.0007
Jul 1986-0.0293
Aug 1986-0.0506
Sep 1986-0.0231
Oct 19860.0460
Nov 1986-0.0790
Dec 19860.0495
Jan 1987-0.0272
Feb 19870.0649
Mar 19870.0124
Apr 1987-0.0373
May 1987-0.0044
Jun 1987-0.0346
Jul 19870.0814
Aug 1987-0.0414
Sep 19870.0780
Oct 1987-0.0528
Nov 1987-0.0711
Dec 1987-0.0254
Jan 1988-0.0324
Feb 19880.0084
Mar 19880.1114
Apr 19880.0879
May 19880.0150
Jun 19880.0180
Jul 19880.0498
Aug 1988-0.0014
Sep 19880.0795
Oct 1988-0.0523
Nov 19880.0007
Dec 1988-0.0099
Jan 1989-0.0175
Feb 1989-0.0173
Mar 19890.0261
Apr 19890.2164
May 1989-0.0097
Jun 19890.0113
Jul 19890.0552
Aug 19890.0391
Sep 19890.0860
Oct 1989-0.0116
Nov 1989-0.0558
Dec 19890.0198
Jan 1990-0.0883
Feb 1990-0.0383
Mar 1990-0.0885
Apr 19900.0207
May 1990-0.0096
Jun 19900.0073
Jul 1990-0.0410
Aug 1990-0.0212
Sep 1990-0.0628
Oct 19900.0063
Nov 19900.0175
Dec 19900.0191
Jan 19910.0921
Feb 19910.0379
Mar 1991-0.0183
Apr 1991-0.0066
May 19910.0346
Jun 1991-0.0215
Jul 1991-0.0289
Aug 19910.0053
Sep 19910.0225
Oct 1991-0.0522
Nov 1991-0.0106
Dec 1991-0.0085
Jan 19920.0039
Feb 1992-0.0350
Mar 19920.0258
Apr 1992-0.0317
May 1992-0.0186
Jun 19920.0042
Jul 1992-0.0131
Aug 1992-0.0404
Sep 19920.0158
Oct 19920.0053
Nov 19920.1194
Dec 19920.0791
Jan 19930.0140
Feb 1993-0.0109
Mar 1993-0.0066
Apr 19930.0024
May 19930.1707
Jun 19930.0150
Jul 19930.0314
Aug 19930.0591
Sep 1993-0.0448
Oct 19930.0156
Nov 19930.0084
Dec 1993-0.0757
Jan 1994-0.0386
Feb 1994-0.0240
Mar 19940.0579
Apr 1994-0.0073
May 1994-0.0181
Jun 19940.0082
Jul 19940.1822
Aug 1994-0.0589
Sep 19940.0039
Oct 19940.0428
Nov 19940.0409
Dec 1994-0.0171
Jan 19950.1690
Feb 1995-0.1372
Mar 1995-0.0150
Apr 1995-0.0780
May 19950.0069
Jun 19950.0166
Jul 19950.0284
Aug 19950.0220
Sep 19950.1036
Oct 1995-0.0166
Nov 19950.0201
Dec 19950.0057
Jan 1996-0.0434
Feb 19960.1036
Mar 1996-0.0625
Apr 1996-0.0156
May 1996-0.1128
Jun 1996-0.0210
Jul 19960.0242
Aug 1996-0.0075
Sep 1996-0.0265
Oct 1996-0.0400
Nov 1996-0.0578
Dec 19960.0371
Jan 1997-0.0404
Feb 1997-0.0149
Mar 19970.0364
Apr 1997-0.0176
May 19970.0926
Jun 19970.0444
Jul 1997-0.0799
Aug 1997-0.0715
Sep 19970.0256
Oct 1997-0.0162
Nov 1997-0.0288
Dec 1997-0.0331
Jan 19980.0839
Feb 19980.0446
Mar 19980.1462
Apr 19980.0059
May 19980.0233
Jun 19980.0695
Jul 1998-0.1016
Aug 1998-0.0608
Sep 1998-0.0618
Oct 19980.0279
Nov 19980.0167
Dec 1998-0.0065
Jan 1999-0.0752
Feb 19990.1118
Mar 1999-0.0151
Apr 19990.0245
May 1999-0.0541
Jun 1999-0.0733
Jul 19990.0100
Aug 1999-0.0552
Sep 1999-0.0945
Oct 19990.1014
Nov 1999-0.0628
Dec 1999-0.0286
Jan 2000-0.0236
Feb 2000-0.0197
Mar 20000.1789
Apr 2000-0.0017
May 2000-0.0340
Jun 2000-0.0309
Jul 2000-0.0162
Aug 20000.0078
Sep 20000.1115
Oct 2000-0.0561
Nov 20000.0111
Dec 20000.0360
Jan 2001-0.0091
Feb 20010.0128
Mar 2001-0.0704
Apr 20010.0038
May 2001-0.0026
Jun 20010.0238
Jul 2001-0.0400
Aug 20010.0230
Sep 20010.0423
Oct 20010.0362
Nov 2001-0.0718
Dec 20010.0737
Jan 2002-0.0360
Feb 2002-0.0403
Mar 2002-0.0587
Apr 20020.0427
May 2002-0.0146
Jun 2002-0.0647
Jul 20020.0684
Aug 20020.0406
Sep 20020.0878
Oct 2002-0.0580
Nov 2002-0.0234
Dec 20020.0069
Jan 2003-0.0505
Feb 2003-0.0835
Mar 20030.0217
Apr 20030.0400
May 20030.0031
Jun 20030.0070
Jul 20030.0013
Aug 20030.0369
Sep 2003-0.0028
Oct 2003-0.0057
Nov 20030.0533
Dec 2003-0.0649
Jan 20040.0709
Feb 20040.0216
Mar 2004-0.0167
Apr 2004-0.0089
May 2004-0.0582
Jun 2004-0.0276
Jul 2004-0.0345
Aug 2004-0.0182
Sep 2004-0.0162
Oct 2004-0.0494
Nov 2004-0.0424
Dec 20040.0174
Jan 20050.0215
Feb 2005-0.0345
Mar 2005-0.0428
Apr 2005-0.0284
May 2005-0.0253
Jun 2005-0.0193
Jul 2005-0.0327
Aug 2005-0.0009
Sep 2005-0.0234
Oct 20050.0580
Nov 20050.0064
Dec 2005-0.0098
Jan 2006-0.0031
Feb 2006-0.0305
Mar 20060.0347
Apr 2006-0.0357
May 20060.0448
Jun 2006-0.0156
Jul 2006-0.0218
Aug 20060.0307
Sep 2006-0.0326
Oct 20060.0753
Nov 2006-0.0053
Dec 20060.0045
Jan 2007-0.0197
Feb 2007-0.0214
Mar 20070.0115
Apr 2007-0.0422
May 2007-0.0359
Jun 20070.0103
Jul 20070.0238
Aug 20070.0680
Sep 2007-0.0385
Oct 20070.1038
Nov 20070.0878
Dec 20070.0155
Jan 20080.0035
Feb 20080.0427
Mar 2008-0.0301
Apr 2008-0.0383
May 2008-0.0018
Jun 2008-0.0298
Jul 2008-0.0317
Aug 2008-0.0025
Sep 20080.2076
Oct 20080.0227
Nov 2008-0.0527
Dec 2008-0.0732
Jan 2009-0.0248
Feb 2009-0.0351
Mar 20090.0233
Apr 2009-0.0063
May 2009-0.0873
Jun 2009-0.0386
Jul 20090.0205
Aug 20090.0254
Sep 2009-0.0233
Oct 2009-0.0299
Nov 2009-0.0413
Dec 2009-0.0248
Jan 20100.1826
Feb 20100.0139
Mar 2010-0.0338
Apr 2010-0.0542
May 2010-0.0173
Jun 20100.1622
Jul 2010-0.0840
Aug 20100.0395
Sep 2010-0.0178
Oct 2010-0.0785
Nov 20100.0175
Dec 2010-0.0451
Jan 2011-0.0162
Feb 20110.0449
Mar 2011-0.0472
Apr 2011-0.0362
May 2011-0.0525
Jun 2011-0.0209
Jul 2011-0.0204
Aug 20110.0034
Sep 20110.0100
Oct 20110.0268
Nov 20110.0048
Dec 2011-0.0499
Jan 2012-0.0002
Feb 2012-0.0471
Mar 2012-0.0033
Apr 2012-0.0122
May 20120.0233
Jun 20120.0172
Jul 2012-0.0008
Aug 2012-0.0283
Sep 20120.0262
Oct 2012-0.0200
Nov 20120.0132
Dec 20120.0160
Jan 20130.0353
Feb 20130.0292
Mar 2013-0.0108
Apr 2013-0.0041
May 20130.0644
Jun 2013-0.0120
Jul 2013-0.0147
Aug 2013-0.0189
Sep 2013-0.0016
Oct 2013-0.0431
Nov 2013-0.0213
Dec 2013-0.0009
Jan 2014-0.0063
Feb 2014-0.0118
Mar 20140.0522
Apr 20140.0096
May 2014-0.0331
Jun 2014-0.0193
Jul 2014-0.0121
Aug 20140.0571
Sep 2014-0.0028
Oct 2014-0.0165
Nov 20140.0220
Dec 20140.0174
Jan 2015-0.0143
Feb 2015-0.0203
Mar 2015-0.0016
Apr 2015-0.0325
May 2015-0.0044
Jun 2015-0.0352
Jul 20150.0130
Aug 2015-0.0073
Sep 2015-0.0510
Oct 2015-0.0243
Nov 2015-0.0148
Dec 2015-0.0120
Jan 2016-0.0130
Feb 20160.0281
Mar 2016-0.0087
Apr 20160.0274
May 2016-0.0496
Jun 20160.0119
Jul 2016-0.0335
Aug 20160.0453
Sep 2016-0.0263
Oct 2016-0.0179
Nov 20160.0614
Dec 2016-0.0096
Jan 2017-0.0029
Feb 20170.0029
Mar 2017-0.0292
Apr 2017-0.0262
May 2017-0.0201
Jun 20170.0231
Jul 20170.0109
Aug 20170.0332
Sep 2017-0.0024
Oct 2017-0.0083
Nov 2017-0.0016
Dec 20170.0085
Jan 20180.0328
Feb 2018-0.0019
Mar 2018-0.0170
Apr 2018-0.0298
May 2018-0.0154
Jun 2018-0.0314
Jul 20180.0264
Aug 20180.0299
Sep 20180.0031
Oct 2018-0.0138
Nov 20180.0336
Dec 20180.0112
Jan 2019-0.0433
Feb 2019-0.0455
Mar 2019-0.0189
Apr 20190.0271
May 2019-0.0368
Jun 20190.0062