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 - May 2020
Regression Basis 421 monthly samples
Coefficient of Determination (R2) 32.0%
Adjusted R2 31.0%
Regression F statistic 32.45 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.051 with p-value 0.691)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.644 with p-value 0.725)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.86 0.071 12.065 0.000 0.722...1.003
Size (SMB) -0.36 0.113 -3.185 0.002 -0.580...-0.137
Value (HML-DEV) 0.23 0.113 2.003 0.046 0.004...0.449
Momentum (MOM) 0.01 0.095 0.091 0.927 -0.179...0.196
Quality (QMJ) 0.40 0.154 2.627 0.009 0.102...0.707
Bet Against Beta (BAB) 0.23 0.081 2.915 0.004 0.076...0.393
Alpha (α) 14.93bps 0.003 0.538 0.591 -0.40%...0.69%
Annualized Alpha (α) 1.79%  
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) 67.19 -2.04 3.70 60.35 46.60 75.76  
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 May 2020 1.79% 57.93 0.73 0.84 0.53 18.84 17.80 111.60 32.0%
Regression residuals
MonthBRK.A
May 1985-0.0560
Jun 19850.1302
Jul 1985-0.0105
Aug 1985-0.0377
Sep 19850.0499
Oct 19850.1838
Nov 1985-0.0691
Dec 1985-0.1125
Jan 1986-0.0909
Feb 19860.1445
Mar 19860.0648
Apr 1986-0.0590
May 1986-0.0790
Jun 19860.0014
Jul 1986-0.0303
Aug 1986-0.0500
Sep 1986-0.0243
Oct 19860.0465
Nov 1986-0.0786
Dec 19860.0492
Jan 1987-0.0250
Feb 19870.0655
Mar 19870.0134
Apr 1987-0.0379
May 1987-0.0041
Jun 1987-0.0335
Jul 19870.0830
Aug 1987-0.0403
Sep 19870.0772
Oct 1987-0.0577
Nov 1987-0.0719
Dec 1987-0.0243
Jan 1988-0.0308
Feb 19880.0099
Mar 19880.1122
Apr 19880.0884
May 19880.0150
Jun 19880.0191
Jul 19880.0496
Aug 1988-0.0017
Sep 19880.0798
Oct 1988-0.0522
Nov 19880.0001
Dec 1988-0.0093
Jan 1989-0.0169
Feb 1989-0.0172
Mar 19890.0263
Apr 19890.2171
May 1989-0.0094
Jun 19890.0113
Jul 19890.0554
Aug 19890.0396
Sep 19890.0855
Oct 1989-0.0123
Nov 1989-0.0558
Dec 19890.0200
Jan 1990-0.0898
Feb 1990-0.0382
Mar 1990-0.0879
Apr 19900.0201
May 1990-0.0093
Jun 19900.0074
Jul 1990-0.0411
Aug 1990-0.0234
Sep 1990-0.0635
Oct 19900.0056
Nov 19900.0178
Dec 19900.0199
Jan 19910.0933
Feb 19910.0398
Mar 1991-0.0171
Apr 1991-0.0062
May 19910.0349
Jun 1991-0.0213
Jul 1991-0.0285
Aug 19910.0057
Sep 19910.0221
Oct 1991-0.0520
Nov 1991-0.0107
Dec 1991-0.0074
Jan 19920.0056
Feb 1992-0.0340
Mar 19920.0261
Apr 1992-0.0317
May 1992-0.0183
Jun 19920.0039
Jul 1992-0.0121
Aug 1992-0.0402
Sep 19920.0164
Oct 19920.0057
Nov 19920.1202
Dec 19920.0801
Jan 19930.0151
Feb 1993-0.0102
Mar 1993-0.0059
Apr 19930.0016
May 19930.1711
Jun 19930.0150
Jul 19930.0320
Aug 19930.0600
Sep 1993-0.0441
Oct 19930.0161
Nov 19930.0079
Dec 1993-0.0749
Jan 1994-0.0380
Feb 1994-0.0236
Mar 19940.0574
Apr 1994-0.0071
May 1994-0.0183
Jun 19940.0083
Jul 19940.1825
Aug 1994-0.0577
Sep 19940.0042
Oct 19940.0431
Nov 19940.0405
Dec 1994-0.0167
Jan 19950.1694
Feb 1995-0.1364
Mar 1995-0.0146
Apr 1995-0.0772
May 19950.0074
Jun 19950.0170
Jul 19950.0291
Aug 19950.0222
Sep 19950.1042
Oct 1995-0.0163
Nov 19950.0204
Dec 19950.0059
Jan 1996-0.0435
Feb 19960.1042
Mar 1996-0.0621
Apr 1996-0.0147
May 1996-0.1118
Jun 1996-0.0208
Jul 19960.0238
Aug 1996-0.0066
Sep 1996-0.0257
Oct 1996-0.0394
Nov 1996-0.0566
Dec 19960.0376
Jan 1997-0.0395
Feb 1997-0.0145
Mar 19970.0363
Apr 1997-0.0171
May 19970.0943
Jun 19970.0462
Jul 1997-0.0787
Aug 1997-0.0712
Sep 19970.0270
Oct 1997-0.0165
Nov 1997-0.0284
Dec 1997-0.0327
Jan 19980.0839
Feb 19980.0458
Mar 19980.1472
Apr 19980.0062
May 19980.0229
Jun 19980.0692
Jul 1998-0.1028
Aug 1998-0.0627
Sep 1998-0.0612
Oct 19980.0279
Nov 19980.0176
Dec 1998-0.0059
Jan 1999-0.0757
Feb 19990.1099
Mar 1999-0.0162
Apr 19990.0255
May 1999-0.0528
Jun 1999-0.0720
Jul 19990.0105
Aug 1999-0.0553
Sep 1999-0.0950
Oct 19990.1003
Nov 1999-0.0627
Dec 1999-0.0283
Jan 2000-0.0245
Feb 2000-0.0217
Mar 20000.1802
Apr 2000-0.0006
May 2000-0.0342
Jun 2000-0.0314
Jul 2000-0.0149
Aug 20000.0078
Sep 20000.1122
Oct 2000-0.0551
Nov 20000.0132
Dec 20000.0368
Jan 2001-0.0077
Feb 20010.0158
Mar 2001-0.0695
Apr 20010.0037
May 2001-0.0010
Jun 20010.0248
Jul 2001-0.0388
Aug 20010.0240
Sep 20010.0408
Oct 20010.0373
Nov 2001-0.0705
Dec 20010.0756
Jan 2002-0.0340
Feb 2002-0.0393
Mar 2002-0.0570
Apr 20020.0447
May 2002-0.0146
Jun 2002-0.0645
Jul 20020.0669
Aug 20020.0407
Sep 20020.0872
Oct 2002-0.0574
Nov 2002-0.0233
Dec 20020.0080
Jan 2003-0.0505
Feb 2003-0.0838
Mar 20030.0220
Apr 20030.0406
May 20030.0042
Jun 20030.0078
Jul 20030.0018
Aug 20030.0379
Sep 2003-0.0024
Oct 2003-0.0037
Nov 20030.0549
Dec 2003-0.0641
Jan 20040.0711
Feb 20040.0222
Mar 2004-0.0159
Apr 2004-0.0090
May 2004-0.0581
Jun 2004-0.0261
Jul 2004-0.0343
Aug 2004-0.0184
Sep 2004-0.0153
Oct 2004-0.0489
Nov 2004-0.0404
Dec 20040.0181
Jan 20050.0214
Feb 2005-0.0336
Mar 2005-0.0426
Apr 2005-0.0296
May 2005-0.0241
Jun 2005-0.0182
Jul 2005-0.0316
Aug 2005-0.0015
Sep 2005-0.0223
Oct 20050.0574
Nov 20050.0073
Dec 2005-0.0102
Jan 2006-0.0017
Feb 2006-0.0307
Mar 20060.0356
Apr 2006-0.0357
May 20060.0440
Jun 2006-0.0154
Jul 2006-0.0223
Aug 20060.0308
Sep 2006-0.0323
Oct 20060.0761
Nov 2006-0.0048
Dec 20060.0048
Jan 2007-0.0194
Feb 2007-0.0216
Mar 20070.0116
Apr 2007-0.0420
May 2007-0.0352
Jun 20070.0101
Jul 20070.0223
Aug 20070.0680
Sep 2007-0.0389
Oct 20070.1036
Nov 20070.0865
Dec 20070.0155
Jan 20080.0027
Feb 20080.0424
Mar 2008-0.0300
Apr 2008-0.0383
May 2008-0.0011
Jun 2008-0.0320
Jul 2008-0.0309
Aug 2008-0.0008
Sep 20080.2062
Oct 20080.0194
Nov 2008-0.0549
Dec 2008-0.0714
Jan 2009-0.0259
Feb 2009-0.0376
Mar 20090.0252
Apr 2009-0.0012
May 2009-0.0869
Jun 2009-0.0369
Jul 20090.0220
Aug 20090.0250
Sep 2009-0.0225
Oct 2009-0.0299
Nov 2009-0.0409
Dec 2009-0.0229
Jan 20100.1822
Feb 20100.0150
Mar 2010-0.0322
Apr 2010-0.0531
May 2010-0.0189
Jun 20100.1606
Jul 2010-0.0827
Aug 20100.0380
Sep 2010-0.0154
Oct 2010-0.0776
Nov 20100.0181
Dec 2010-0.0441
Jan 2011-0.0162
Feb 20110.0458
Mar 2011-0.0465
Apr 2011-0.0356
May 2011-0.0523
Jun 2011-0.0207
Jul 2011-0.0213
Aug 20110.0028
Sep 20110.0089
Oct 20110.0289
Nov 20110.0056
Dec 2011-0.0492
Jan 20120.0003
Feb 2012-0.0465
Mar 2012-0.0025
Apr 2012-0.0124
May 20120.0229
Jun 20120.0181
Jul 2012-0.0008
Aug 2012-0.0277
Sep 20120.0267
Oct 2012-0.0206
Nov 20120.0135
Dec 20120.0163
Jan 20130.0363
Feb 20130.0297
Mar 2013-0.0099
Apr 2013-0.0045
May 20130.0656
Jun 2013-0.0115
Jul 2013-0.0132
Aug 2013-0.0196
Sep 2013-0.0005
Oct 2013-0.0418
Nov 2013-0.0199
Dec 2013-0.0009
Jan 2014-0.0081
Feb 2014-0.0111
Mar 20140.0532
Apr 20140.0091
May 2014-0.0329
Jun 2014-0.0186
Jul 2014-0.0131
Aug 20140.0579
Sep 2014-0.0036
Oct 2014-0.0148
Nov 20140.0221
Dec 20140.0181
Jan 2015-0.0160
Feb 2015-0.0190
Mar 2015-0.0017
Apr 2015-0.0323
May 2015-0.0044
Jun 2015-0.0348
Jul 20150.0127
Aug 2015-0.0078
Sep 2015-0.0509
Oct 2015-0.0230
Nov 2015-0.0145
Dec 2015-0.0132
Jan 2016-0.0128
Feb 20160.0292
Mar 2016-0.0065
Apr 20160.0279
May 2016-0.0499
Jun 20160.0124
Jul 2016-0.0326
Aug 20160.0456
Sep 2016-0.0270
Oct 2016-0.0178
Nov 20160.0643
Dec 2016-0.0079
Jan 2017-0.0035
Feb 20170.0032
Mar 2017-0.0294
Apr 2017-0.0258
May 2017-0.0206
Jun 20170.0238
Jul 20170.0108
Aug 20170.0329
Sep 2017-0.0012
Oct 2017-0.0075
Nov 2017-0.0004
Dec 20170.0084
Jan 20180.0333
Feb 2018-0.0028
Mar 2018-0.0168
Apr 2018-0.0299
May 2018-0.0144
Jun 2018-0.0308
Jul 20180.0268
Aug 20180.0308
Sep 20180.0029
Oct 2018-0.0145
Nov 20180.0337
Dec 20180.0089
Jan 2019-0.0421
Feb 2019-0.0451
Mar 2019-0.0196
Apr 20190.0285
May 2019-0.0386
Jun 20190.0069
Jul 2019-0.0570
Aug 2019-0.0094
Sep 2019-0.0035
Oct 20190.0078
Nov 20190.0229
Dec 20190.0100
Jan 2020-0.0088
Feb 20200.0099
Mar 20200.0018
Apr 2020-0.0687
May 2020-0.0455