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 - Feb 2020
Regression Basis 418 monthly samples
Coefficient of Determination (R2) 31.6%
Adjusted R2 30.6%
Regression F statistic 31.69 (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 3.882 with p-value 0.693)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.88 0.074 11.955 0.000 0.735...1.024
Size (SMB) -0.34 0.115 -2.948 0.003 -0.563...-0.113
Value (HML-DEV) 0.24 0.118 2.045 0.042 0.009...0.474
Momentum (MOM) 0.01 0.097 0.092 0.927 -0.181...0.199
Quality (QMJ) 0.42 0.156 2.701 0.007 0.115...0.728
Bet Against Beta (BAB) 0.24 0.082 2.898 0.004 0.076...0.398
Alpha (α) 15.38bps 0.003 0.549 0.584 -0.40%...0.70%
Annualized Alpha (α) 1.85%  
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) 66.60 -2.20 5.43 61.62 46.69 77.95  
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 Feb 2020 1.85% 58.57 0.74 1.31 0.55 19.68 18.48 114.71 31.6%
Regression residuals
MonthBRK.A
May 1985-0.0562
Jun 19850.1300
Jul 1985-0.0112
Aug 1985-0.0378
Sep 19850.0504
Oct 19850.1833
Nov 1985-0.0702
Dec 1985-0.1132
Jan 1986-0.0907
Feb 19860.1435
Mar 19860.0639
Apr 1986-0.0593
May 1986-0.0797
Jun 19860.0012
Jul 1986-0.0293
Aug 1986-0.0506
Sep 1986-0.0238
Oct 19860.0463
Nov 1986-0.0788
Dec 19860.0494
Jan 1987-0.0266
Feb 19870.0648
Mar 19870.0127
Apr 1987-0.0374
May 1987-0.0043
Jun 1987-0.0343
Jul 19870.0825
Aug 1987-0.0410
Sep 19870.0777
Oct 1987-0.0539
Nov 1987-0.0715
Dec 1987-0.0249
Jan 1988-0.0325
Feb 19880.0086
Mar 19880.1113
Apr 19880.0880
May 19880.0151
Jun 19880.0181
Jul 19880.0497
Aug 1988-0.0015
Sep 19880.0796
Oct 1988-0.0521
Nov 19880.0006
Dec 1988-0.0098
Jan 1989-0.0173
Feb 1989-0.0175
Mar 19890.0262
Apr 19890.2167
May 1989-0.0096
Jun 19890.0112
Jul 19890.0557
Aug 19890.0392
Sep 19890.0859
Oct 1989-0.0115
Nov 1989-0.0557
Dec 19890.0201
Jan 1990-0.0888
Feb 1990-0.0385
Mar 1990-0.0882
Apr 19900.0207
May 1990-0.0094
Jun 19900.0073
Jul 1990-0.0407
Aug 1990-0.0216
Sep 1990-0.0624
Oct 19900.0065
Nov 19900.0173
Dec 19900.0195
Jan 19910.0919
Feb 19910.0378
Mar 1991-0.0182
Apr 1991-0.0065
May 19910.0346
Jun 1991-0.0213
Jul 1991-0.0287
Aug 19910.0054
Sep 19910.0223
Oct 1991-0.0522
Nov 1991-0.0105
Dec 1991-0.0077
Jan 19920.0037
Feb 1992-0.0349
Mar 19920.0259
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 1993-0.0064
Apr 19930.0020
May 19930.1706
Jun 19930.0151
Jul 19930.0315
Aug 19930.0593
Sep 1993-0.0447
Oct 19930.0155
Nov 19930.0081
Dec 1993-0.0755
Jan 1994-0.0387
Feb 1994-0.0239
Mar 19940.0578
Apr 1994-0.0072
May 1994-0.0183
Jun 19940.0082
Jul 19940.1823
Aug 1994-0.0586
Sep 19940.0040
Oct 19940.0431
Nov 19940.0409
Dec 1994-0.0169
Jan 19950.1691
Feb 1995-0.1371
Mar 1995-0.0148
Apr 1995-0.0778
May 19950.0070
Jun 19950.0166
Jul 19950.0285
Aug 19950.0218
Sep 19950.1039
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 19960.0243
Aug 1996-0.0075
Sep 1996-0.0261
Oct 1996-0.0395
Nov 1996-0.0575
Dec 19960.0371
Jan 1997-0.0401
Feb 1997-0.0148
Mar 19970.0365
Apr 1997-0.0169
May 19970.0926
Jun 19970.0450
Jul 1997-0.0795
Aug 1997-0.0719
Sep 19970.0257
Oct 1997-0.0162
Nov 1997-0.0284
Dec 1997-0.0328
Jan 19980.0839
Feb 19980.0448
Mar 19980.1464
Apr 19980.0059
May 19980.0234
Jun 19980.0699
Jul 1998-0.1016
Aug 1998-0.0606
Sep 1998-0.0618
Oct 19980.0277
Nov 19980.0168
Dec 1998-0.0060
Jan 1999-0.0755
Feb 19990.1113
Mar 1999-0.0156
Apr 19990.0241
May 1999-0.0540
Jun 1999-0.0728
Jul 19990.0102
Aug 1999-0.0549
Sep 1999-0.0945
Oct 19990.1014
Nov 1999-0.0629
Dec 1999-0.0284
Jan 2000-0.0242
Feb 2000-0.0205
Mar 20000.1796
Apr 2000-0.0012
May 2000-0.0341
Jun 2000-0.0310
Jul 2000-0.0156
Aug 20000.0078
Sep 20000.1119
Oct 2000-0.0554
Nov 20000.0124
Dec 20000.0364
Jan 2001-0.0106
Feb 20010.0147
Mar 2001-0.0694
Apr 20010.0031
May 2001-0.0024
Jun 20010.0240
Jul 2001-0.0391
Aug 20010.0237
Sep 20010.0428
Oct 20010.0358
Nov 2001-0.0721
Dec 20010.0739
Jan 2002-0.0351
Feb 2002-0.0395
Mar 2002-0.0586
Apr 20020.0436
May 2002-0.0143
Jun 2002-0.0643
Jul 20020.0685
Aug 20020.0407
Sep 20020.0881
Oct 2002-0.0581
Nov 2002-0.0248
Dec 20020.0078
Jan 2003-0.0506
Feb 2003-0.0835
Mar 20030.0217
Apr 20030.0394
May 20030.0024
Jun 20030.0070
Jul 20030.0010
Aug 20030.0369
Sep 2003-0.0029
Oct 2003-0.0052
Nov 20030.0537
Dec 2003-0.0649
Jan 20040.0707
Feb 20040.0217
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 20040.0174
Jan 20050.0217
Feb 2005-0.0341
Mar 2005-0.0427
Apr 2005-0.0287
May 2005-0.0251
Jun 2005-0.0191
Jul 2005-0.0326
Aug 2005-0.0011
Sep 2005-0.0233
Oct 20050.0579
Nov 20050.0065
Dec 2005-0.0101
Jan 2006-0.0029
Feb 2006-0.0308
Mar 20060.0348
Apr 2006-0.0357
May 20060.0445
Jun 2006-0.0155
Jul 2006-0.0219
Aug 20060.0305
Sep 2006-0.0326
Oct 20060.0753
Nov 2006-0.0053
Dec 20060.0045
Jan 2007-0.0197
Feb 2007-0.0216
Mar 20070.0116
Apr 2007-0.0422
May 2007-0.0358
Jun 20070.0102
Jul 20070.0236
Aug 20070.0680
Sep 2007-0.0385
Oct 20070.1040
Nov 20070.0877
Dec 20070.0158
Jan 20080.0026
Feb 20080.0430
Mar 2008-0.0299
Apr 2008-0.0384
May 2008-0.0016
Jun 2008-0.0298
Jul 2008-0.0320
Aug 2008-0.0023
Sep 20080.2074
Oct 20080.0226
Nov 2008-0.0524
Dec 2008-0.0733
Jan 2009-0.0251
Feb 2009-0.0353
Mar 20090.0232
Apr 2009-0.0071
May 2009-0.0882
Jun 2009-0.0379
Jul 20090.0203
Aug 20090.0244
Sep 2009-0.0237
Oct 2009-0.0295
Nov 2009-0.0411
Dec 2009-0.0244
Jan 20100.1821
Feb 20100.0142
Mar 2010-0.0335
Apr 2010-0.0542
May 2010-0.0177
Jun 20100.1618
Jul 2010-0.0838
Aug 20100.0392
Sep 2010-0.0173
Oct 2010-0.0783
Nov 20100.0175
Dec 2010-0.0453
Jan 2011-0.0162
Feb 20110.0450
Mar 2011-0.0470
Apr 2011-0.0360
May 2011-0.0524
Jun 2011-0.0206
Jul 2011-0.0206
Aug 20110.0036
Sep 20110.0100
Oct 20110.0269
Nov 20110.0053
Dec 2011-0.0496
Jan 2012-0.0007
Feb 2012-0.0470
Mar 2012-0.0030
Apr 2012-0.0121
May 20120.0236
Jun 20120.0173
Jul 2012-0.0007
Aug 2012-0.0284
Sep 20120.0261
Oct 2012-0.0203
Nov 20120.0133
Dec 20120.0157
Jan 20130.0353
Feb 20130.0294
Mar 2013-0.0106
Apr 2013-0.0042
May 20130.0645
Jun 2013-0.0119
Jul 2013-0.0144
Aug 2013-0.0191
Sep 2013-0.0013
Oct 2013-0.0426
Nov 2013-0.0209
Dec 2013-0.0010
Jan 2014-0.0071
Feb 2014-0.0117
Mar 20140.0524
Apr 20140.0094
May 2014-0.0330
Jun 2014-0.0194
Jul 2014-0.0123
Aug 20140.0572
Sep 2014-0.0027
Oct 2014-0.0161
Nov 20140.0222
Dec 20140.0177
Jan 2015-0.0147
Feb 2015-0.0202
Mar 2015-0.0017
Apr 2015-0.0327
May 2015-0.0042
Jun 2015-0.0350
Jul 20150.0136
Aug 2015-0.0076
Sep 2015-0.0504
Oct 2015-0.0241
Nov 2015-0.0146
Dec 2015-0.0120
Jan 2016-0.0124
Feb 20160.0282
Mar 2016-0.0086
Apr 20160.0268
May 2016-0.0496
Jun 20160.0123
Jul 2016-0.0335
Aug 20160.0451
Sep 2016-0.0268
Oct 2016-0.0176
Nov 20160.0618
Dec 2016-0.0091
Jan 2017-0.0033
Feb 20170.0030
Mar 2017-0.0294
Apr 2017-0.0261
May 2017-0.0200
Jun 20170.0231
Jul 20170.0107
Aug 20170.0331
Sep 2017-0.0023
Oct 2017-0.0078
Nov 2017-0.0012
Dec 20170.0083
Jan 20180.0330
Feb 2018-0.0021
Mar 2018-0.0172
Apr 2018-0.0300
May 2018-0.0153
Jun 2018-0.0314
Jul 20180.0265
Aug 20180.0303
Sep 20180.0031
Oct 2018-0.0138
Nov 20180.0336
Dec 20180.0109
Jan 2019-0.0437
Feb 2019-0.0456
Mar 2019-0.0192
Apr 20190.0275
May 2019-0.0369
Jun 20190.0056
Jul 2019-0.0571
Aug 2019-0.0077
Sep 2019-0.0053
Oct 20190.0077
Nov 20190.0222
Dec 20190.0086
Jan 2020-0.0073
Feb 20200.0121