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 4
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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

Vanguard 500 Index Investor

Factor regression results for Vanguard 500 Index Investor
Ticker VFINX
Time Period Sep 1976 - May 2020
Regression Basis 525 monthly samples
Coefficient of Determination (R2) 99.4%
Adjusted R2 99.4%
Regression F statistic 31,029.46 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.004 with p-value 0.517)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 8.357 with p-value 0.039)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.99 0.003 298.393 0.000 0.986...0.999
Size (SMB) -0.19 0.005 -37.964 0.000 -0.199...-0.179
Value (HML) 0.02 0.005 4.129 0.000 0.011...0.030
Alpha (α) -0.58bps 0.000 -0.408 0.684 -0.03%...0.02%
Annualized Alpha (α) -0.07%  
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.
  • 3-factor model: Ra = Rrf + Bmkt × ( Rmkt - Rrf ) + Bsmb × SMB + Bhml × HML + 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
    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) 64.07 18.46 16.74  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML Total R2
Vanguard 500 Index Investor VFINX Sep 1976 May 2020 -0.07% 63.61 -3.49 0.34 59.88 99.4%
Regression residuals
MonthVFINX
Sep 1976-0.0008
Oct 1976-0.0002
Nov 1976-0.0048
Dec 1976-0.0025
Jan 1977-0.0047
Feb 19770.0035
Mar 1977-0.0016
Apr 1977-0.0062
May 1977-0.0020
Jun 1977-0.0014
Jul 19770.0015
Aug 19770.0025
Sep 19770.0014
Oct 1977-0.0009
Nov 1977-0.0030
Dec 19770.0004
Jan 1978-0.0016
Feb 1978-0.0014
Mar 1978-0.0014
Apr 19780.0032
May 1978-0.0009
Jun 1978-0.0012
Jul 19780.0012
Aug 19780.0010
Sep 19780.0014
Oct 19780.0035
Nov 1978-0.0019
Dec 19780.0031
Jan 1979-0.0020
Feb 19790.0001
Mar 1979-0.0010
Apr 19790.0002
May 1979-0.0027
Jun 1979-0.0042
Jul 1979-0.0024
Aug 19790.0028
Sep 19790.0016
Oct 19790.0005
Nov 1979-0.0044
Dec 1979-0.0013
Jan 1980-0.0005
Feb 19800.0036
Mar 19800.0056
Apr 1980-0.0071
May 1980-0.0010
Jun 1980-0.0051
Jul 19800.0059
Aug 1980-0.0036
Sep 19800.0003
Oct 19800.0052
Nov 19800.0001
Dec 1980-0.0007
Jan 1981-0.0003
Feb 19810.0040
Mar 1981-0.0033
Apr 1981-0.0037
May 1981-0.0024
Jun 1981-0.0012
Jul 1981-0.0010
Aug 1981-0.0020
Sep 19810.0025
Oct 1981-0.0038
Nov 1981-0.0022
Dec 19810.0021
Jan 19820.0063
Feb 1982-0.0023
Mar 19820.0008
Apr 19820.0012
May 19820.0012
Jun 19820.0040
Jul 19820.0006
Aug 1982-0.0019
Sep 1982-0.0023
Oct 1982-0.0015
Nov 1982-0.0010
Dec 19820.0049
Jan 1983-0.0031
Feb 1983-0.0011
Mar 19830.0037
Apr 19830.0036
May 1983-0.0088
Jun 19830.0029
Jul 19830.0022
Aug 19830.0064
Sep 1983-0.0032
Oct 19830.0047
Nov 1983-0.0019
Dec 19830.0032
Jan 19840.0041
Feb 19840.0037
Mar 19840.0029
Apr 19840.0013
May 1984-0.0021
Jun 1984-0.0036
Jul 19840.0001
Aug 19840.0016
Sep 1984-0.0013
Oct 1984-0.0015
Nov 1984-0.0018
Dec 19840.0002
Jan 1985-0.0026
Feb 1985-0.0026
Mar 1985-0.0008
Apr 1985-0.0010
May 1985-0.0008
Jun 1985-0.0029
Jul 19850.0047
Aug 1985-0.0031
Sep 19850.0044
Oct 1985-0.0055
Nov 19850.0001
Dec 19850.0012
Jan 1986-0.0054
Feb 1986-0.0013
Mar 1986-0.0005
Apr 19860.0004
May 19860.0014
Jun 1986-0.0007
Jul 1986-0.0059
Aug 19860.0011
Sep 19860.0015
Oct 19860.0011
Nov 19860.0065
Dec 19860.0013
Jan 19870.0020
Feb 1987-0.0003
Mar 19870.0080
Apr 19870.0036
May 19870.0045
Jun 19870.0020
Jul 19870.0050
Aug 1987-0.0023
Sep 1987-0.0007
Oct 1987-0.0093
Nov 1987-0.0036
Dec 19870.0052
Jan 1988-0.0054
Feb 19880.0009
Mar 1988-0.0007
Apr 19880.0015
May 19880.0005
Jun 1988-0.0025
Jul 19880.0028
Aug 1988-0.0073
Sep 19880.0014
Oct 19880.0041
Nov 1988-0.0012
Dec 19880.0004
Jan 19890.0031
Feb 1989-0.0033
Mar 19890.0017
Apr 19890.0014
May 1989-0.0006
Jun 1989-0.0019
Jul 19890.0046
Aug 1989-0.0022
Sep 1989-0.0021
Oct 19890.0003
Nov 19890.0012
Dec 19890.0016
Jan 19900.0025
Feb 1990-0.0021
Mar 19900.0050
Apr 19900.0011
May 19900.0025
Jun 19900.0011
Jul 19900.0025
Aug 1990-0.0032
Sep 1990-0.0012
Oct 1990-0.0022
Nov 1990-0.0030
Dec 1990-0.0014
Jan 1991-0.0006
Feb 19910.0026
Mar 19910.0010
Apr 19910.0002
May 19910.0013
Jun 1991-0.0008
Jul 1991-0.0022
Aug 1991-0.0011
Sep 1991-0.0022
Oct 1991-0.0019
Nov 1991-0.0029
Dec 1991-0.0006
Jan 1992-0.0012
Feb 1992-0.0008
Mar 19920.0011
Apr 19920.0029
May 1992-0.0004
Jun 1992-0.0014
Jul 1992-0.0008
Aug 19920.0004
Sep 1992-0.0016
Oct 1992-0.0048
Nov 1992-0.0019
Dec 1992-0.0032
Jan 1993-0.0008
Feb 19930.0024
Mar 1993-0.0040
Apr 19930.0018
May 19930.0001
Jun 1993-0.0040
Jul 1993-0.0021
Aug 1993-0.0007
Sep 1993-0.0033
Oct 19930.0077
Nov 19930.0037
Dec 1993-0.0042
Jan 19940.0027
Feb 19940.0016
Mar 1994-0.0012
Apr 19940.0014
May 19940.0034
Jun 19940.0014
Jul 1994-0.0013
Aug 19940.0004
Sep 19940.0006
Oct 19940.0013
Nov 19940.0006
Dec 19940.0017
Jan 1995-0.0014
Feb 1995-0.0027
Mar 19950.0022
Apr 19950.0025
May 19950.0009
Jun 1995-0.0025
Jul 1995-0.0040
Aug 1995-0.0050
Sep 19950.0008
Oct 1995-0.0001
Nov 1995-0.0020
Dec 19950.0052
Jan 19960.0022
Feb 1996-0.0039
Mar 19960.0010
Apr 1996-0.0003
May 19960.0039
Jun 19960.0041
Jul 19960.0025
Aug 1996-0.0061
Sep 19960.0010
Oct 19960.0054
Nov 19960.0020
Dec 1996-0.0014
Jan 19970.0051
Feb 19970.0023
Mar 19970.0027
Apr 19970.0045
May 1997-0.0008
Jun 19970.0024
Jul 1997-0.0028
Aug 1997-0.0054
Sep 19970.0022
Oct 1997-0.0016
Nov 19970.0030
Dec 1997-0.0058
Jan 19980.0035
Feb 1998-0.0018
Mar 1998-0.0020
Apr 1998-0.0012
May 19980.0012
Jun 1998-0.0004
Jul 19980.0005
Aug 1998-0.0001
Sep 1998-0.0011
Oct 19980.0020
Nov 1998-0.0002
Dec 1998-0.0066
Jan 19990.0054
Feb 1999-0.0052
Mar 1999-0.0054
Apr 1999-0.0011
May 19990.0032
Jun 19990.0108
Jul 19990.0048
Aug 19990.0028
Sep 19990.0035
Oct 1999-0.0139
Nov 1999-0.0015
Dec 1999-0.0059
Jan 20000.0021
Feb 2000-0.0045
Mar 20000.0079
Apr 20000.0126
May 20000.0084
Jun 20000.0031
Jul 2000-0.0016
Aug 2000-0.0149
Sep 2000-0.0076
Oct 20000.0092
Nov 20000.0150
Dec 2000-0.0114
Jan 20010.0124
Feb 20010.0006
Mar 20010.0037
Apr 2001-0.0030
May 20010.0004
Jun 20010.0037
Jul 2001-0.0012
Aug 20010.0026
Sep 2001-0.0037
Oct 20010.0085
Nov 2001-0.0011
Dec 2001-0.0003
Jan 2002-0.0002
Feb 2002-0.0005
Mar 20020.0019
Apr 2002-0.0001
May 2002-0.0016
Jun 20020.0070
Jul 2002-0.0067
Aug 2002-0.0049
Sep 2002-0.0028
Oct 20020.0043
Nov 20020.0040
Dec 2002-0.0032
Jan 20030.0011
Feb 20030.0023
Mar 2003-0.0001
Apr 20030.0008
May 20030.0007
Jun 20030.0006
Jul 20030.0036
Aug 2003-0.0000
Sep 20030.0024
Oct 20030.0001
Nov 2003-0.0020
Dec 20030.0027
Jan 20040.0011
Feb 2004-0.0035
Mar 20040.0004
Apr 2004-0.0017
May 20040.0011
Jun 20040.0041
Jul 2004-0.0018
Aug 2004-0.0013
Sep 2004-0.0005
Oct 20040.0006
Nov 20040.0010
Dec 2004-0.0014
Jan 2005-0.0019
Feb 2005-0.0007
Mar 2005-0.0030
Apr 2005-0.0027
May 2005-0.0013
Jun 2005-0.0022
Jul 20050.0015
Aug 2005-0.0020
Sep 2005-0.0010
Oct 2005-0.0017
Nov 20050.0007
Dec 2005-0.0014
Jan 20060.0029
Feb 20060.0016
Mar 20060.0007
Apr 2006-0.0005
May 2006-0.0041
Jun 2006-0.0000
Jul 20060.0016
Aug 20060.0014
Sep 20060.0007
Oct 2006-0.0003
Nov 2006-0.0006
Dec 2006-0.0014
Jan 2007-0.0031
Feb 2007-0.0015
Mar 20070.0001
Apr 20070.0015
May 2007-0.0014
Jun 20070.0004
Jul 2007-0.0018
Aug 20070.0019
Sep 2007-0.0018
Oct 2007-0.0043
Nov 2007-0.0020
Dec 2007-0.0005
Jan 2008-0.0015
Feb 2008-0.0033
Mar 20080.0050
Apr 2008-0.0018
May 2008-0.0009
Jun 20080.0007
Jul 20080.0013
Aug 20080.0045
Sep 2008-0.0023
Oct 2008-0.0014
Nov 20080.0017
Dec 20080.0003
Jan 2009-0.0010
Feb 2009-0.0044
Mar 2009-0.0023
Apr 20090.0023
May 20090.0001
Jun 20090.0034
Jul 20090.0019
Aug 2009-0.0004
Sep 20090.0011
Oct 2009-0.0000
Nov 2009-0.0000
Dec 20090.0037
Jan 2010-0.0020
Feb 2010-0.0011
Mar 2010-0.0003
Apr 20100.0047
May 2010-0.0012
Jun 2010-0.0000
Jul 20100.0015
Aug 2010-0.0033
Sep 20100.0025
Oct 20100.0020
Nov 20100.0012
Dec 2010-0.0005
Jan 2011-0.0011
Feb 20110.0021
Mar 20110.0010
Apr 20110.0006
May 20110.0003
Jun 20110.0005
Jul 20110.0007
Aug 2011-0.0003
Sep 2011-0.0014
Oct 20110.0030
Nov 20110.0002
Dec 20110.0012
Jan 2012-0.0011
Feb 2012-0.0041
Mar 20120.0006
Apr 20120.0012
May 20120.0014
Jun 20120.0039
Jul 20120.0010
Aug 2012-0.0025
Sep 2012-0.0008
Oct 2012-0.0041
Nov 2012-0.0009
Dec 2012-0.0007
Jan 2013-0.0029
Feb 2013-0.0002
Mar 2013-0.0010
Apr 2013-0.0009
May 2013-0.0019
Jun 20130.0007
Jul 2013-0.0019
Aug 2013-0.0010
Sep 2013-0.0004
Oct 20130.0013
Nov 20130.0016
Dec 2013-0.0036
Jan 20140.0004
Feb 20140.0002
Mar 2014-0.0006
Apr 20140.0009
May 2014-0.0005
Jun 20140.0006
Jul 2014-0.0016
Aug 2014-0.0014
Sep 2014-0.0015
Oct 20140.0076
Nov 2014-0.0018
Dec 20140.0024
Jan 20150.0004
Feb 2015-0.0021
Mar 20150.0011
Apr 2015-0.0023
May 20150.0012
Jun 20150.0014
Jul 2015-0.0014
Aug 2015-0.0000
Sep 20150.0006
Oct 20150.0036
Nov 20150.0044
Dec 20150.0008
Jan 20160.0007
Feb 20160.0007
Mar 2016-0.0001
Apr 2016-0.0048
May 2016-0.0000
Jun 20160.0044
Jul 20160.0026
Aug 2016-0.0023
Sep 20160.0016
Oct 2016-0.0076
Nov 2016-0.0027
Dec 20160.0008
Jan 2017-0.0022
Feb 20170.0004
Mar 20170.0020
Apr 20170.0006
May 2017-0.0012
Jun 20170.0017
Jul 2017-0.0014
Aug 2017-0.0022
Sep 20170.0028
Oct 2017-0.0037
Nov 2017-0.0023
Dec 2017-0.0028
Jan 2018-0.0048
Feb 2018-0.0010
Mar 20180.0041
Apr 20180.0015
May 20180.0068
Jun 20180.0027
Jul 2018-0.0003
Aug 2018-0.0002
Sep 2018-0.0007
Oct 2018-0.0038
Nov 20180.0002
Dec 2018-0.0021
Jan 20190.0003
Feb 20190.0010
Mar 20190.0015
Apr 2019-0.0045
May 20190.0014
Jun 20190.0007
Jul 2019-0.0033
Aug 20190.0046
Sep 2019-0.0005
Oct 20190.0006
Nov 2019-0.0013
Dec 20190.0021
Jan 2020-0.0052
Feb 2020-0.0002
Mar 20200.0012
Apr 2020-0.0018
May 2020-0.0023