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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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 30.64 (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 3.838 with p-value 0.699)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.88 0.076 11.651 0.000 0.735...1.034
Size (SMB) -0.34 0.117 -2.874 0.004 -0.568...-0.107
Value (HML-DEV) 0.25 0.122 2.011 0.045 0.006...0.487
Momentum (MOM) 0.01 0.098 0.139 0.889 -0.179...0.206
Quality (QMJ) 0.43 0.162 2.668 0.008 0.114...0.751
Bet Against Beta (BAB) 0.24 0.083 2.874 0.004 0.075...0.402
Alpha (α) 14.69bps 0.003 0.509 0.611 -0.42%...0.71%
Annualized Alpha (α) 1.76%  
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) 67.96 -0.95 8.55 60.85 48.07 79.47  
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 1.76% 60.11 0.32 2.10 0.83 20.78 18.98 117.81 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 19850.1830
Nov 1985-0.0706
Dec 1985-0.1135
Jan 1986-0.0906
Feb 19860.1430
Mar 19860.0634
Apr 1986-0.0593
May 1986-0.0801
Jun 19860.0007
Jul 1986-0.0293
Aug 1986-0.0507
Sep 1986-0.0232
Oct 19860.0460
Nov 1986-0.0790
Dec 19860.0495
Jan 1987-0.0272
Feb 19870.0649
Mar 19870.0125
Apr 1987-0.0374
May 1987-0.0044
Jun 1987-0.0346
Jul 19870.0823
Aug 1987-0.0413
Sep 19870.0779
Oct 1987-0.0530
Nov 1987-0.0712
Dec 1987-0.0252
Jan 1988-0.0325
Feb 19880.0085
Mar 19880.1114
Apr 19880.0879
May 19880.0150
Jun 19880.0181
Jul 19880.0497
Aug 1988-0.0014
Sep 19880.0795
Oct 1988-0.0523
Nov 19880.0006
Dec 1988-0.0099
Jan 1989-0.0175
Feb 1989-0.0173
Mar 19890.0261
Apr 19890.2164
May 1989-0.0097
Jun 19890.0112
Jul 19890.0552
Aug 19890.0391
Sep 19890.0860
Oct 1989-0.0116
Nov 1989-0.0558
Dec 19890.0198
Jan 1990-0.0884
Feb 1990-0.0383
Mar 1990-0.0884
Apr 19900.0207
May 1990-0.0096
Jun 19900.0073
Jul 1990-0.0410
Aug 1990-0.0213
Sep 1990-0.0627
Oct 19900.0063
Nov 19900.0175
Dec 19900.0192
Jan 19910.0921
Feb 19910.0379
Mar 1991-0.0182
Apr 1991-0.0067
May 19910.0345
Jun 1991-0.0215
Jul 1991-0.0289
Aug 19910.0053
Sep 19910.0225
Oct 1991-0.0522
Nov 1991-0.0106
Dec 1991-0.0084
Jan 19920.0040
Feb 1992-0.0350
Mar 19920.0258
Apr 1992-0.0318
May 1992-0.0186
Jun 19920.0041
Jul 1992-0.0131
Aug 1992-0.0404
Sep 19920.0159
Oct 19920.0053
Nov 19920.1194
Dec 19920.0792
Jan 19930.0140
Feb 1993-0.0109
Mar 1993-0.0066
Apr 19930.0022
May 19930.1707
Jun 19930.0150
Jul 19930.0314
Aug 19930.0591
Sep 1993-0.0448
Oct 19930.0156
Nov 19930.0083
Dec 1993-0.0756
Jan 1994-0.0387
Feb 1994-0.0240
Mar 19940.0579
Apr 1994-0.0073
May 1994-0.0182
Jun 19940.0082
Jul 19940.1822
Aug 1994-0.0588
Sep 19940.0039
Oct 19940.0428
Nov 19940.0409
Dec 1994-0.0170
Jan 19950.1690
Feb 1995-0.1372
Mar 1995-0.0150
Apr 1995-0.0779
May 19950.0069
Jun 19950.0166
Jul 19950.0284
Aug 19950.0220
Sep 19950.1036
Oct 1995-0.0165
Nov 19950.0200
Dec 19950.0057
Jan 1996-0.0435
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 1997-0.0150
Mar 19970.0364
Apr 1997-0.0176
May 19970.0927
Jun 19970.0445
Jul 1997-0.0799
Aug 1997-0.0715
Sep 19970.0255
Oct 1997-0.0162
Nov 1997-0.0288
Dec 1997-0.0332
Jan 19980.0839
Feb 19980.0446
Mar 19980.1462
Apr 19980.0059
May 19980.0232
Jun 19980.0695
Jul 1998-0.1016
Aug 1998-0.0608
Sep 1998-0.0618
Oct 19980.0278
Nov 19980.0167
Dec 1998-0.0064
Jan 1999-0.0752
Feb 19990.1117
Mar 1999-0.0152
Apr 19990.0244
May 1999-0.0541
Jun 1999-0.0731
Jul 19990.0101
Aug 1999-0.0551
Sep 1999-0.0944
Oct 19990.1013
Nov 1999-0.0626
Dec 1999-0.0284
Jan 2000-0.0237
Feb 2000-0.0196
Mar 20000.1789
Apr 2000-0.0017
May 2000-0.0341
Jun 2000-0.0307
Jul 2000-0.0161
Aug 20000.0078
Sep 20000.1115
Oct 2000-0.0561
Nov 20000.0113
Dec 20000.0360
Jan 2001-0.0092
Feb 20010.0132
Mar 2001-0.0702
Apr 20010.0037
May 2001-0.0025
Jun 20010.0239
Jul 2001-0.0399
Aug 20010.0231
Sep 20010.0423
Oct 20010.0363
Nov 2001-0.0718
Dec 20010.0738
Jan 2002-0.0358
Feb 2002-0.0402
Mar 2002-0.0587
Apr 20020.0429
May 2002-0.0147
Jun 2002-0.0646
Jul 20020.0684
Aug 20020.0405
Sep 20020.0879
Oct 2002-0.0580
Nov 2002-0.0236
Dec 20020.0070
Jan 2003-0.0505
Feb 2003-0.0835
Mar 20030.0217
Apr 20030.0399
May 20030.0031
Jun 20030.0070
Jul 20030.0013
Aug 20030.0370
Sep 2003-0.0028
Oct 2003-0.0056
Nov 20030.0534
Dec 2003-0.0650
Jan 20040.0709
Feb 20040.0215
Mar 2004-0.0167
Apr 2004-0.0090
May 2004-0.0583
Jun 2004-0.0275
Jul 2004-0.0345
Aug 2004-0.0183
Sep 2004-0.0161
Oct 2004-0.0494
Nov 2004-0.0423
Dec 20040.0174
Jan 20050.0215
Feb 2005-0.0344
Mar 2005-0.0428
Apr 2005-0.0286
May 2005-0.0252
Jun 2005-0.0193
Jul 2005-0.0326
Aug 2005-0.0009
Sep 2005-0.0235
Oct 20050.0580
Nov 20050.0064
Dec 2005-0.0099
Jan 2006-0.0030
Feb 2006-0.0306
Mar 20060.0347
Apr 2006-0.0357
May 20060.0447
Jun 2006-0.0156
Jul 2006-0.0219
Aug 20060.0307
Sep 2006-0.0327
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 20070.0102
Jul 20070.0237
Aug 20070.0680
Sep 2007-0.0386
Oct 20070.1038
Nov 20070.0878
Dec 20070.0156
Jan 20080.0034
Feb 20080.0428
Mar 2008-0.0300
Apr 2008-0.0384
May 2008-0.0018
Jun 2008-0.0298
Jul 2008-0.0317
Aug 2008-0.0024
Sep 20080.2077
Oct 20080.0227
Nov 2008-0.0526
Dec 2008-0.0731
Jan 2009-0.0249
Feb 2009-0.0351
Mar 20090.0233
Apr 2009-0.0063
May 2009-0.0876
Jun 2009-0.0384
Jul 20090.0205
Aug 20090.0252
Sep 2009-0.0234
Oct 2009-0.0299
Nov 2009-0.0414
Dec 2009-0.0246
Jan 20100.1825
Feb 20100.0139
Mar 2010-0.0337
Apr 2010-0.0542
May 2010-0.0174
Jun 20100.1621
Jul 2010-0.0840
Aug 20100.0393
Sep 2010-0.0177
Oct 2010-0.0784
Nov 20100.0176
Dec 2010-0.0451
Jan 2011-0.0162
Feb 20110.0449
Mar 2011-0.0472
Apr 2011-0.0362
May 2011-0.0525
Jun 2011-0.0208
Jul 2011-0.0205
Aug 20110.0034
Sep 20110.0099
Oct 20110.0269
Nov 20110.0049
Dec 2011-0.0498
Jan 2012-0.0003
Feb 2012-0.0471
Mar 2012-0.0033
Apr 2012-0.0122
May 20120.0234
Jun 20120.0172
Jul 2012-0.0009
Aug 2012-0.0284
Sep 20120.0262
Oct 2012-0.0201
Nov 20120.0132
Dec 20120.0160
Jan 20130.0352
Feb 20130.0292
Mar 2013-0.0108
Apr 2013-0.0042
May 20130.0645
Jun 2013-0.0119
Jul 2013-0.0147
Aug 2013-0.0190
Sep 2013-0.0015
Oct 2013-0.0430
Nov 2013-0.0212
Dec 2013-0.0010
Jan 2014-0.0065
Feb 2014-0.0118
Mar 20140.0522
Apr 20140.0095
May 2014-0.0331
Jun 2014-0.0193
Jul 2014-0.0122
Aug 20140.0571
Sep 2014-0.0029
Oct 2014-0.0164
Nov 20140.0220
Dec 20140.0174
Jan 2015-0.0144
Feb 2015-0.0203
Mar 2015-0.0016
Apr 2015-0.0326
May 2015-0.0044
Jun 2015-0.0351
Jul 20150.0130
Aug 2015-0.0073
Sep 2015-0.0509
Oct 2015-0.0243
Nov 2015-0.0147
Dec 2015-0.0121
Jan 2016-0.0129
Feb 20160.0281
Mar 2016-0.0087
Apr 20160.0273
May 2016-0.0496
Jun 20160.0119
Jul 2016-0.0335
Aug 20160.0453
Sep 2016-0.0263
Oct 2016-0.0179
Nov 20160.0615
Dec 2016-0.0095
Jan 2017-0.0030
Feb 20170.0029
Mar 2017-0.0293
Apr 2017-0.0262
May 2017-0.0201
Jun 20170.0231
Jul 20170.0108
Aug 20170.0332
Sep 2017-0.0023
Oct 2017-0.0082
Nov 2017-0.0015
Dec 20170.0084
Jan 20180.0327
Feb 2018-0.0021
Mar 2018-0.0171
Apr 2018-0.0299
May 2018-0.0154
Jun 2018-0.0313
Jul 20180.0264
Aug 20180.0299
Sep 20180.0030
Oct 2018-0.0140
Nov 20180.0336
Dec 20180.0110
Jan 2019-0.0433
Feb 2019-0.0455
Mar 2019-0.0190
Apr 20190.0272
May 2019-0.0369
Jun 20190.0056