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 - Aug 2019
Coefficient of Determination (R2) 31.2%
Adjusted R2 30.2%
Regression F statistic 30.67 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.059 with p-value 0.719)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.836 with p-value 0.699)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.88 0.076 11.671 0.000 0.734...1.032
Size (SMB) -0.34 0.117 -2.875 0.004 -0.565...-0.106
Value (HML-DEV) 0.25 0.122 2.019 0.044 0.007...0.486
Momentum (MOM) 0.01 0.098 0.121 0.904 -0.181...0.204
Quality (QMJ) 0.43 0.161 2.667 0.008 0.113...0.746
Bet Against Beta (BAB) 0.24 0.083 2.870 0.004 0.075...0.401
Alpha (α) 13.51bps 0.003 0.470 0.639 -0.43%...0.70%
Annualized Alpha (α) 1.62%  
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) 67.31 -1.96 6.99 63.00 48.45 80.17  
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 Aug 2019 1.62% 59.44 0.66 1.72 0.75 20.81 19.09 115.98 31.2%
Regression residuals
MonthBRK.A
May 1985-0.0562
Jun 19850.1300
Jul 1985-0.0110
Aug 1985-0.0377
Sep 19850.0504
Oct 19850.1833
Nov 1985-0.0703
Dec 1985-0.1133
Jan 1986-0.0905
Feb 19860.1433
Mar 19860.0637
Apr 1986-0.0592
May 1986-0.0798
Jun 19860.0011
Jul 1986-0.0292
Aug 1986-0.0505
Sep 1986-0.0234
Oct 19860.0463
Nov 1986-0.0788
Dec 19860.0496
Jan 1987-0.0268
Feb 19870.0650
Mar 19870.0126
Apr 1987-0.0372
May 1987-0.0042
Jun 1987-0.0344
Jul 19870.0825
Aug 1987-0.0411
Sep 19870.0780
Oct 1987-0.0532
Nov 1987-0.0712
Dec 1987-0.0249
Jan 1988-0.0325
Feb 19880.0086
Mar 19880.1114
Apr 19880.0881
May 19880.0152
Jun 19880.0182
Jul 19880.0498
Aug 1988-0.0013
Sep 19880.0797
Oct 1988-0.0521
Nov 19880.0008
Dec 1988-0.0097
Jan 1989-0.0173
Feb 1989-0.0173
Mar 19890.0263
Apr 19890.2167
May 1989-0.0095
Jun 19890.0113
Jul 19890.0556
Aug 19890.0393
Sep 19890.0861
Oct 1989-0.0114
Nov 1989-0.0556
Dec 19890.0201
Jan 1990-0.0885
Feb 1990-0.0382
Mar 1990-0.0882
Apr 19900.0209
May 1990-0.0093
Jun 19900.0074
Jul 1990-0.0407
Aug 1990-0.0212
Sep 1990-0.0624
Oct 19900.0067
Nov 19900.0176
Dec 19900.0194
Jan 19910.0921
Feb 19910.0379
Mar 1991-0.0181
Apr 1991-0.0065
May 19910.0347
Jun 1991-0.0214
Jul 1991-0.0286
Aug 19910.0055
Sep 19910.0226
Oct 1991-0.0520
Nov 1991-0.0105
Dec 1991-0.0079
Jan 19920.0038
Feb 1992-0.0349
Mar 19920.0259
Apr 1992-0.0316
May 1992-0.0185
Jun 19920.0043
Jul 1992-0.0128
Aug 1992-0.0402
Sep 19920.0161
Oct 19920.0055
Nov 19920.1195
Dec 19920.0793
Jan 19930.0142
Feb 1993-0.0107
Mar 1993-0.0064
Apr 19930.0023
May 19930.1708
Jun 19930.0152
Jul 19930.0315
Aug 19930.0593
Sep 1993-0.0447
Oct 19930.0157
Nov 19930.0084
Dec 1993-0.0755
Jan 1994-0.0385
Feb 1994-0.0239
Mar 19940.0580
Apr 1994-0.0072
May 1994-0.0180
Jun 19940.0083
Jul 19940.1824
Aug 1994-0.0586
Sep 19940.0041
Oct 19940.0431
Nov 19940.0411
Dec 1994-0.0168
Jan 19950.1692
Feb 1995-0.1370
Mar 1995-0.0148
Apr 1995-0.0778
May 19950.0071
Jun 19950.0168
Jul 19950.0286
Aug 19950.0220
Sep 19950.1038
Oct 1995-0.0161
Nov 19950.0202
Dec 19950.0058
Jan 1996-0.0433
Feb 19960.1037
Mar 1996-0.0625
Apr 1996-0.0155
May 1996-0.1126
Jun 1996-0.0208
Jul 19960.0244
Aug 1996-0.0074
Sep 1996-0.0262
Oct 1996-0.0397
Nov 1996-0.0575
Dec 19960.0372
Jan 1997-0.0401
Feb 1997-0.0148
Mar 19970.0365
Apr 1997-0.0171
May 19970.0927
Jun 19970.0448
Jul 1997-0.0796
Aug 1997-0.0716
Sep 19970.0257
Oct 1997-0.0161
Nov 1997-0.0285
Dec 1997-0.0329
Jan 19980.0840
Feb 19980.0448
Mar 19980.1464
Apr 19980.0060
May 19980.0234
Jun 19980.0699
Jul 1998-0.1014
Aug 1998-0.0606
Sep 1998-0.0617
Oct 19980.0280
Nov 19980.0169
Dec 1998-0.0060
Jan 1999-0.0751
Feb 19990.1118
Mar 1999-0.0151
Apr 19990.0243
May 1999-0.0540
Jun 1999-0.0729
Jul 19990.0102
Aug 1999-0.0549
Sep 1999-0.0943
Oct 19990.1017
Nov 1999-0.0625
Dec 1999-0.0282
Jan 2000-0.0238
Feb 2000-0.0196
Mar 20000.1793
Apr 2000-0.0016
May 2000-0.0340
Jun 2000-0.0306
Jul 2000-0.0159
Aug 20000.0081
Sep 20000.1117
Oct 2000-0.0558
Nov 20000.0116
Dec 20000.0363
Jan 2001-0.0099
Feb 20010.0136
Mar 2001-0.0699
Apr 20010.0037
May 2001-0.0024
Jun 20010.0240
Jul 2001-0.0395
Aug 20010.0234
Sep 20010.0427
Oct 20010.0361
Nov 2001-0.0718
Dec 20010.0738
Jan 2002-0.0355
Feb 2002-0.0398
Mar 2002-0.0586
Apr 20020.0432
May 2002-0.0144
Jun 2002-0.0644
Jul 20020.0687
Aug 20020.0408
Sep 20020.0882
Oct 2002-0.0579
Nov 2002-0.0240
Dec 20020.0074
Jan 2003-0.0504
Feb 2003-0.0833
Mar 20030.0218
Apr 20030.0398
May 20030.0028
Jun 20030.0071
Jul 20030.0013
Aug 20030.0370
Sep 2003-0.0028
Oct 2003-0.0054
Nov 20030.0536
Dec 2003-0.0649
Jan 20040.0709
Feb 20040.0217
Mar 2004-0.0166
Apr 2004-0.0088
May 2004-0.0581
Jun 2004-0.0273
Jul 2004-0.0343
Aug 2004-0.0182
Sep 2004-0.0159
Oct 2004-0.0493
Nov 2004-0.0422
Dec 20040.0175
Jan 20050.0217
Feb 2005-0.0342
Mar 2005-0.0426
Apr 2005-0.0284
May 2005-0.0250
Jun 2005-0.0191
Jul 2005-0.0325
Aug 2005-0.0008
Sep 2005-0.0233
Oct 20050.0581
Nov 20050.0066
Dec 2005-0.0098
Jan 2006-0.0029
Feb 2006-0.0305
Mar 20060.0348
Apr 2006-0.0356
May 20060.0448
Jun 2006-0.0154
Jul 2006-0.0217
Aug 20060.0307
Sep 2006-0.0325
Oct 20060.0754
Nov 2006-0.0052
Dec 20060.0046
Jan 2007-0.0196
Feb 2007-0.0214
Mar 20070.0117
Apr 2007-0.0420
May 2007-0.0357
Jun 20070.0104
Jul 20070.0239
Aug 20070.0682
Sep 2007-0.0383
Oct 20070.1041
Nov 20070.0880
Dec 20070.0158
Jan 20080.0032
Feb 20080.0431
Mar 2008-0.0298
Apr 2008-0.0382
May 2008-0.0016
Jun 2008-0.0295
Jul 2008-0.0318
Aug 2008-0.0024
Sep 20080.2077
Oct 20080.0229
Nov 2008-0.0523
Dec 2008-0.0732
Jan 2009-0.0248
Feb 2009-0.0349
Mar 20090.0233
Apr 2009-0.0070
May 2009-0.0877
Jun 2009-0.0381
Jul 20090.0205
Aug 20090.0250
Sep 2009-0.0234
Oct 2009-0.0296
Nov 2009-0.0411
Dec 2009-0.0245
Jan 20100.1825
Feb 20100.0141
Mar 2010-0.0335
Apr 2010-0.0542
May 2010-0.0173
Jun 20100.1622
Jul 2010-0.0838
Aug 20100.0395
Sep 2010-0.0175
Oct 2010-0.0782
Nov 20100.0177
Dec 2010-0.0451
Jan 2011-0.0161
Feb 20110.0451
Mar 2011-0.0470
Apr 2011-0.0360
May 2011-0.0523
Jun 2011-0.0206
Jul 2011-0.0203
Aug 20110.0037
Sep 20110.0101
Oct 20110.0269
Nov 20110.0052
Dec 2011-0.0496
Jan 2012-0.0003
Feb 2012-0.0469
Mar 2012-0.0030
Apr 2012-0.0120
May 20120.0236
Jun 20120.0174
Jul 2012-0.0006
Aug 2012-0.0283
Sep 20120.0263
Oct 2012-0.0201
Nov 20120.0133
Dec 20120.0160
Jan 20130.0354
Feb 20130.0294
Mar 2013-0.0106
Apr 2013-0.0040
May 20130.0645
Jun 2013-0.0118
Jul 2013-0.0145
Aug 2013-0.0189
Sep 2013-0.0013
Oct 2013-0.0428
Nov 2013-0.0210
Dec 2013-0.0008
Jan 2014-0.0065
Feb 2014-0.0116
Mar 20140.0524
Apr 20140.0096
May 2014-0.0329
Jun 2014-0.0192
Jul 2014-0.0120
Aug 20140.0573
Sep 2014-0.0026
Oct 2014-0.0162
Nov 20140.0223
Dec 20140.0176
Jan 2015-0.0142
Feb 2015-0.0202
Mar 2015-0.0015
Apr 2015-0.0327
May 2015-0.0041
Jun 2015-0.0349
Jul 20150.0135
Aug 2015-0.0073
Sep 2015-0.0505
Oct 2015-0.0241
Nov 2015-0.0145
Dec 2015-0.0118
Jan 2016-0.0126
Feb 20160.0282
Mar 2016-0.0087
Apr 20160.0271
May 2016-0.0494
Jun 20160.0122
Jul 2016-0.0334
Aug 20160.0454
Sep 2016-0.0263
Oct 2016-0.0177
Nov 20160.0616
Dec 2016-0.0093
Jan 2017-0.0029
Feb 20170.0031
Mar 2017-0.0291
Apr 2017-0.0259
May 2017-0.0198
Jun 20170.0232
Jul 20170.0110
Aug 20170.0333
Sep 2017-0.0023
Oct 2017-0.0079
Nov 2017-0.0013
Dec 20170.0085
Jan 20180.0331
Feb 2018-0.0019
Mar 2018-0.0170
Apr 2018-0.0298
May 2018-0.0153
Jun 2018-0.0312
Jul 20180.0266
Aug 20180.0302
Sep 20180.0032
Oct 2018-0.0139
Nov 20180.0338
Dec 20180.0111
Jan 2019-0.0434
Feb 2019-0.0454
Mar 2019-0.0187
Apr 20190.0274
May 2019-0.0367
Jun 20190.0058
Jul 2019-0.0571
Aug 2019-0.0075