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 - Oct 2020
Regression Basis 426 monthly samples
Coefficient of Determination (R2) 32.5%
Adjusted R2 31.6%
Regression F statistic 33.66 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.048 with p-value 0.682)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.737 with p-value 0.712)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.87 0.071 12.341 0.000 0.734...1.012
Size (SMB) -0.37 0.112 -3.311 0.001 -0.590...-0.150
Value (HML-DEV) 0.23 0.112 2.042 0.042 0.009...0.450
Momentum (MOM) 0.02 0.095 0.178 0.859 -0.170...0.203
Quality (QMJ) 0.41 0.153 2.696 0.007 0.112...0.712
Bet Against Beta (BAB) 0.23 0.080 2.868 0.004 0.072...0.384
Alpha (α) 14.34bps 0.003 0.521 0.603 -0.40%...0.68%
Annualized Alpha (α) 1.72%  
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) 68.63 -0.84 2.28 61.33 45.94 76.69  
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 Oct 2020 1.72% 59.91 0.31 0.52 1.04 18.91 17.50 112.52 32.5%
Regression residuals
MonthBRK.A
May 1985-0.0570
Jun 19850.1299
Jul 1985-0.0099
Aug 1985-0.0376
Sep 19850.0499
Oct 19850.1831
Nov 1985-0.0696
Dec 1985-0.1128
Jan 1986-0.0908
Feb 19860.1438
Mar 19860.0642
Apr 1986-0.0584
May 1986-0.0796
Jun 19860.0010
Jul 1986-0.0301
Aug 1986-0.0508
Sep 1986-0.0229
Oct 19860.0454
Nov 1986-0.0792
Dec 19860.0493
Jan 1987-0.0262
Feb 19870.0659
Mar 19870.0135
Apr 1987-0.0379
May 1987-0.0042
Jun 1987-0.0341
Jul 19870.0827
Aug 1987-0.0408
Sep 19870.0776
Oct 1987-0.0570
Nov 1987-0.0704
Dec 1987-0.0260
Jan 1988-0.0303
Feb 19880.0099
Mar 19880.1136
Apr 19880.0885
May 19880.0147
Jun 19880.0190
Jul 19880.0498
Aug 1988-0.0013
Sep 19880.0792
Oct 1988-0.0527
Nov 1988-0.0000
Dec 1988-0.0094
Jan 1989-0.0176
Feb 1989-0.0165
Mar 19890.0262
Apr 19890.2165
May 1989-0.0098
Jun 19890.0114
Jul 19890.0539
Aug 19890.0396
Sep 19890.0855
Oct 1989-0.0125
Nov 1989-0.0562
Dec 19890.0192
Jan 1990-0.0888
Feb 1990-0.0382
Mar 1990-0.0881
Apr 19900.0201
May 1990-0.0106
Jun 19900.0076
Jul 1990-0.0417
Aug 1990-0.0231
Sep 1990-0.0639
Oct 19900.0044
Nov 19900.0172
Dec 19900.0194
Jan 19910.0934
Feb 19910.0401
Mar 1991-0.0168
Apr 1991-0.0057
May 19910.0345
Jun 1991-0.0207
Jul 1991-0.0294
Aug 19910.0055
Sep 19910.0226
Oct 1991-0.0521
Nov 1991-0.0103
Dec 1991-0.0097
Jan 19920.0075
Feb 1992-0.0336
Mar 19920.0264
Apr 1992-0.0326
May 1992-0.0183
Jun 19920.0041
Jul 1992-0.0126
Aug 1992-0.0399
Sep 19920.0166
Oct 19920.0057
Nov 19920.1204
Dec 19920.0803
Jan 19930.0157
Feb 1993-0.0105
Mar 1993-0.0059
Apr 19930.0023
May 19930.1712
Jun 19930.0149
Jul 19930.0322
Aug 19930.0598
Sep 1993-0.0437
Oct 19930.0167
Nov 19930.0080
Dec 1993-0.0751
Jan 1994-0.0380
Feb 1994-0.0232
Mar 19940.0578
Apr 1994-0.0074
May 1994-0.0182
Jun 19940.0088
Jul 19940.1821
Aug 1994-0.0583
Sep 19940.0049
Oct 19940.0424
Nov 19940.0405
Dec 1994-0.0174
Jan 19950.1692
Feb 1995-0.1366
Mar 1995-0.0148
Apr 1995-0.0775
May 19950.0070
Jun 19950.0171
Jul 19950.0290
Aug 19950.0227
Sep 19950.1037
Oct 1995-0.0172
Nov 19950.0198
Dec 19950.0058
Jan 1996-0.0435
Feb 19960.1043
Mar 1996-0.0616
Apr 1996-0.0141
May 1996-0.1115
Jun 1996-0.0210
Jul 19960.0239
Aug 1996-0.0065
Sep 1996-0.0264
Oct 1996-0.0401
Nov 1996-0.0575
Dec 19960.0382
Jan 1997-0.0399
Feb 1997-0.0142
Mar 19970.0367
Apr 1997-0.0189
May 19970.0945
Jun 19970.0461
Jul 1997-0.0800
Aug 1997-0.0697
Sep 19970.0274
Oct 1997-0.0159
Nov 1997-0.0295
Dec 1997-0.0330
Jan 19980.0838
Feb 19980.0452
Mar 19980.1468
Apr 19980.0065
May 19980.0226
Jun 19980.0678
Jul 1998-0.1033
Aug 1998-0.0625
Sep 1998-0.0619
Oct 19980.0267
Nov 19980.0170
Dec 1998-0.0073
Jan 1999-0.0761
Feb 19990.1101
Mar 1999-0.0171
Apr 19990.0260
May 1999-0.0518
Jun 1999-0.0726
Jul 19990.0109
Aug 1999-0.0560
Sep 1999-0.0951
Oct 19990.0985
Nov 1999-0.0632
Dec 1999-0.0299
Jan 2000-0.0233
Feb 2000-0.0217
Mar 20000.1785
Apr 2000-0.0001
May 2000-0.0335
Jun 2000-0.0321
Jul 2000-0.0149
Aug 20000.0065
Sep 20000.1132
Oct 2000-0.0551
Nov 20000.0141
Dec 20000.0369
Jan 2001-0.0059
Feb 20010.0158
Mar 2001-0.0693
Apr 20010.0036
May 2001-0.0002
Jun 20010.0256
Jul 2001-0.0393
Aug 20010.0244
Sep 20010.0408
Oct 20010.0380
Nov 2001-0.0708
Dec 20010.0763
Jan 2002-0.0338
Feb 2002-0.0393
Mar 2002-0.0567
Apr 20020.0456
May 2002-0.0147
Jun 2002-0.0635
Jul 20020.0666
Aug 20020.0409
Sep 20020.0883
Oct 2002-0.0588
Nov 2002-0.0229
Dec 20020.0087
Jan 2003-0.0501
Feb 2003-0.0839
Mar 20030.0222
Apr 20030.0406
May 20030.0051
Jun 20030.0082
Jul 20030.0025
Aug 20030.0380
Sep 2003-0.0020
Oct 2003-0.0044
Nov 20030.0552
Dec 2003-0.0640
Jan 20040.0714
Feb 20040.0223
Mar 2004-0.0151
Apr 2004-0.0089
May 2004-0.0583
Jun 2004-0.0259
Jul 2004-0.0341
Aug 2004-0.0183
Sep 2004-0.0153
Oct 2004-0.0488
Nov 2004-0.0404
Dec 20040.0182
Jan 20050.0216
Feb 2005-0.0340
Mar 2005-0.0426
Apr 2005-0.0297
May 2005-0.0242
Jun 2005-0.0179
Jul 2005-0.0316
Aug 2005-0.0017
Sep 2005-0.0227
Oct 20050.0576
Nov 20050.0069
Dec 2005-0.0101
Jan 2006-0.0015
Feb 2006-0.0306
Mar 20060.0360
Apr 2006-0.0357
May 20060.0443
Jun 2006-0.0156
Jul 2006-0.0225
Aug 20060.0310
Sep 2006-0.0325
Oct 20060.0762
Nov 2006-0.0047
Dec 20060.0049
Jan 2007-0.0196
Feb 2007-0.0210
Mar 20070.0112
Apr 2007-0.0427
May 2007-0.0357
Jun 20070.0104
Jul 20070.0220
Aug 20070.0677
Sep 2007-0.0396
Oct 20070.1031
Nov 20070.0861
Dec 20070.0150
Jan 20080.0040
Feb 20080.0420
Mar 2008-0.0305
Apr 2008-0.0391
May 2008-0.0010
Jun 2008-0.0322
Jul 2008-0.0305
Aug 2008-0.0007
Sep 20080.2066
Oct 20080.0190
Nov 2008-0.0557
Dec 2008-0.0715
Jan 2009-0.0240
Feb 2009-0.0374
Mar 20090.0250
Apr 20090.0009
May 2009-0.0856
Jun 2009-0.0365
Jul 20090.0217
Aug 20090.0251
Sep 2009-0.0223
Oct 2009-0.0302
Nov 2009-0.0416
Dec 2009-0.0225
Jan 20100.1832
Feb 20100.0143
Mar 2010-0.0325
Apr 2010-0.0527
May 2010-0.0181
Jun 20100.1611
Jul 2010-0.0837
Aug 20100.0382
Sep 2010-0.0160
Oct 2010-0.0778
Nov 20100.0184
Dec 2010-0.0442
Jan 2011-0.0164
Feb 20110.0457
Mar 2011-0.0465
Apr 2011-0.0359
May 2011-0.0523
Jun 2011-0.0209
Jul 2011-0.0213
Aug 20110.0027
Sep 20110.0095
Oct 20110.0279
Nov 20110.0053
Dec 2011-0.0494
Jan 20120.0012
Feb 2012-0.0471
Mar 2012-0.0023
Apr 2012-0.0124
May 20120.0231
Jun 20120.0180
Jul 2012-0.0012
Aug 2012-0.0278
Sep 20120.0269
Oct 2012-0.0203
Nov 20120.0135
Dec 20120.0166
Jan 20130.0364
Feb 20130.0296
Mar 2013-0.0098
Apr 2013-0.0046
May 20130.0656
Jun 2013-0.0112
Jul 2013-0.0133
Aug 2013-0.0193
Sep 2013-0.0006
Oct 2013-0.0423
Nov 2013-0.0201
Dec 2013-0.0011
Jan 2014-0.0072
Feb 2014-0.0114
Mar 20140.0532
Apr 20140.0090
May 2014-0.0332
Jun 2014-0.0185
Jul 2014-0.0133
Aug 20140.0571
Sep 2014-0.0039
Oct 2014-0.0147
Nov 20140.0217
Dec 20140.0182
Jan 2015-0.0156
Feb 2015-0.0192
Mar 2015-0.0014
Apr 2015-0.0320
May 2015-0.0047
Jun 2015-0.0347
Jul 20150.0106
Aug 2015-0.0073
Sep 2015-0.0513
Oct 2015-0.0237
Nov 2015-0.0143
Dec 2015-0.0134
Jan 2016-0.0132
Feb 20160.0295
Mar 2016-0.0071
Apr 20160.0285
May 2016-0.0497
Jun 20160.0120
Jul 2016-0.0324
Aug 20160.0457
Sep 2016-0.0265
Oct 2016-0.0181
Nov 20160.0646
Dec 2016-0.0079
Jan 2017-0.0034
Feb 20170.0030
Mar 2017-0.0290
Apr 2017-0.0257
May 2017-0.0210
Jun 20170.0242
Jul 20170.0104
Aug 20170.0325
Sep 2017-0.0008
Oct 2017-0.0082
Nov 2017-0.0007
Dec 20170.0085
Jan 20180.0322
Feb 2018-0.0031
Mar 2018-0.0159
Apr 2018-0.0298
May 2018-0.0143
Jun 2018-0.0303
Jul 20180.0258
Aug 20180.0323
Sep 20180.0029
Oct 2018-0.0136
Nov 20180.0302
Dec 20180.0094
Jan 2019-0.0421
Feb 2019-0.0452
Mar 2019-0.0192
Apr 20190.0279
May 2019-0.0381
Jun 20190.0074
Jul 2019-0.0565
Aug 2019-0.0096
Sep 2019-0.0028
Oct 20190.0091
Nov 20190.0235
Dec 20190.0110
Jan 2020-0.0076
Feb 20200.0101
Mar 20200.0022
Apr 2020-0.0695
May 2020-0.0450
Jun 2020-0.0590
Jul 20200.0349
Aug 20200.0589
Sep 20200.0110
Oct 2020-0.0327