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
Allocation
Asset 1
%
Asset 2
%
Asset 3
%
Asset 4
%
Asset 5
%
Asset 6
%
Asset 7
%
Asset 8
%
Asset 9
%
Asset 10
%
Total
%

Factor Analysis Results

Berkshire Hathaway Inc.

Factor regression results for Berkshire Hathaway Inc.
Ticker BRK.A
Time Period May 1985 - Nov 2020
Regression Basis 427 monthly samples
Coefficient of Determination (R2) 34.8%
Adjusted R2 34.0%
Regression F statistic 44.95 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.110 with p-value 0.868)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 5.164 with p-value 0.396)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.82 0.062 13.301 0.000 0.701...0.945
Size (SMB) -0.34 0.092 -3.707 0.000 -0.523...-0.161
Value (HML) 0.42 0.114 3.684 0.000 0.196...0.644
Profitability (RMW) 0.34 0.121 2.837 0.005 0.105...0.581
Investment (CMA) -0.05 0.172 -0.268 0.789 -0.385...0.293
Alpha (α) 42.41bps 0.003 1.644 0.101 -0.08%...0.93%
Annualized Alpha (α) 5.09%  
Notes on results:
  • Past performance is no guarantee of future results, which may vary. All use is subject to terms of service.
  • Investing involves risk, including possible loss of principal. The value of the investments and the income derived from them may fluctuate over time.
  • The results are based on information from a variety of sources we consider reliable, but we do not represent that the information is accurate or complete.
  • The results do not constitute investment advice or recommendation, are provided solely for informational purposes, and are not an offer to buy or sell any securities.
  • The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
  • Refer to the FAQ section regarding the list of factor data sources and methodology descriptions
  • 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

Factor Performance Attribution in Basis Points

Factor regression results
Monthly Factor Premiums (BPS) 74.05 4.74 7.80 34.33 19.90  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML RMW CMA Total R2
Berkshire Hathaway Inc. BRK.A May 1985 Nov 2020 5.09% 60.94 -1.62 3.27 11.78 -0.92 115.85 34.8%
Regression residuals
MonthBRK.A
May 1985-0.0568
Jun 19850.1289
Jul 1985-0.0048
Aug 1985-0.0442
Sep 19850.0514
Oct 19850.1798
Nov 1985-0.0518
Dec 1985-0.1008
Jan 1986-0.0950
Feb 19860.1525
Mar 19860.0765
Apr 1986-0.0540
May 1986-0.0748
Jun 19860.0076
Jul 1986-0.0367
Aug 1986-0.0545
Sep 1986-0.0376
Oct 19860.0456
Nov 1986-0.0745
Dec 19860.0428
Jan 1987-0.0048
Feb 19870.0778
Mar 19870.0161
Apr 1987-0.0328
May 1987-0.0038
Jun 1987-0.0329
Jul 19870.0868
Aug 1987-0.0373
Sep 19870.0743
Oct 1987-0.0823
Nov 1987-0.0682
Dec 1987-0.0392
Jan 1988-0.0330
Feb 19880.0046
Mar 19880.1171
Apr 19880.0871
May 19880.0168
Jun 19880.0144
Jul 19880.0477
Aug 1988-0.0053
Sep 19880.0709
Oct 1988-0.0570
Nov 1988-0.0056
Dec 1988-0.0118
Jan 1989-0.0182
Feb 1989-0.0233
Mar 19890.0248
Apr 19890.2220
May 1989-0.0141
Jun 19890.0102
Jul 19890.0612
Aug 19890.0367
Sep 19890.0798
Oct 1989-0.0011
Nov 1989-0.0459
Dec 19890.0236
Jan 1990-0.0896
Feb 1990-0.0481
Mar 1990-0.0851
Apr 19900.0158
May 1990-0.0120
Jun 19900.0217
Jul 1990-0.0323
Aug 1990-0.0299
Sep 1990-0.0557
Oct 1990-0.0110
Nov 19900.0125
Dec 19900.0194
Jan 19910.0746
Feb 19910.0397
Mar 1991-0.0176
Apr 1991-0.0012
May 19910.0328
Jun 1991-0.0178
Jul 1991-0.0333
Aug 19910.0064
Sep 19910.0314
Oct 1991-0.0426
Nov 19910.0022
Dec 1991-0.0185
Jan 1992-0.0061
Feb 1992-0.0517
Mar 19920.0229
Apr 1992-0.0392
May 1992-0.0133
Jun 19920.0027
Jul 1992-0.0109
Aug 1992-0.0402
Sep 19920.0104
Oct 19920.0036
Nov 19920.1126
Dec 19920.0724
Jan 19930.0050
Feb 1993-0.0113
Mar 1993-0.0078
Apr 19930.0101
May 19930.1761
Jun 19930.0107
Jul 19930.0333
Aug 19930.0635
Sep 1993-0.0442
Oct 19930.0329
Nov 1993-0.0004
Dec 1993-0.0744
Jan 1994-0.0366
Feb 1994-0.0240
Mar 19940.0512
Apr 1994-0.0156
May 1994-0.0251
Jun 19940.0053
Jul 19940.1805
Aug 1994-0.0553
Sep 19940.0194
Oct 19940.0475
Nov 19940.0407
Dec 1994-0.0223
Jan 19950.1606
Feb 1995-0.1414
Mar 1995-0.0024
Apr 1995-0.0810
May 1995-0.0005
Jun 19950.0229
Jul 19950.0285
Aug 19950.0152
Sep 19950.1067
Oct 1995-0.0118
Nov 19950.0158
Dec 19950.0151
Jan 1996-0.0425
Feb 19960.1027
Mar 1996-0.0624
Apr 1996-0.0033
May 1996-0.1036
Jun 1996-0.0253
Jul 19960.0032
Aug 1996-0.0058
Sep 1996-0.0209
Oct 1996-0.0452
Nov 1996-0.0616
Dec 19960.0372
Jan 1997-0.0335
Feb 1997-0.0179
Mar 19970.0356
Apr 1997-0.0236
May 19970.1025
Jun 19970.0517
Jul 1997-0.0812
Aug 1997-0.0702
Sep 19970.0393
Oct 1997-0.0160
Nov 1997-0.0276
Dec 1997-0.0307
Jan 19980.0828
Feb 19980.0461
Mar 19980.1494
Apr 19980.0076
May 19980.0211
Jun 19980.0678
Jul 1998-0.1099
Aug 1998-0.0555
Sep 1998-0.0583
Oct 19980.0115
Nov 19980.0142
Dec 1998-0.0151
Jan 1999-0.0834
Feb 19990.1000
Mar 1999-0.0226
Apr 19990.0407
May 1999-0.0436
Jun 1999-0.0731
Jul 19990.0148
Aug 1999-0.0483
Sep 1999-0.1027
Oct 19990.0990
Nov 1999-0.0803
Dec 1999-0.0160
Jan 2000-0.0127
Feb 2000-0.0064
Mar 20000.1260
Apr 20000.0064
May 2000-0.0338
Jun 2000-0.0342
Jul 2000-0.0230
Aug 2000-0.0059
Sep 20000.1145
Oct 2000-0.0618
Nov 20000.0164
Dec 20000.0320
Jan 2001-0.0149
Feb 20010.0318
Mar 2001-0.0467
Apr 2001-0.0070
May 2001-0.0047
Jun 20010.0415
Jul 2001-0.0501
Aug 20010.0369
Sep 20010.0355
Oct 20010.0503
Nov 2001-0.0814
Dec 20010.0726
Jan 2002-0.0414
Feb 2002-0.0358
Mar 2002-0.0498
Apr 20020.0626
May 2002-0.0023
Jun 2002-0.0497
Jul 20020.0642
Aug 20020.0358
Sep 20020.0831
Oct 2002-0.0517
Nov 2002-0.0302
Dec 20020.0181
Jan 2003-0.0456
Feb 2003-0.0780
Mar 20030.0238
Apr 20030.0376
May 20030.0037
Jun 20030.0066
Jul 20030.0048
Aug 20030.0391
Sep 2003-0.0074
Oct 2003-0.0107
Nov 20030.0606
Dec 2003-0.0512
Jan 20040.0516
Feb 20040.0247
Mar 2004-0.0071
Apr 20040.0035
May 2004-0.0578
Jun 2004-0.0215
Jul 2004-0.0336
Aug 2004-0.0220
Sep 2004-0.0074
Oct 2004-0.0416
Nov 2004-0.0396
Dec 20040.0207
Jan 20050.0167
Feb 2005-0.0308
Mar 2005-0.0406
Apr 2005-0.0324
May 2005-0.0239
Jun 2005-0.0232
Jul 2005-0.0221
Aug 2005-0.0022
Sep 2005-0.0307
Oct 20050.0532
Nov 20050.0135
Dec 2005-0.0164
Jan 2006-0.0050
Feb 2006-0.0325
Mar 20060.0301
Apr 2006-0.0478
May 20060.0341
Jun 2006-0.0216
Jul 2006-0.0312
Aug 20060.0410
Sep 2006-0.0345
Oct 20060.0742
Nov 2006-0.0057
Dec 20060.0006
Jan 2007-0.0181
Feb 2007-0.0204
Mar 20070.0140
Apr 2007-0.0397
May 2007-0.0343
Jun 20070.0130
Jul 20070.0313
Aug 20070.0715
Sep 2007-0.0314
Oct 20070.1081
Nov 20070.0780
Dec 20070.0104
Jan 2008-0.0177
Feb 20080.0463
Mar 2008-0.0466
Apr 2008-0.0481
May 2008-0.0025
Jun 2008-0.0417
Jul 2008-0.0573
Aug 2008-0.0003
Sep 20080.1579
Oct 20080.0101
Nov 2008-0.0415
Dec 2008-0.0794
Jan 20090.0270
Feb 2009-0.0239
Mar 20090.0208
Apr 2009-0.0052
May 2009-0.0794
Jun 2009-0.0021
Jul 20090.0002
Aug 2009-0.0132
Sep 2009-0.0360
Oct 2009-0.0166
Nov 2009-0.0454
Dec 2009-0.0218
Jan 20100.1828
Feb 20100.0069
Mar 2010-0.0394
Apr 2010-0.0714
May 2010-0.0150
Jun 20100.1855
Jul 2010-0.0847
Aug 20100.0440
Sep 2010-0.0060
Oct 2010-0.0692
Nov 20100.0146
Dec 2010-0.0572
Jan 2011-0.0132
Feb 20110.0465
Mar 2011-0.0429
Apr 2011-0.0275
May 2011-0.0425
Jun 2011-0.0186
Jul 2011-0.0354
Aug 20110.0169
Sep 20110.0182
Oct 20110.0166
Nov 20110.0063
Dec 2011-0.0529
Jan 2012-0.0005
Feb 2012-0.0464
Mar 2012-0.0006
Apr 2012-0.0087
May 20120.0262
Jun 20120.0201
Jul 2012-0.0028
Aug 2012-0.0313
Sep 20120.0228
Oct 2012-0.0260
Nov 20120.0119
Dec 20120.0004
Jan 20130.0427
Feb 20130.0322
Mar 2013-0.0108
Apr 2013-0.0100
May 20130.0523
Jun 2013-0.0042
Jul 2013-0.0107
Aug 2013-0.0133
Sep 20130.0004
Oct 2013-0.0428
Nov 2013-0.0170
Dec 2013-0.0095
Jan 2014-0.0008
Feb 2014-0.0152
Mar 20140.0397
Apr 2014-0.0015
May 2014-0.0344
Jun 2014-0.0176
Jul 2014-0.0143
Aug 20140.0605
Sep 20140.0051
Oct 20140.0122
Nov 20140.0362
Dec 20140.0144
Jan 2015-0.0183
Feb 2015-0.0183
Mar 2015-0.0000
Apr 2015-0.0462
May 20150.0048
Jun 2015-0.0271
Jul 20150.0284
Aug 2015-0.0196
Sep 2015-0.0332
Oct 2015-0.0295
Nov 2015-0.0024
Dec 2015-0.0054
Jan 2016-0.0025
Feb 20160.0336
Mar 2016-0.0114
Apr 20160.0151
May 2016-0.0446
Jun 20160.0248
Jul 2016-0.0318
Aug 20160.0348
Sep 2016-0.0303
Oct 2016-0.0242
Nov 20160.0455
Dec 2016-0.0067
Jan 2017-0.0047
Feb 20170.0095
Mar 2017-0.0210
Apr 2017-0.0192
May 2017-0.0104
Jun 20170.0240
Jul 20170.0097
Aug 20170.0284
Sep 2017-0.0048
Oct 2017-0.0145
Nov 2017-0.0036
Dec 20170.0007
Jan 20180.0320
Feb 2018-0.0134
Mar 2018-0.0076
Apr 2018-0.0264
May 2018-0.0037
Jun 2018-0.0177
Jul 20180.0229
Aug 20180.0308
Sep 20180.0043
Oct 2018-0.0135
Nov 20180.0383
Dec 20180.0091
Jan 2019-0.0431
Feb 2019-0.0473
Mar 2019-0.0164
Apr 20190.0213
May 2019-0.0289
Jun 20190.0096
Jul 2019-0.0534
Aug 20190.0049
Sep 2019-0.0217
Oct 20190.0083
Nov 20190.0134
Dec 2019-0.0054
Jan 2020-0.0003
Feb 20200.0023
Mar 20200.0204
Apr 2020-0.0748
May 2020-0.0377
Jun 2020-0.0493
Jul 20200.0404
Aug 20200.0423
Sep 20200.0166
Oct 2020-0.0399
Nov 20200.0531