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

Vanguard Total Stock Mkt Idx Inv

Factor regression results for Vanguard Total Stock Mkt Idx Inv
Ticker VTSMX
Time Period May 1992 - Oct 2018
Coefficient of Determination (R2) 99.9%
Adjusted R2 99.9%
Regression F statistic 93,212.44 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.910 with p-value 0.208)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 2.200 with p-value 0.532)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.00 0.002 514.373 0.000 0.993...1.000
Size (SMB) -0.00 0.003 -1.809 0.071 -0.010...0.000
Value (HML) 0.02 0.003 6.093 0.000 0.011...0.022
Alpha (α) -1.76bps 0.000 -2.210 0.028 -0.03%...-0.00%
Annualized Alpha (α) -0.21%  
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) 66.24 14.77 20.31  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML Total R2
Vanguard Total Stock Mkt Idx Inv VTSMX May 1992 Oct 2018 -0.21% 66.00 -0.07 0.34 64.51 99.9%
Regression residuals
MonthVTSMX
May 19920.0011
Jun 1992-0.0009
Jul 1992-0.0006
Aug 1992-0.0006
Sep 1992-0.0015
Oct 1992-0.0002
Nov 1992-0.0006
Dec 1992-0.0025
Jan 1993-0.0021
Feb 19930.0001
Mar 1993-0.0008
Apr 19930.0000
May 19930.0001
Jun 1993-0.0004
Jul 1993-0.0020
Aug 19930.0001
Sep 1993-0.0010
Oct 19930.0007
Nov 19930.0003
Dec 19930.0004
Jan 1994-0.0005
Feb 19940.0014
Mar 19940.0004
Apr 1994-0.0007
May 19940.0009
Jun 1994-0.0003
Jul 1994-0.0001
Aug 19940.0010
Sep 19940.0014
Oct 1994-0.0013
Nov 19940.0004
Dec 1994-0.0005
Jan 1995-0.0002
Feb 19950.0002
Mar 19950.0004
Apr 1995-0.0006
May 19950.0002
Jun 1995-0.0013
Jul 1995-0.0008
Aug 19950.0004
Sep 1995-0.0013
Oct 1995-0.0011
Nov 1995-0.0020
Dec 19950.0003
Jan 1996-0.0002
Feb 1996-0.0005
Mar 19960.0003
Apr 19960.0000
May 1996-0.0006
Jun 1996-0.0013
Jul 19960.0006
Aug 1996-0.0004
Sep 19960.0001
Oct 19960.0006
Nov 19960.0015
Dec 1996-0.0002
Jan 19970.0008
Feb 1997-0.0009
Mar 19970.0007
Apr 19970.0003
May 1997-0.0000
Jun 1997-0.0008
Jul 19970.0003
Aug 19970.0004
Sep 19970.0003
Oct 1997-0.0005
Nov 1997-0.0005
Dec 1997-0.0015
Jan 1998-0.0010
Feb 1998-0.0004
Mar 1998-0.0008
Apr 1998-0.0005
May 1998-0.0012
Jun 19980.0001
Jul 1998-0.0021
Aug 1998-0.0013
Sep 19980.0016
Oct 19980.0013
Nov 1998-0.0014
Dec 19980.0002
Jan 1999-0.0010
Feb 1999-0.0005
Mar 19990.0011
Apr 1999-0.0001
May 19990.0011
Jun 19990.0010
Jul 1999-0.0006
Aug 19990.0010
Sep 19990.0004
Oct 1999-0.0017
Nov 1999-0.0014
Dec 1999-0.0035
Jan 20000.0017
Feb 2000-0.0004
Mar 2000-0.0015
Apr 20000.0055
May 20000.0045
Jun 2000-0.0036
Jul 2000-0.0006
Aug 2000-0.0020
Sep 20000.0016
Oct 20000.0005
Nov 20000.0009
Dec 2000-0.0000
Jan 20010.0030
Feb 20010.0002
Mar 20010.0001
Apr 2001-0.0004
May 2001-0.0005
Jun 20010.0008
Jul 20010.0002
Aug 20010.0011
Sep 2001-0.0010
Oct 20010.0004
Nov 2001-0.0007
Dec 20010.0005
Jan 20020.0002
Feb 20020.0008
Mar 20020.0004
Apr 20020.0011
May 2002-0.0001
Jun 20020.0003
Jul 20020.0003
Aug 2002-0.0014
Sep 20020.0011
Oct 2002-0.0021
Nov 20020.0005
Dec 20020.0004
Jan 2003-0.0004
Feb 20030.0014
Mar 2003-0.0004
Apr 2003-0.0008
May 20030.0003
Jun 2003-0.0007
Jul 20030.0001
Aug 2003-0.0002
Sep 20030.0003
Oct 2003-0.0001
Nov 2003-0.0004
Dec 20030.0009
Jan 20040.0002
Feb 2004-0.0002
Mar 20040.0018
Apr 2004-0.0031
May 20040.0014
Jun 20040.0016
Jul 20040.0008
Aug 20040.0011
Sep 20040.0007
Oct 20040.0017
Nov 20040.0002
Dec 20040.0008
Jan 2005-0.0011
Feb 20050.0002
Mar 2005-0.0001
Apr 20050.0007
May 2005-0.0006
Jun 20050.0000
Jul 2005-0.0000
Aug 2005-0.0004
Sep 20050.0008
Oct 2005-0.0011
Nov 20050.0011
Dec 20050.0007
Jan 20060.0015
Feb 2006-0.0002
Mar 20060.0000
Apr 2006-0.0001
May 2006-0.0015
Jun 20060.0012
Jul 20060.0020
Aug 2006-0.0008
Sep 20060.0003
Oct 2006-0.0007
Nov 20060.0013
Dec 2006-0.0017
Jan 20070.0006
Feb 2007-0.0001
Mar 20070.0002
Apr 20070.0012
May 20070.0007
Jun 2007-0.0008
Jul 2007-0.0003
Aug 20070.0017
Sep 20070.0010
Oct 2007-0.0020
Nov 20070.0001
Dec 20070.0002
Jan 2008-0.0000
Feb 2008-0.0009
Mar 20080.0020
Apr 20080.0028
May 20080.0011
Jun 20080.0011
Jul 2008-0.0022
Aug 2008-0.0006
Sep 2008-0.0030
Oct 2008-0.0048
Nov 20080.0000
Dec 20080.0016
Jan 20090.0004
Feb 2009-0.0026
Mar 2009-0.0033
Apr 20090.0039
May 20090.0020
Jun 2009-0.0002
Jul 20090.0006
Aug 20090.0018
Sep 20090.0016
Oct 20090.0008
Nov 20090.0009
Dec 20090.0015
Jan 2010-0.0013
Feb 2010-0.0006
Mar 2010-0.0004
Apr 20100.0016
May 2010-0.0009
Jun 2010-0.0005
Jul 20100.0010
Aug 20100.0003
Sep 20100.0004
Oct 20100.0013
Nov 20100.0002
Dec 2010-0.0004
Jan 20110.0019
Feb 20110.0012
Mar 20110.0005
Apr 20110.0016
May 20110.0015
Jun 2011-0.0002
Jul 20110.0010
Aug 20110.0001
Sep 2011-0.0017
Oct 20110.0023
Nov 20110.0001
Dec 20110.0005
Jan 20120.0010
Feb 2012-0.0014
Mar 2012-0.0003
Apr 20120.0022
May 2012-0.0005
Jun 20120.0005
Jul 20120.0026
Aug 2012-0.0007
Sep 2012-0.0016
Oct 2012-0.0006
Nov 2012-0.0001
Dec 2012-0.0003
Jan 2013-0.0005
Feb 20130.0001
Mar 2013-0.0011
Apr 20130.0015
May 2013-0.0049
Jun 2013-0.0005
Jul 2013-0.0013
Aug 2013-0.0006
Sep 2013-0.0004
Oct 20130.0005
Nov 2013-0.0021
Dec 2013-0.0015
Jan 20140.0026
Feb 20140.0012
Mar 20140.0001
Apr 20140.0023
May 20140.0013
Jun 2014-0.0002
Jul 20140.0005
Aug 2014-0.0001
Sep 2014-0.0015
Oct 20140.0029
Nov 2014-0.0007
Dec 20140.0005
Jan 20150.0040
Feb 2015-0.0030
Mar 20150.0012
Apr 2015-0.0019
May 20150.0008
Jun 2015-0.0014
Jul 20150.0016
Aug 2015-0.0003
Sep 20150.0013
Oct 20150.0013
Nov 20150.0003
Dec 20150.0017
Jan 20160.0004
Feb 20160.0004
Mar 20160.0006
Apr 2016-0.0033
May 20160.0005
Jun 20160.0030
Jul 20160.0004
Aug 2016-0.0029
Sep 2016-0.0007
Oct 2016-0.0029
Nov 2016-0.0051
Dec 20160.0004
Jan 2017-0.0001
Feb 20170.0015
Mar 2017-0.0006
Apr 2017-0.0003
May 2017-0.0004
Jun 20170.0009
Jul 2017-0.0005
Aug 2017-0.0006
Sep 2017-0.0015
Oct 2017-0.0016
Nov 2017-0.0013
Dec 2017-0.0014
Jan 2018-0.0034
Feb 2018-0.0015
Mar 20180.0027
Apr 2018-0.0004
May 20180.0011
Jun 20180.0012
Jul 2018-0.0000
Aug 2018-0.0006
Sep 2018-0.0002
Oct 2018-0.0000