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 2019
Regression Basis 410 monthly samples
Coefficient of Determination (R2) 31.3%
Adjusted R2 30.3%
Regression F statistic 30.66 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.060 with p-value 0.720)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.875 with p-value 0.694)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.88 0.076 11.659 0.000 0.736...1.034
Size (SMB) -0.34 0.117 -2.873 0.004 -0.568...-0.106
Value (HML-DEV) 0.25 0.122 2.019 0.044 0.007...0.488
Momentum (MOM) 0.01 0.098 0.147 0.883 -0.178...0.207
Quality (QMJ) 0.43 0.162 2.678 0.008 0.115...0.752
Bet Against Beta (BAB) 0.24 0.083 2.868 0.004 0.075...0.402
Alpha (α) 14.63bps 0.003 0.507 0.612 -0.42%...0.71%
Annualized Alpha (α) 1.76%  
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) 67.96 -1.00 8.60 60.64 47.94 79.43  
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 2019 1.76% 60.13 0.34 2.13 0.88 20.79 18.92 117.81 31.3%
Regression residuals
MonthBRK.A
May 1985-0.0566
Jun 19850.1298
Jul 1985-0.0110
Aug 1985-0.0378
Sep 19850.0502
Oct 19850.1829
Nov 1985-0.0706
Dec 1985-0.1135
Jan 1986-0.0906
Feb 19860.1430
Mar 19860.0633
Apr 1986-0.0593
May 1986-0.0801
Jun 19860.0007
Jul 1986-0.0293
Aug 1986-0.0507
Sep 1986-0.0232
Oct 19860.0460
Nov 1986-0.0790
Dec 19860.0495
Jan 1987-0.0272
Feb 19870.0650
Mar 19870.0125
Apr 1987-0.0374
May 1987-0.0044
Jun 1987-0.0346
Jul 19870.0823
Aug 1987-0.0414
Sep 19870.0780
Oct 1987-0.0531
Nov 1987-0.0711
Dec 1987-0.0253
Jan 1988-0.0325
Feb 19880.0084
Mar 19880.1115
Apr 19880.0879
May 19880.0150
Jun 19880.0180
Jul 19880.0497
Aug 1988-0.0013
Sep 19880.0795
Oct 1988-0.0523
Nov 19880.0006
Dec 1988-0.0099
Jan 1989-0.0176
Feb 1989-0.0172
Mar 19890.0261
Apr 19890.2163
May 1989-0.0097
Jun 19890.0112
Jul 19890.0547
Aug 19890.0391
Sep 19890.0857
Oct 1989-0.0115
Nov 1989-0.0558
Dec 19890.0196
Jan 1990-0.0884
Feb 1990-0.0380
Mar 1990-0.0885
Apr 19900.0208
May 1990-0.0097
Jun 19900.0073
Jul 1990-0.0410
Aug 1990-0.0213
Sep 1990-0.0627
Oct 19900.0063
Nov 19900.0174
Dec 19900.0191
Jan 19910.0921
Feb 19910.0379
Mar 1991-0.0183
Apr 1991-0.0064
May 19910.0345
Jun 1991-0.0213
Jul 1991-0.0290
Aug 19910.0053
Sep 19910.0225
Oct 1991-0.0522
Nov 1991-0.0107
Dec 1991-0.0085
Jan 19920.0040
Feb 1992-0.0350
Mar 19920.0258
Apr 1992-0.0319
May 1992-0.0187
Jun 19920.0041
Jul 1992-0.0131
Aug 1992-0.0404
Sep 19920.0158
Oct 19920.0053
Nov 19920.1195
Dec 19920.0792
Jan 19930.0140
Feb 1993-0.0110
Mar 1993-0.0066
Apr 19930.0022
May 19930.1707
Jun 19930.0150
Jul 19930.0314
Aug 19930.0591
Sep 1993-0.0448
Oct 19930.0156
Nov 19930.0083
Dec 1993-0.0757
Jan 1994-0.0386
Feb 1994-0.0240
Mar 19940.0579
Apr 1994-0.0073
May 1994-0.0182
Jun 19940.0082
Jul 19940.1822
Aug 1994-0.0588
Sep 19940.0039
Oct 19940.0428
Nov 19940.0409
Dec 1994-0.0171
Jan 19950.1690
Feb 1995-0.1372
Mar 1995-0.0150
Apr 1995-0.0780
May 19950.0069
Jun 19950.0166
Jul 19950.0284
Aug 19950.0220
Sep 19950.1036
Oct 1995-0.0166
Nov 19950.0200
Dec 19950.0057
Jan 1996-0.0435
Feb 19960.1036
Mar 1996-0.0625
Apr 1996-0.0155
May 1996-0.1128
Jun 1996-0.0210
Jul 19960.0242
Aug 1996-0.0075
Sep 1996-0.0265
Oct 1996-0.0400
Nov 1996-0.0578
Dec 19960.0371
Jan 1997-0.0404
Feb 1997-0.0150
Mar 19970.0364
Apr 1997-0.0176
May 19970.0927
Jun 19970.0445
Jul 1997-0.0799
Aug 1997-0.0715
Sep 19970.0256
Oct 1997-0.0162
Nov 1997-0.0289
Dec 1997-0.0332
Jan 19980.0838
Feb 19980.0446
Mar 19980.1462
Apr 19980.0059
May 19980.0232
Jun 19980.0695
Jul 1998-0.1016
Aug 1998-0.0609
Sep 1998-0.0618
Oct 19980.0278
Nov 19980.0167
Dec 1998-0.0064
Jan 1999-0.0752
Feb 19990.1117
Mar 1999-0.0152
Apr 19990.0244
May 1999-0.0541
Jun 1999-0.0732
Jul 19990.0100
Aug 1999-0.0552
Sep 1999-0.0944
Oct 19990.1013
Nov 1999-0.0626
Dec 1999-0.0285
Jan 2000-0.0236
Feb 2000-0.0195
Mar 20000.1788
Apr 2000-0.0018
May 2000-0.0341
Jun 2000-0.0307
Jul 2000-0.0162
Aug 20000.0077
Sep 20000.1115
Oct 2000-0.0562
Nov 20000.0112
Dec 20000.0360
Jan 2001-0.0091
Feb 20010.0130
Mar 2001-0.0703
Apr 20010.0038
May 2001-0.0025
Jun 20010.0238
Jul 2001-0.0400
Aug 20010.0231
Sep 20010.0422
Oct 20010.0363
Nov 2001-0.0718
Dec 20010.0738
Jan 2002-0.0358
Feb 2002-0.0403
Mar 2002-0.0586
Apr 20020.0429
May 2002-0.0147
Jun 2002-0.0647
Jul 20020.0684
Aug 20020.0405
Sep 20020.0879
Oct 2002-0.0581
Nov 2002-0.0235
Dec 20020.0070
Jan 2003-0.0505
Feb 2003-0.0835
Mar 20030.0217
Apr 20030.0399
May 20030.0031
Jun 20030.0070
Jul 20030.0013
Aug 20030.0370
Sep 2003-0.0028
Oct 2003-0.0056
Nov 20030.0534
Dec 2003-0.0649
Jan 20040.0709
Feb 20040.0216
Mar 2004-0.0167
Apr 2004-0.0090
May 2004-0.0583
Jun 2004-0.0275
Jul 2004-0.0345
Aug 2004-0.0183
Sep 2004-0.0161
Oct 2004-0.0495
Nov 2004-0.0423
Dec 20040.0174
Jan 20050.0214
Feb 2005-0.0345
Mar 2005-0.0429
Apr 2005-0.0285
May 2005-0.0252
Jun 2005-0.0192
Jul 2005-0.0326
Aug 2005-0.0009
Sep 2005-0.0221
Oct 20050.0579
Nov 20050.0064
Dec 2005-0.0099
Jan 2006-0.0028
Feb 2006-0.0304
Mar 20060.0348
Apr 2006-0.0357
May 20060.0447
Jun 2006-0.0156
Jul 2006-0.0219
Aug 20060.0306
Sep 2006-0.0327
Oct 20060.0753
Nov 2006-0.0053
Dec 20060.0045
Jan 2007-0.0197
Feb 2007-0.0214
Mar 20070.0115
Apr 2007-0.0422
May 2007-0.0360
Jun 20070.0103
Jul 20070.0238
Aug 20070.0681
Sep 2007-0.0386
Oct 20070.1038
Nov 20070.0877
Dec 20070.0155
Jan 20080.0036
Feb 20080.0427
Mar 2008-0.0301
Apr 2008-0.0384
May 2008-0.0017
Jun 2008-0.0299
Jul 2008-0.0316
Aug 2008-0.0027
Sep 20080.2074
Oct 20080.0228
Nov 2008-0.0528
Dec 2008-0.0730
Jan 2009-0.0249
Feb 2009-0.0351
Mar 20090.0233
Apr 2009-0.0063
May 2009-0.0874
Jun 2009-0.0384
Jul 20090.0204
Aug 20090.0252
Sep 2009-0.0233
Oct 2009-0.0300
Nov 2009-0.0414
Dec 2009-0.0247
Jan 20100.1825
Feb 20100.0139
Mar 2010-0.0337
Apr 2010-0.0542
May 2010-0.0173
Jun 20100.1621
Jul 2010-0.0840
Aug 20100.0394
Sep 2010-0.0177
Oct 2010-0.0784
Nov 20100.0176
Dec 2010-0.0451
Jan 2011-0.0162
Feb 20110.0449
Mar 2011-0.0472
Apr 2011-0.0362
May 2011-0.0525
Jun 2011-0.0209
Jul 2011-0.0205
Aug 20110.0034
Sep 20110.0099
Oct 20110.0268
Nov 20110.0049
Dec 2011-0.0499
Jan 2012-0.0002
Feb 2012-0.0471
Mar 2012-0.0033
Apr 2012-0.0122
May 20120.0234
Jun 20120.0172
Jul 2012-0.0009
Aug 2012-0.0284
Sep 20120.0262
Oct 2012-0.0201
Nov 20120.0132
Dec 20120.0160
Jan 20130.0352
Feb 20130.0292
Mar 2013-0.0108
Apr 2013-0.0042
May 20130.0644
Jun 2013-0.0119
Jul 2013-0.0147
Aug 2013-0.0189
Sep 2013-0.0015
Oct 2013-0.0431
Nov 2013-0.0212
Dec 2013-0.0010
Jan 2014-0.0064
Feb 2014-0.0118
Mar 20140.0522
Apr 20140.0095
May 2014-0.0331
Jun 2014-0.0193
Jul 2014-0.0123
Aug 20140.0571
Sep 2014-0.0029
Oct 2014-0.0165
Nov 20140.0219
Dec 20140.0177
Jan 2015-0.0145
Feb 2015-0.0203
Mar 2015-0.0017
Apr 2015-0.0323
May 2015-0.0044
Jun 2015-0.0352
Jul 20150.0131
Aug 2015-0.0074
Sep 2015-0.0511
Oct 2015-0.0243
Nov 2015-0.0147
Dec 2015-0.0120
Jan 2016-0.0131
Feb 20160.0281
Mar 2016-0.0087
Apr 20160.0273
May 2016-0.0496
Jun 20160.0120
Jul 2016-0.0335
Aug 20160.0453
Sep 2016-0.0263
Oct 2016-0.0180
Nov 20160.0615
Dec 2016-0.0094
Jan 2017-0.0029
Feb 20170.0028
Mar 2017-0.0292
Apr 2017-0.0262
May 2017-0.0201
Jun 20170.0232
Jul 20170.0109
Aug 20170.0335
Sep 2017-0.0027
Oct 2017-0.0079
Nov 2017-0.0015
Dec 20170.0084
Jan 20180.0326
Feb 2018-0.0020
Mar 2018-0.0171
Apr 2018-0.0298
May 2018-0.0153
Jun 2018-0.0313
Jul 20180.0263
Aug 20180.0301
Sep 20180.0032
Oct 2018-0.0139
Nov 20180.0336
Dec 20180.0113
Jan 2019-0.0436
Feb 2019-0.0456
Mar 2019-0.0190
Apr 20190.0274
May 2019-0.0364
Jun 20190.0055