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 - Jun 2020
Regression Basis 422 monthly samples
Coefficient of Determination (R2) 31.9%
Adjusted R2 30.9%
Regression F statistic 32.38 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.045 with p-value 0.672)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.600 with p-value 0.731)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.86 0.071 12.068 0.000 0.722...1.003
Size (SMB) -0.36 0.112 -3.233 0.001 -0.585...-0.142
Value (HML-DEV) 0.23 0.113 2.066 0.039 0.011...0.456
Momentum (MOM) 0.01 0.095 0.156 0.876 -0.172...0.202
Quality (QMJ) 0.41 0.154 2.647 0.008 0.105...0.710
Bet Against Beta (BAB) 0.23 0.080 2.825 0.005 0.069...0.385
Alpha (α) 13.56bps 0.003 0.489 0.625 -0.41%...0.68%
Annualized Alpha (α) 1.63%  
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) 67.65 -1.25 3.61 60.02 46.23 76.81  
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 2020 1.63% 58.35 0.45 0.84 0.89 18.83 17.44 110.37 31.9%
Regression residuals
MonthBRK.A
May 1985-0.0561
Jun 19850.1303
Jul 1985-0.0101
Aug 1985-0.0377
Sep 19850.0498
Oct 19850.1838
Nov 1985-0.0687
Dec 1985-0.1121
Jan 1986-0.0907
Feb 19860.1448
Mar 19860.0650
Apr 1986-0.0584
May 1986-0.0788
Jun 19860.0016
Jul 1986-0.0305
Aug 1986-0.0503
Sep 1986-0.0242
Oct 19860.0462
Nov 1986-0.0788
Dec 19860.0491
Jan 1987-0.0246
Feb 19870.0663
Mar 19870.0137
Apr 1987-0.0379
May 1987-0.0041
Jun 1987-0.0334
Jul 19870.0833
Aug 1987-0.0402
Sep 19870.0774
Oct 1987-0.0592
Nov 1987-0.0713
Dec 1987-0.0250
Jan 1988-0.0304
Feb 19880.0102
Mar 19880.1131
Apr 19880.0886
May 19880.0149
Jun 19880.0194
Jul 19880.0497
Aug 1988-0.0016
Sep 19880.0797
Oct 1988-0.0524
Nov 1988-0.0001
Dec 1988-0.0092
Jan 1989-0.0168
Feb 1989-0.0169
Mar 19890.0265
Apr 19890.2173
May 1989-0.0093
Jun 19890.0113
Jul 19890.0553
Aug 19890.0398
Sep 19890.0856
Oct 1989-0.0124
Nov 1989-0.0557
Dec 19890.0197
Jan 1990-0.0896
Feb 1990-0.0381
Mar 1990-0.0876
Apr 19900.0201
May 1990-0.0093
Jun 19900.0077
Jul 1990-0.0414
Aug 1990-0.0239
Sep 1990-0.0639
Oct 19900.0050
Nov 19900.0178
Dec 19900.0199
Jan 19910.0934
Feb 19910.0404
Mar 1991-0.0166
Apr 1991-0.0057
May 19910.0350
Jun 1991-0.0211
Jul 1991-0.0285
Aug 19910.0059
Sep 19910.0225
Oct 1991-0.0518
Nov 1991-0.0104
Dec 1991-0.0078
Jan 19920.0065
Feb 1992-0.0337
Mar 19920.0262
Apr 1992-0.0322
May 1992-0.0182
Jun 19920.0039
Jul 1992-0.0120
Aug 1992-0.0400
Sep 19920.0167
Oct 19920.0060
Nov 19920.1207
Dec 19920.0804
Jan 19930.0155
Feb 1993-0.0104
Mar 1993-0.0055
Apr 19930.0019
May 19930.1715
Jun 19930.0150
Jul 19930.0321
Aug 19930.0602
Sep 1993-0.0437
Oct 19930.0167
Nov 19930.0078
Dec 1993-0.0748
Jan 1994-0.0376
Feb 1994-0.0234
Mar 19940.0574
Apr 1994-0.0073
May 1994-0.0181
Jun 19940.0084
Jul 19940.1824
Aug 1994-0.0577
Sep 19940.0048
Oct 19940.0429
Nov 19940.0403
Dec 1994-0.0171
Jan 19950.1695
Feb 1995-0.1362
Mar 1995-0.0143
Apr 1995-0.0772
May 19950.0075
Jun 19950.0175
Jul 19950.0295
Aug 19950.0226
Sep 19950.1044
Oct 1995-0.0167
Nov 19950.0204
Dec 19950.0060
Jan 1996-0.0431
Feb 19960.1046
Mar 1996-0.0617
Apr 1996-0.0140
May 1996-0.1112
Jun 1996-0.0208
Jul 19960.0234
Aug 1996-0.0062
Sep 1996-0.0254
Oct 1996-0.0396
Nov 1996-0.0565
Dec 19960.0379
Jan 1997-0.0391
Feb 1997-0.0142
Mar 19970.0363
Apr 1997-0.0177
May 19970.0949
Jun 19970.0467
Jul 1997-0.0788
Aug 1997-0.0705
Sep 19970.0279
Oct 1997-0.0161
Nov 1997-0.0286
Dec 1997-0.0325
Jan 19980.0840
Feb 19980.0461
Mar 19980.1475
Apr 19980.0066
May 19980.0227
Jun 19980.0688
Jul 1998-0.1031
Aug 1998-0.0636
Sep 1998-0.0612
Oct 19980.0276
Nov 19980.0177
Dec 1998-0.0061
Jan 1999-0.0756
Feb 19990.1100
Mar 1999-0.0167
Apr 19990.0258
May 1999-0.0523
Jun 1999-0.0718
Jul 19990.0106
Aug 1999-0.0557
Sep 1999-0.0951
Oct 19990.0999
Nov 1999-0.0628
Dec 1999-0.0289
Jan 2000-0.0241
Feb 2000-0.0215
Mar 20000.1796
Apr 2000-0.0006
May 2000-0.0338
Jun 2000-0.0315
Jul 2000-0.0149
Aug 20000.0075
Sep 20000.1125
Oct 2000-0.0553
Nov 20000.0136
Dec 20000.0371
Jan 2001-0.0075
Feb 20010.0154
Mar 2001-0.0695
Apr 20010.0045
May 2001-0.0004
Jun 20010.0253
Jul 2001-0.0389
Aug 20010.0243
Sep 20010.0406
Oct 20010.0378
Nov 2001-0.0705
Dec 20010.0760
Jan 2002-0.0338
Feb 2002-0.0390
Mar 2002-0.0564
Apr 20020.0455
May 2002-0.0144
Jun 2002-0.0639
Jul 20020.0667
Aug 20020.0408
Sep 20020.0876
Oct 2002-0.0579
Nov 2002-0.0236
Dec 20020.0084
Jan 2003-0.0503
Feb 2003-0.0836
Mar 20030.0223
Apr 20030.0407
May 20030.0044
Jun 20030.0081
Jul 20030.0025
Aug 20030.0381
Sep 2003-0.0021
Oct 2003-0.0037
Nov 20030.0553
Dec 2003-0.0636
Jan 20040.0712
Feb 20040.0227
Mar 2004-0.0153
Apr 2004-0.0089
May 2004-0.0580
Jun 2004-0.0260
Jul 2004-0.0341
Aug 2004-0.0181
Sep 2004-0.0150
Oct 2004-0.0486
Nov 2004-0.0401
Dec 20040.0185
Jan 20050.0215
Feb 2005-0.0335
Mar 2005-0.0427
Apr 2005-0.0295
May 2005-0.0239
Jun 2005-0.0179
Jul 2005-0.0312
Aug 2005-0.0015
Sep 2005-0.0223
Oct 20050.0574
Nov 20050.0075
Dec 2005-0.0100
Jan 2006-0.0013
Feb 2006-0.0305
Mar 20060.0359
Apr 2006-0.0357
May 20060.0440
Jun 2006-0.0154
Jul 2006-0.0222
Aug 20060.0312
Sep 2006-0.0322
Oct 20060.0764
Nov 2006-0.0045
Dec 20060.0050
Jan 2007-0.0193
Feb 2007-0.0212
Mar 20070.0116
Apr 2007-0.0419
May 2007-0.0351
Jun 20070.0104
Jul 20070.0223
Aug 20070.0680
Sep 2007-0.0388
Oct 20070.1038
Nov 20070.0861
Dec 20070.0152
Jan 20080.0027
Feb 20080.0424
Mar 2008-0.0305
Apr 2008-0.0384
May 2008-0.0007
Jun 2008-0.0320
Jul 2008-0.0311
Aug 2008-0.0007
Sep 20080.2054
Oct 20080.0187
Nov 2008-0.0554
Dec 2008-0.0717
Jan 2009-0.0243
Feb 2009-0.0373
Mar 20090.0253
Apr 2009-0.0010
May 2009-0.0856
Jun 2009-0.0362
Jul 20090.0219
Aug 20090.0252
Sep 2009-0.0220
Oct 2009-0.0300
Nov 2009-0.0411
Dec 2009-0.0226
Jan 20100.1825
Feb 20100.0149
Mar 2010-0.0322
Apr 2010-0.0528
May 2010-0.0187
Jun 20100.1611
Jul 2010-0.0830
Aug 20100.0381
Sep 2010-0.0151
Oct 2010-0.0772
Nov 20100.0183
Dec 2010-0.0439
Jan 2011-0.0159
Feb 20110.0460
Mar 2011-0.0464
Apr 2011-0.0354
May 2011-0.0521
Jun 2011-0.0207
Jul 2011-0.0212
Aug 20110.0028
Sep 20110.0091
Oct 20110.0288
Nov 20110.0055
Dec 2011-0.0492
Jan 20120.0011
Feb 2012-0.0463
Mar 2012-0.0022
Apr 2012-0.0121
May 20120.0228
Jun 20120.0184
Jul 2012-0.0009
Aug 2012-0.0275
Sep 20120.0270
Oct 2012-0.0205
Nov 20120.0136
Dec 20120.0164
Jan 20130.0369
Feb 20130.0298
Mar 2013-0.0096
Apr 2013-0.0044
May 20130.0657
Jun 2013-0.0113
Jul 2013-0.0129
Aug 2013-0.0194
Sep 2013-0.0002
Oct 2013-0.0416
Nov 2013-0.0197
Dec 2013-0.0007
Jan 2014-0.0076
Feb 2014-0.0110
Mar 20140.0532
Apr 20140.0092
May 2014-0.0328
Jun 2014-0.0183
Jul 2014-0.0131
Aug 20140.0582
Sep 2014-0.0035
Oct 2014-0.0144
Nov 20140.0224
Dec 20140.0183
Jan 2015-0.0156
Feb 2015-0.0188
Mar 2015-0.0014
Apr 2015-0.0322
May 2015-0.0042
Jun 2015-0.0346
Jul 20150.0127
Aug 2015-0.0079
Sep 2015-0.0509
Oct 2015-0.0230
Nov 2015-0.0141
Dec 2015-0.0130
Jan 2016-0.0131
Feb 20160.0294
Mar 2016-0.0068
Apr 20160.0278
May 2016-0.0495
Jun 20160.0125
Jul 2016-0.0319
Aug 20160.0458
Sep 2016-0.0266
Oct 2016-0.0181
Nov 20160.0644
Dec 2016-0.0077
Jan 2017-0.0033
Feb 20170.0036
Mar 2017-0.0289
Apr 2017-0.0254
May 2017-0.0203
Jun 20170.0240
Jul 20170.0108
Aug 20170.0330
Sep 2017-0.0010
Oct 2017-0.0077
Nov 2017-0.0001
Dec 20170.0086
Jan 20180.0332
Feb 2018-0.0029
Mar 2018-0.0163
Apr 2018-0.0297
May 2018-0.0139
Jun 2018-0.0303
Jul 20180.0267
Aug 20180.0308
Sep 20180.0029
Oct 2018-0.0146
Nov 20180.0335
Dec 20180.0091
Jan 2019-0.0416
Feb 2019-0.0447
Mar 2019-0.0197
Apr 20190.0284
May 2019-0.0381
Jun 20190.0070
Jul 2019-0.0569
Aug 2019-0.0093
Sep 2019-0.0036
Oct 20190.0079
Nov 20190.0231
Dec 20190.0101
Jan 2020-0.0082
Feb 20200.0099
Mar 20200.0012
Apr 2020-0.0686
May 2020-0.0444
Jun 2020-0.0590