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 - Dec 2019
Coefficient of Determination (R2) 31.2%
Adjusted R2 30.2%
Regression F statistic 30.98 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.059 with p-value 0.718)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.801 with p-value 0.704)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.88 0.075 11.727 0.000 0.734...1.030
Size (SMB) -0.34 0.116 -2.916 0.004 -0.566...-0.110
Value (HML-DEV) 0.24 0.121 2.003 0.046 0.004...0.478
Momentum (MOM) 0.01 0.097 0.093 0.926 -0.182...0.200
Quality (QMJ) 0.42 0.160 2.654 0.008 0.110...0.737
Bet Against Beta (BAB) 0.24 0.082 2.893 0.004 0.076...0.401
Alpha (α) 14.87bps 0.003 0.523 0.602 -0.41%...0.71%
Annualized Alpha (α) 1.78%  
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.
  • 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

Factor Performance Attribution in Basis Points

Factor regression results
Monthly Factor Premiums (BPS) 68.96 -1.55 8.18 60.23 47.52 78.19  
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 Dec 2019 1.78% 60.81 0.52 1.97 0.55 20.12 18.65 117.50 31.2%
Regression residuals
MonthBRK.A
May 1985-0.0563
Jun 19850.1300
Jul 1985-0.0111
Aug 1985-0.0377
Sep 19850.0504
Oct 19850.1832
Nov 1985-0.0704
Dec 1985-0.1134
Jan 1986-0.0907
Feb 19860.1433
Mar 19860.0637
Apr 1986-0.0593
May 1986-0.0798
Jun 19860.0011
Jul 1986-0.0292
Aug 1986-0.0507
Sep 1986-0.0235
Oct 19860.0462
Nov 1986-0.0788
Dec 19860.0496
Jan 1987-0.0269
Feb 19870.0647
Mar 19870.0126
Apr 1987-0.0374
May 1987-0.0043
Jun 1987-0.0344
Jul 19870.0824
Aug 1987-0.0411
Sep 19870.0778
Oct 1987-0.0533
Nov 1987-0.0713
Dec 1987-0.0249
Jan 1988-0.0325
Feb 19880.0085
Mar 19880.1114
Apr 19880.0880
May 19880.0151
Jun 19880.0181
Jul 19880.0498
Aug 1988-0.0014
Sep 19880.0796
Oct 1988-0.0521
Nov 19880.0007
Dec 1988-0.0098
Jan 1989-0.0174
Feb 1989-0.0174
Mar 19890.0262
Apr 19890.2166
May 1989-0.0096
Jun 19890.0113
Jul 19890.0555
Aug 19890.0392
Sep 19890.0860
Oct 1989-0.0115
Nov 1989-0.0557
Dec 19890.0201
Jan 1990-0.0886
Feb 1990-0.0385
Mar 1990-0.0883
Apr 19900.0208
May 1990-0.0096
Jun 19900.0074
Jul 1990-0.0406
Aug 1990-0.0213
Sep 1990-0.0624
Oct 19900.0067
Nov 19900.0173
Dec 19900.0194
Jan 19910.0920
Feb 19910.0378
Mar 1991-0.0182
Apr 1991-0.0067
May 19910.0346
Jun 1991-0.0213
Jul 1991-0.0287
Aug 19910.0054
Sep 19910.0224
Oct 1991-0.0522
Nov 1991-0.0105
Dec 1991-0.0080
Jan 19920.0038
Feb 1992-0.0349
Mar 19920.0260
Apr 1992-0.0316
May 1992-0.0186
Jun 19920.0042
Jul 1992-0.0128
Aug 1992-0.0402
Sep 19920.0160
Oct 19920.0054
Nov 19920.1193
Dec 19920.0793
Jan 19930.0142
Feb 1993-0.0106
Mar 1993-0.0065
Apr 19930.0021
May 19930.1706
Jun 19930.0151
Jul 19930.0315
Aug 19930.0592
Sep 1993-0.0447
Oct 19930.0155
Nov 19930.0082
Dec 1993-0.0755
Jan 1994-0.0387
Feb 1994-0.0239
Mar 19940.0579
Apr 1994-0.0072
May 1994-0.0182
Jun 19940.0083
Jul 19940.1823
Aug 1994-0.0586
Sep 19940.0040
Oct 19940.0430
Nov 19940.0410
Dec 1994-0.0168
Jan 19950.1691
Feb 1995-0.1371
Mar 1995-0.0149
Apr 1995-0.0778
May 19950.0070
Jun 19950.0166
Jul 19950.0284
Aug 19950.0219
Sep 19950.1038
Oct 1995-0.0160
Nov 19950.0201
Dec 19950.0057
Jan 1996-0.0435
Feb 19960.1036
Mar 1996-0.0626
Apr 1996-0.0156
May 1996-0.1127
Jun 1996-0.0207
Jul 19960.0244
Aug 1996-0.0075
Sep 1996-0.0263
Oct 1996-0.0396
Nov 1996-0.0576
Dec 19960.0372
Jan 1997-0.0403
Feb 1997-0.0148
Mar 19970.0366
Apr 1997-0.0171
May 19970.0925
Jun 19970.0448
Jul 1997-0.0796
Aug 1997-0.0717
Sep 19970.0256
Oct 1997-0.0162
Nov 1997-0.0285
Dec 1997-0.0329
Jan 19980.0839
Feb 19980.0447
Mar 19980.1463
Apr 19980.0059
May 19980.0234
Jun 19980.0698
Jul 1998-0.1015
Aug 1998-0.0604
Sep 1998-0.0619
Oct 19980.0277
Nov 19980.0168
Dec 1998-0.0061
Jan 1999-0.0755
Feb 19990.1115
Mar 1999-0.0155
Apr 19990.0241
May 1999-0.0539
Jun 1999-0.0729
Jul 19990.0102
Aug 1999-0.0549
Sep 1999-0.0944
Oct 19990.1013
Nov 1999-0.0627
Dec 1999-0.0284
Jan 2000-0.0240
Feb 2000-0.0202
Mar 20000.1794
Apr 2000-0.0012
May 2000-0.0341
Jun 2000-0.0309
Jul 2000-0.0156
Aug 20000.0078
Sep 20000.1119
Oct 2000-0.0555
Nov 20000.0122
Dec 20000.0363
Jan 2001-0.0102
Feb 20010.0146
Mar 2001-0.0695
Apr 20010.0031
May 2001-0.0024
Jun 20010.0240
Jul 2001-0.0392
Aug 20010.0237
Sep 20010.0428
Oct 20010.0359
Nov 2001-0.0720
Dec 20010.0739
Jan 2002-0.0352
Feb 2002-0.0397
Mar 2002-0.0586
Apr 20020.0435
May 2002-0.0144
Jun 2002-0.0643
Jul 20020.0686
Aug 20020.0407
Sep 20020.0883
Oct 2002-0.0581
Nov 2002-0.0244
Dec 20020.0077
Jan 2003-0.0505
Feb 2003-0.0835
Mar 20030.0217
Apr 20030.0394
May 20030.0025
Jun 20030.0070
Jul 20030.0011
Aug 20030.0370
Sep 2003-0.0028
Oct 2003-0.0053
Nov 20030.0536
Dec 2003-0.0650
Jan 20040.0708
Feb 20040.0216
Mar 2004-0.0166
Apr 2004-0.0089
May 2004-0.0582
Jun 2004-0.0272
Jul 2004-0.0343
Aug 2004-0.0184
Sep 2004-0.0160
Oct 2004-0.0494
Nov 2004-0.0421
Dec 20040.0173
Jan 20050.0217
Feb 2005-0.0341
Mar 2005-0.0426
Apr 2005-0.0286
May 2005-0.0251
Jun 2005-0.0191
Jul 2005-0.0326
Aug 2005-0.0010
Sep 2005-0.0233
Oct 20050.0580
Nov 20050.0065
Dec 2005-0.0100
Jan 2006-0.0029
Feb 2006-0.0307
Mar 20060.0348
Apr 2006-0.0357
May 20060.0446
Jun 2006-0.0155
Jul 2006-0.0219
Aug 20060.0305
Sep 2006-0.0326
Oct 20060.0753
Nov 2006-0.0053
Dec 20060.0046
Jan 2007-0.0197
Feb 2007-0.0215
Mar 20070.0116
Apr 2007-0.0422
May 2007-0.0358
Jun 20070.0102
Jul 20070.0237
Aug 20070.0681
Sep 2007-0.0385
Oct 20070.1039
Nov 20070.0879
Dec 20070.0158
Jan 20080.0029
Feb 20080.0430
Mar 2008-0.0298
Apr 2008-0.0384
May 2008-0.0017
Jun 2008-0.0297
Jul 2008-0.0318
Aug 2008-0.0022
Sep 20080.2078
Oct 20080.0229
Nov 2008-0.0523
Dec 2008-0.0731
Jan 2009-0.0251
Feb 2009-0.0352
Mar 20090.0231
Apr 2009-0.0069
May 2009-0.0883
Jun 2009-0.0380
Jul 20090.0203
Aug 20090.0246
Sep 2009-0.0236
Oct 2009-0.0295
Nov 2009-0.0412
Dec 2009-0.0244
Jan 20100.1823
Feb 20100.0142
Mar 2010-0.0335
Apr 2010-0.0542
May 2010-0.0175
Jun 20100.1619
Jul 2010-0.0838
Aug 20100.0393
Sep 2010-0.0175
Oct 2010-0.0784
Nov 20100.0176
Dec 2010-0.0453
Jan 2011-0.0163
Feb 20110.0450
Mar 2011-0.0470
Apr 2011-0.0361
May 2011-0.0524
Jun 2011-0.0206
Jul 2011-0.0205
Aug 20110.0037
Sep 20110.0100
Oct 20110.0268
Nov 20110.0053
Dec 2011-0.0496
Jan 2012-0.0007
Feb 2012-0.0471
Mar 2012-0.0031
Apr 2012-0.0121
May 20120.0237
Jun 20120.0172
Jul 2012-0.0007
Aug 2012-0.0284
Sep 20120.0261
Oct 2012-0.0202
Nov 20120.0133
Dec 20120.0158
Jan 20130.0352
Feb 20130.0294
Mar 2013-0.0107
Apr 2013-0.0042
May 20130.0645
Jun 2013-0.0118
Jul 2013-0.0145
Aug 2013-0.0190
Sep 2013-0.0014
Oct 2013-0.0427
Nov 2013-0.0209
Dec 2013-0.0010
Jan 2014-0.0069
Feb 2014-0.0118
Mar 20140.0524
Apr 20140.0094
May 2014-0.0331
Jun 2014-0.0193
Jul 2014-0.0123
Aug 20140.0572
Sep 2014-0.0028
Oct 2014-0.0161
Nov 20140.0221
Dec 20140.0175
Jan 2015-0.0146
Feb 2015-0.0203
Mar 2015-0.0016
Apr 2015-0.0329
May 2015-0.0042
Jun 2015-0.0349
Jul 20150.0134
Aug 2015-0.0074
Sep 2015-0.0504
Oct 2015-0.0242
Nov 2015-0.0146
Dec 2015-0.0120
Jan 2016-0.0124
Feb 20160.0282
Mar 2016-0.0086
Apr 20160.0270
May 2016-0.0496
Jun 20160.0122
Jul 2016-0.0336
Aug 20160.0452
Sep 2016-0.0267
Oct 2016-0.0176
Nov 20160.0618
Dec 2016-0.0091
Jan 2017-0.0032
Feb 20170.0029
Mar 2017-0.0294
Apr 2017-0.0261
May 2017-0.0200
Jun 20170.0231
Jul 20170.0108
Aug 20170.0331
Sep 2017-0.0022
Oct 2017-0.0079
Nov 2017-0.0012
Dec 20170.0083
Jan 20180.0329
Feb 2018-0.0019
Mar 2018-0.0172
Apr 2018-0.0299
May 2018-0.0153
Jun 2018-0.0313
Jul 20180.0264
Aug 20180.0300
Sep 20180.0032
Oct 2018-0.0138
Nov 20180.0336
Dec 20180.0111
Jan 2019-0.0437
Feb 2019-0.0456
Mar 2019-0.0192
Apr 20190.0275
May 2019-0.0368
Jun 20190.0056
Jul 2019-0.0572
Aug 2019-0.0080
Sep 2019-0.0054
Oct 20190.0077
Nov 20190.0225
Dec 20190.0083