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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Asset 2
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Asset 3
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Asset 5
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Asset 6
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Asset 7
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Asset 9
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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 30.64 (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 3.856 with p-value 0.696)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.88 0.076 11.646 0.000 0.736...1.034
Size (SMB) -0.34 0.117 -2.867 0.004 -0.568...-0.106
Value (HML-DEV) 0.25 0.123 2.029 0.043 0.008...0.489
Momentum (MOM) 0.02 0.098 0.158 0.874 -0.177...0.208
Quality (QMJ) 0.43 0.162 2.669 0.008 0.114...0.752
Bet Against Beta (BAB) 0.24 0.083 2.857 0.004 0.074...0.401
Alpha (α) 14.67bps 0.003 0.508 0.611 -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 -0.97 8.59 60.48 47.92 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% 60.14 0.33 2.14 0.94 20.74 18.86 117.81 31.3%
Regression residuals
MonthBRK.A
May 1985-5.66%
Jun 198512.98%
Jul 1985-1.09%
Aug 1985-3.79%
Sep 19855.02%
Oct 198518.29%
Nov 1985-7.05%
Dec 1985-11.34%
Jan 1986-9.06%
Feb 198614.30%
Mar 19866.34%
Apr 1986-5.92%
May 1986-8.01%
Jun 19860.07%
Jul 1986-2.94%
Aug 1986-5.08%
Sep 1986-2.32%
Oct 19864.59%
Nov 1986-7.90%
Dec 19864.95%
Jan 1987-2.71%
Feb 19876.51%
Mar 19871.25%
Apr 1987-3.74%
May 1987-0.44%
Jun 1987-3.46%
Jul 19878.23%
Aug 1987-4.13%
Sep 19877.80%
Oct 1987-5.32%
Nov 1987-7.11%
Dec 1987-2.53%
Jan 1988-3.25%
Feb 19880.84%
Mar 198811.15%
Apr 19888.79%
May 19881.50%
Jun 19881.80%
Jul 19884.97%
Aug 1988-0.13%
Sep 19887.95%
Oct 1988-5.23%
Nov 19880.06%
Dec 1988-0.99%
Jan 1989-1.76%
Feb 1989-1.73%
Mar 19892.61%
Apr 198921.63%
May 1989-0.97%
Jun 19891.12%
Jul 19895.47%
Aug 19893.91%
Sep 19898.57%
Oct 1989-1.15%
Nov 1989-5.58%
Dec 19891.96%
Jan 1990-8.84%
Feb 1990-3.80%
Mar 1990-8.85%
Apr 19902.09%
May 1990-0.97%
Jun 19900.73%
Jul 1990-4.11%
Aug 1990-2.13%
Sep 1990-6.27%
Oct 19900.63%
Nov 19901.74%
Dec 19901.92%
Jan 19919.20%
Feb 19913.78%
Mar 1991-1.83%
Apr 1991-0.63%
May 19913.45%
Jun 1991-2.13%
Jul 1991-2.90%
Aug 19910.53%
Sep 19912.25%
Oct 1991-5.22%
Nov 1991-1.06%
Dec 1991-0.85%
Jan 19920.39%
Feb 1992-3.51%
Mar 19922.57%
Apr 1992-3.20%
May 1992-1.88%
Jun 19920.43%
Jul 1992-1.32%
Aug 1992-4.03%
Sep 19921.61%
Oct 19920.53%
Nov 199211.95%
Dec 19927.91%
Jan 19931.39%
Feb 1993-1.11%
Mar 1993-0.66%
Apr 19930.22%
May 199317.08%
Jun 19931.49%
Jul 19933.13%
Aug 19935.92%
Sep 1993-4.49%
Oct 19931.58%
Nov 19930.83%
Dec 1993-7.57%
Jan 1994-3.88%
Feb 1994-2.40%
Mar 19945.79%
Apr 1994-0.74%
May 1994-1.82%
Jun 19940.84%
Jul 199418.21%
Aug 1994-5.88%
Sep 19940.40%
Oct 19944.28%
Nov 19944.09%
Dec 1994-1.72%
Jan 199516.90%
Feb 1995-13.72%
Mar 1995-1.49%
Apr 1995-7.80%
May 19950.69%
Jun 19951.66%
Jul 19952.84%
Aug 19952.20%
Sep 199510.36%
Oct 1995-1.66%
Nov 19952.00%
Dec 19950.56%
Jan 1996-4.34%
Feb 199610.36%
Mar 1996-6.25%
Apr 1996-1.55%
May 1996-11.27%
Jun 1996-2.10%
Jul 19962.42%
Aug 1996-0.75%
Sep 1996-2.64%
Oct 1996-4.01%
Nov 1996-5.78%
Dec 19963.71%
Jan 1997-4.03%
Feb 1997-1.49%
Mar 19973.63%
Apr 1997-1.76%
May 19979.28%
Jun 19974.45%
Jul 1997-8.00%
Aug 1997-7.15%
Sep 19972.57%
Oct 1997-1.62%
Nov 1997-2.88%
Dec 1997-3.32%
Jan 19988.39%
Feb 19984.46%
Mar 199814.62%
Apr 19980.59%
May 19982.30%
Jun 19986.94%
Jul 1998-10.17%
Aug 1998-6.11%
Sep 1998-6.18%
Oct 19982.80%
Nov 19981.66%
Dec 1998-0.65%
Jan 1999-7.51%
Feb 199911.16%
Mar 1999-1.53%
Apr 19992.44%
May 1999-5.39%
Jun 1999-7.33%
Jul 19991.00%
Aug 1999-5.52%
Sep 1999-9.48%
Oct 199910.13%
Nov 1999-6.25%
Dec 1999-2.85%
Jan 2000-2.37%
Feb 2000-1.97%
Mar 200017.92%
Apr 2000-0.17%
May 2000-3.41%
Jun 2000-3.08%
Jul 2000-1.61%
Aug 20000.78%
Sep 200011.17%
Oct 2000-5.53%
Nov 20001.13%
Dec 20003.63%
Jan 2001-0.91%
Feb 20011.26%
Mar 2001-7.03%
Apr 20010.35%
May 2001-0.25%
Jun 20012.40%
Jul 2001-4.01%
Aug 20012.28%
Sep 20014.25%
Oct 20013.62%
Nov 2001-7.21%
Dec 20017.37%
Jan 2002-3.58%
Feb 2002-4.02%
Mar 2002-5.89%
Apr 20024.25%
May 2002-1.46%
Jun 2002-6.46%
Jul 20026.83%
Aug 20024.09%
Sep 20028.80%
Oct 2002-5.82%
Nov 2002-2.36%
Dec 20020.71%
Jan 2003-5.04%
Feb 2003-8.36%
Mar 20032.20%
Apr 20033.97%
May 20030.33%
Jun 20030.71%
Jul 20030.13%
Aug 20033.69%
Sep 2003-0.29%
Oct 2003-0.59%
Nov 20035.33%
Dec 2003-6.49%
Jan 20047.10%
Feb 20042.16%
Mar 2004-1.66%
Apr 2004-0.89%
May 2004-5.83%
Jun 2004-2.74%
Jul 2004-3.46%
Aug 2004-1.83%
Sep 2004-1.63%
Oct 2004-4.94%
Nov 2004-4.24%
Dec 20041.74%
Jan 20052.16%
Feb 2005-3.46%
Mar 2005-4.28%
Apr 2005-2.85%
May 2005-2.52%
Jun 2005-1.94%
Jul 2005-3.27%
Aug 2005-0.11%
Sep 2005-2.22%
Oct 20055.81%
Nov 20050.63%
Dec 2005-0.99%
Jan 2006-0.29%
Feb 2006-3.06%
Mar 20063.49%
Apr 2006-3.56%
May 20064.46%
Jun 2006-1.56%
Jul 2006-2.21%
Aug 20063.07%
Sep 2006-3.27%
Oct 20067.53%
Nov 2006-0.53%
Dec 20060.45%
Jan 2007-1.97%
Feb 2007-2.13%
Mar 20071.13%
Apr 2007-4.24%
May 2007-3.60%
Jun 20071.03%
Jul 20072.38%
Aug 20076.81%
Sep 2007-3.86%
Oct 200710.38%
Nov 20078.77%
Dec 20071.55%
Jan 20080.35%
Feb 20084.26%
Mar 2008-3.00%
Apr 2008-3.84%
May 2008-0.16%
Jun 2008-3.00%
Jul 2008-3.17%
Aug 2008-0.27%
Sep 200820.75%
Oct 20082.22%
Nov 2008-5.26%
Dec 2008-7.35%
Jan 2009-2.48%
Feb 2009-3.53%
Mar 20092.33%
Apr 2009-0.60%
May 2009-8.73%
Jun 2009-3.83%
Jul 20092.04%
Aug 20092.46%
Sep 2009-2.36%
Oct 2009-2.97%
Nov 2009-4.10%
Dec 2009-2.45%
Jan 201018.25%
Feb 20101.37%
Mar 2010-3.37%
Apr 2010-5.43%
May 2010-1.73%
Jun 201016.21%
Jul 2010-8.40%
Aug 20103.94%
Sep 2010-1.77%
Oct 2010-7.84%
Nov 20101.76%
Dec 2010-4.51%
Jan 2011-1.63%
Feb 20114.50%
Mar 2011-4.71%
Apr 2011-3.62%
May 2011-5.24%
Jun 2011-2.08%
Jul 2011-2.04%
Aug 20110.35%
Sep 20111.01%
Oct 20112.67%
Nov 20110.48%
Dec 2011-4.99%
Jan 2012-0.01%
Feb 2012-4.74%
Mar 2012-0.33%
Apr 2012-1.21%
May 20122.35%
Jun 20121.73%
Jul 2012-0.10%
Aug 2012-2.82%
Sep 20122.59%
Oct 2012-2.01%
Nov 20121.32%
Dec 20121.60%
Jan 20133.53%
Feb 20132.91%
Mar 2013-1.09%
Apr 2013-0.38%
May 20136.44%
Jun 2013-1.19%
Jul 2013-1.47%
Aug 2013-1.89%
Sep 2013-0.14%
Oct 2013-4.29%
Nov 2013-2.14%
Dec 2013-0.10%
Jan 2014-0.63%
Feb 2014-1.18%
Mar 20145.18%
Apr 20140.95%
May 2014-3.33%
Jun 2014-1.92%
Jul 2014-1.23%
Aug 20145.69%
Sep 2014-0.28%
Oct 2014-1.66%
Nov 20142.20%
Dec 20141.77%
Jan 2015-1.44%
Feb 2015-2.03%
Mar 2015-0.16%
Apr 2015-3.23%
May 2015-0.44%
Jun 2015-3.54%
Jul 20151.18%
Aug 2015-0.73%
Sep 2015-5.10%
Oct 2015-2.42%
Nov 2015-1.47%
Dec 2015-1.20%
Jan 2016-1.27%
Feb 20162.91%
Mar 2016-0.90%
Apr 20162.73%
May 2016-4.95%
Jun 20161.17%
Jul 2016-3.33%
Aug 20164.52%
Sep 2016-2.64%
Oct 2016-1.79%
Nov 20166.16%
Dec 2016-0.98%
Jan 2017-0.29%
Feb 20170.29%
Mar 2017-2.93%
Apr 2017-2.62%
May 2017-1.97%
Jun 20172.33%
Jul 20171.06%
Aug 20173.38%
Sep 2017-0.28%
Oct 2017-0.82%
Nov 2017-0.17%
Dec 20170.80%
Jan 20183.31%
Feb 2018-0.22%
Mar 2018-1.70%
Apr 2018-3.01%
May 2018-1.46%
Jun 2018-3.12%
Jul 20182.59%
Aug 20183.27%
Sep 20180.38%
Oct 2018-1.37%
Nov 20183.03%
Dec 20181.17%
Jan 2019-4.39%
Feb 2019-4.61%
Mar 2019-1.79%
Apr 20192.73%
May 2019-3.67%
Jun 20190.67%