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 - Jul 2020
Regression Basis 423 monthly samples
Coefficient of Determination (R2) 33.6%
Adjusted R2 32.8%
Regression F statistic 42.22 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.109 with p-value 0.864)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 4.743 with p-value 0.448)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.81 0.064 12.804 0.000 0.688...0.938
Size (SMB) -0.34 0.093 -3.615 0.000 -0.518...-0.153
Value (HML) 0.39 0.114 3.417 0.001 0.166...0.616
Profitability (RMW) 0.36 0.123 2.930 0.004 0.119...0.603
Investment (CMA) -0.02 0.174 -0.112 0.911 -0.362...0.322
Alpha (α) 41.08bps 0.003 1.574 0.116 -0.10%...0.92%
Annualized Alpha (α) 4.93%  
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) 71.34 2.71 6.42 34.78 20.75  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML RMW CMA Total R2
Berkshire Hathaway Inc. BRK.A May 1985 Jul 2020 4.93% 58.03 -0.91 2.51 12.55 -0.41 112.85 33.6%
Regression residuals
MonthBRK.A
May 1985-0.0561
Jun 19850.1291
Jul 1985-0.0053
Aug 1985-0.0440
Sep 19850.0509
Oct 19850.1808
Nov 1985-0.0513
Dec 1985-0.1004
Jan 1986-0.0938
Feb 19860.1532
Mar 19860.0766
Apr 1986-0.0555
May 1986-0.0749
Jun 19860.0077
Jul 1986-0.0357
Aug 1986-0.0530
Sep 1986-0.0384
Oct 19860.0457
Nov 1986-0.0745
Dec 19860.0426
Jan 1987-0.0040
Feb 19870.0773
Mar 19870.0156
Apr 1987-0.0331
May 1987-0.0040
Jun 1987-0.0325
Jul 19870.0872
Aug 1987-0.0370
Sep 19870.0739
Oct 1987-0.0837
Nov 1987-0.0679
Dec 1987-0.0396
Jan 1988-0.0313
Feb 19880.0042
Mar 19880.1163
Apr 19880.0873
May 19880.0178
Jun 19880.0151
Jul 19880.0481
Aug 1988-0.0051
Sep 19880.0711
Oct 1988-0.0566
Nov 1988-0.0055
Dec 1988-0.0121
Jan 1989-0.0171
Feb 1989-0.0236
Mar 19890.0249
Apr 19890.2221
May 1989-0.0140
Jun 19890.0104
Jul 19890.0612
Aug 19890.0372
Sep 19890.0789
Oct 1989-0.0015
Nov 1989-0.0464
Dec 19890.0237
Jan 1990-0.0901
Feb 1990-0.0475
Mar 1990-0.0857
Apr 19900.0148
May 1990-0.0119
Jun 19900.0212
Jul 1990-0.0326
Aug 1990-0.0308
Sep 1990-0.0566
Oct 1990-0.0109
Nov 19900.0133
Dec 19900.0193
Jan 19910.0749
Feb 19910.0402
Mar 1991-0.0174
Apr 1991-0.0009
May 19910.0331
Jun 1991-0.0185
Jul 1991-0.0330
Aug 19910.0064
Sep 19910.0313
Oct 1991-0.0421
Nov 19910.0011
Dec 1991-0.0181
Jan 1992-0.0059
Feb 1992-0.0502
Mar 19920.0233
Apr 1992-0.0383
May 1992-0.0128
Jun 19920.0034
Jul 1992-0.0111
Aug 1992-0.0407
Sep 19920.0106
Oct 19920.0034
Nov 19920.1135
Dec 19920.0736
Jan 19930.0068
Feb 1993-0.0103
Mar 1993-0.0066
Apr 19930.0110
May 19930.1754
Jun 19930.0117
Jul 19930.0338
Aug 19930.0652
Sep 1993-0.0450
Oct 19930.0286
Nov 1993-0.0007
Dec 1993-0.0737
Jan 1994-0.0377
Feb 1994-0.0262
Mar 19940.0518
Apr 1994-0.0148
May 1994-0.0241
Jun 19940.0052
Jul 19940.1822
Aug 1994-0.0541
Sep 19940.0176
Oct 19940.0467
Nov 19940.0397
Dec 1994-0.0252
Jan 19950.1681
Feb 1995-0.1404
Mar 1995-0.0066
Apr 1995-0.0820
May 19950.0025
Jun 19950.0222
Jul 19950.0282
Aug 19950.0178
Sep 19950.1092
Oct 1995-0.0115
Nov 19950.0161
Dec 19950.0124
Jan 1996-0.0402
Feb 19960.1039
Mar 1996-0.0641
Apr 1996-0.0060
May 1996-0.1033
Jun 1996-0.0223
Jul 19960.0070
Aug 1996-0.0069
Sep 1996-0.0201
Oct 1996-0.0448
Nov 1996-0.0590
Dec 19960.0379
Jan 1997-0.0331
Feb 1997-0.0145
Mar 19970.0347
Apr 1997-0.0225
May 19970.1015
Jun 19970.0524
Jul 1997-0.0804
Aug 1997-0.0715
Sep 19970.0409
Oct 1997-0.0149
Nov 1997-0.0263
Dec 1997-0.0283
Jan 19980.0830
Feb 19980.0471
Mar 19980.1549
Apr 19980.0112
May 19980.0178
Jun 19980.0715
Jul 1998-0.1134
Aug 1998-0.0562
Sep 1998-0.0586
Oct 19980.0117
Nov 19980.0146
Dec 1998-0.0127
Jan 1999-0.0859
Feb 19990.1036
Mar 1999-0.0214
Apr 19990.0417
May 1999-0.0452
Jun 1999-0.0738
Jul 19990.0149
Aug 1999-0.0502
Sep 1999-0.1044
Oct 19990.0975
Nov 1999-0.0796
Dec 1999-0.0124
Jan 2000-0.0192
Feb 2000-0.0026
Mar 20000.1277
Apr 20000.0016
May 2000-0.0240
Jun 2000-0.0303
Jul 2000-0.0201
Aug 2000-0.0090
Sep 20000.1182
Oct 2000-0.0636
Nov 20000.0206
Dec 20000.0348
Jan 2001-0.0184
Feb 20010.0297
Mar 2001-0.0472
Apr 2001-0.0083
May 2001-0.0035
Jun 20010.0376
Jul 2001-0.0494
Aug 20010.0346
Sep 20010.0344
Oct 20010.0493
Nov 2001-0.0796
Dec 20010.0731
Jan 2002-0.0404
Feb 2002-0.0368
Mar 2002-0.0508
Apr 20020.0613
May 2002-0.0032
Jun 2002-0.0517
Jul 20020.0606
Aug 20020.0406
Sep 20020.0840
Oct 2002-0.0459
Nov 2002-0.0312
Dec 20020.0187
Jan 2003-0.0462
Feb 2003-0.0782
Mar 20030.0234
Apr 20030.0386
May 20030.0057
Jun 20030.0054
Jul 20030.0051
Aug 20030.0383
Sep 2003-0.0081
Oct 2003-0.0088
Nov 20030.0608
Dec 2003-0.0521
Jan 20040.0541
Feb 20040.0264
Mar 2004-0.0064
Apr 20040.0013
May 2004-0.0576
Jun 2004-0.0216
Jul 2004-0.0361
Aug 2004-0.0220
Sep 2004-0.0058
Oct 2004-0.0408
Nov 2004-0.0384
Dec 20040.0216
Jan 20050.0168
Feb 2005-0.0295
Mar 2005-0.0381
Apr 2005-0.0312
May 2005-0.0221
Jun 2005-0.0211
Jul 2005-0.0228
Aug 2005-0.0011
Sep 2005-0.0308
Oct 20050.0534
Nov 20050.0133
Dec 2005-0.0169
Jan 2006-0.0043
Feb 2006-0.0327
Mar 20060.0305
Apr 2006-0.0457
May 20060.0344
Jun 2006-0.0213
Jul 2006-0.0317
Aug 20060.0391
Sep 2006-0.0343
Oct 20060.0740
Nov 2006-0.0049
Dec 20060.0001
Jan 2007-0.0194
Feb 2007-0.0204
Mar 20070.0125
Apr 2007-0.0407
May 2007-0.0351
Jun 20070.0127
Jul 20070.0281
Aug 20070.0713
Sep 2007-0.0318
Oct 20070.1074
Nov 20070.0775
Dec 20070.0108
Jan 2008-0.0167
Feb 20080.0481
Mar 2008-0.0462
Apr 2008-0.0452
May 2008-0.0018
Jun 2008-0.0427
Jul 2008-0.0587
Aug 2008-0.0001
Sep 20080.1558
Oct 20080.0075
Nov 2008-0.0462
Dec 2008-0.0770
Jan 20090.0246
Feb 2009-0.0257
Mar 20090.0219
Apr 2009-0.0030
May 2009-0.0759
Jun 2009-0.0032
Jul 20090.0010
Aug 2009-0.0107
Sep 2009-0.0354
Oct 2009-0.0180
Nov 2009-0.0448
Dec 2009-0.0219
Jan 20100.1834
Feb 20100.0076
Mar 2010-0.0386
Apr 2010-0.0714
May 2010-0.0168
Jun 20100.1839
Jul 2010-0.0847
Aug 20100.0432
Sep 2010-0.0071
Oct 2010-0.0694
Nov 20100.0135
Dec 2010-0.0555
Jan 2011-0.0119
Feb 20110.0483
Mar 2011-0.0444
Apr 2011-0.0281
May 2011-0.0434
Jun 2011-0.0196
Jul 2011-0.0335
Aug 20110.0162
Sep 20110.0166
Oct 20110.0181
Nov 20110.0058
Dec 2011-0.0524
Jan 20120.0004
Feb 2012-0.0451
Mar 20120.0008
Apr 2012-0.0102
May 20120.0243
Jun 20120.0215
Jul 2012-0.0026
Aug 2012-0.0310
Sep 20120.0237
Oct 2012-0.0260
Nov 20120.0109
Dec 20120.0021
Jan 20130.0432
Feb 20130.0327
Mar 2013-0.0092
Apr 2013-0.0095
May 20130.0533
Jun 2013-0.0033
Jul 2013-0.0094
Aug 2013-0.0134
Sep 20130.0015
Oct 2013-0.0417
Nov 2013-0.0163
Dec 2013-0.0078
Jan 2014-0.0000
Feb 2014-0.0141
Mar 20140.0399
Apr 2014-0.0015
May 2014-0.0336
Jun 2014-0.0163
Jul 2014-0.0145
Aug 20140.0611
Sep 20140.0048
Oct 20140.0113
Nov 20140.0363
Dec 20140.0155
Jan 2015-0.0194
Feb 2015-0.0180
Mar 2015-0.0001
Apr 2015-0.0447
May 20150.0055
Jun 2015-0.0274
Jul 20150.0283
Aug 2015-0.0201
Sep 2015-0.0332
Oct 2015-0.0291
Nov 2015-0.0021
Dec 2015-0.0053
Jan 2016-0.0031
Feb 20160.0321
Mar 2016-0.0109
Apr 20160.0163
May 2016-0.0442
Jun 20160.0245
Jul 2016-0.0328
Aug 20160.0341
Sep 2016-0.0286
Oct 2016-0.0243
Nov 20160.0463
Dec 2016-0.0053
Jan 2017-0.0062
Feb 20170.0084
Mar 2017-0.0216
Apr 2017-0.0203
May 2017-0.0108
Jun 20170.0244
Jul 20170.0095
Aug 20170.0279
Sep 2017-0.0038
Oct 2017-0.0128
Nov 2017-0.0035
Dec 20170.0012
Jan 20180.0329
Feb 2018-0.0131
Mar 2018-0.0082
Apr 2018-0.0264
May 2018-0.0034
Jun 2018-0.0176
Jul 20180.0236
Aug 20180.0323
Sep 20180.0020
Oct 2018-0.0130
Nov 20180.0383
Dec 20180.0064
Jan 2019-0.0417
Feb 2019-0.0475
Mar 2019-0.0178
Apr 20190.0227
May 2019-0.0299
Jun 20190.0114
Jul 2019-0.0529
Aug 20190.0042
Sep 2019-0.0208
Oct 20190.0075
Nov 20190.0135
Dec 2019-0.0053
Jan 2020-0.0010
Feb 20200.0020
Mar 20200.0157
Apr 2020-0.0752
May 2020-0.0378
Jun 2020-0.0497
Jul 20200.0399