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
Allocation
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Asset 2
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Asset 3
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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 8
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Asset 9
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Asset 10
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Factor Analysis Results

Vanguard Small Cap Index Inv

Factor regression results for Vanguard Small Cap Index Inv
Ticker NAESX
Time Period Jan 1985 - Nov 2020
Regression Basis 431 monthly samples
Coefficient of Determination (R2) 96.8%
Adjusted R2 96.7%
Regression F statistic 2,560.25 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.097 with p-value 0.839)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 2.895 with p-value 0.716)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
FF-MKT-RF Market 1.04 0.013 82.717 0.000 1.012...1.062
FF-SMB5 Size 0.78 0.019 41.920 0.000 0.747...0.820
FF-HML Value 0.04 0.023 1.572 0.117 -0.009...0.081
FF-RMW Profitability 0.05 0.025 1.990 0.047 0.001...0.097
FF-CMA Investment 0.00 0.035 0.135 0.893 -0.064...0.073
Alpha Alpha -12.28bps 0.001 -2.354 0.019 -0.23%...-0.02%
Annualized Alpha Annualized Alpha -1.47%  
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.
  • Symbols:
    MKT-RF
    Market factor (excess return over the risk free rate)
    SMB
    Size factor (Small Minus Big)
    HML
    Value factor (High Minus Low)
    MOM
    Momentum factor (Up Minus Down)
    RMW
    Profitability factor (Robust Minus Weak)
    CMA
    Conservative investment factor (Conservative Minus Aggressive)
    ST-REV
    Short-term reversal factor
    LT-REV
    Long-term reversal factor
    QMJ
    Quality factor (Quality Minus Junk)
    BAB
    Bet Against Beta factor
    TRM
    Term factor (fixed income)
    CDT
    Credit factor (fixed income)
    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) 75.08 5.37 8.25 34.75 20.03  
Name Ticker Start Date End Date Annual Alpha FF-MKT-RF FF-SMB5 FF-HML FF-RMW FF-CMA Total R2
Vanguard Small Cap Index Inv NAESX Jan 1985 Nov 2020 -1.47% 77.85 4.21 0.30 1.69 0.09 71.86 96.8%
Regression residuals
MonthNAESX
Jan 19850.0342
Feb 19850.0060
Mar 1985-0.0367
Apr 1985-0.0047
May 19850.0038
Jun 1985-0.0188
Jul 1985-0.0176
Aug 1985-0.0006
Sep 1985-0.0307
Oct 19850.0048
Nov 1985-0.0102
Dec 19850.0097
Jan 19860.0239
Feb 19860.0099
Mar 1986-0.0350
Apr 19860.0069
May 19860.0083
Jun 1986-0.0129
Jul 1986-0.0258
Aug 1986-0.0327
Sep 1986-0.0302
Oct 19860.0063
Nov 19860.0044
Dec 19860.0115
Jan 19870.0072
Feb 19870.0078
Mar 1987-0.0201
Apr 19870.0143
May 19870.0304
Jun 1987-0.0188
Jul 19870.0010
Aug 19870.0168
Sep 19870.0115
Oct 1987-0.0241
Nov 1987-0.0340
Dec 19870.0459
Jan 1988-0.0041
Feb 19880.0110
Mar 19880.0205
Apr 19880.0146
May 1988-0.0056
Jun 1988-0.0222
Jul 1988-0.0017
Aug 19880.0076
Sep 1988-0.0081
Oct 1988-0.0034
Nov 1988-0.0162
Dec 19880.0293
Jan 1989-0.0004
Feb 1989-0.0208
Mar 19890.0013
Apr 1989-0.0021
May 1989-0.0020
Jun 1989-0.0164
Jul 1989-0.0170
Aug 19890.0174
Sep 1989-0.0126
Oct 1989-0.0083
Nov 19890.0002
Dec 1989-0.0013
Jan 19900.0044
Feb 1990-0.0057
Mar 19900.0113
Apr 1990-0.0017
May 1990-0.0029
Jun 1990-0.0006
Jul 1990-0.0030
Aug 19900.0004
Sep 1990-0.0006
Oct 1990-0.0069
Nov 19900.0095
Dec 19900.0097
Jan 19910.0031
Feb 19910.0049
Mar 19910.0090
Apr 1991-0.0089
May 19910.0003
Jun 1991-0.0098
Jul 1991-0.0026
Aug 19910.0019
Sep 19910.0064
Oct 19910.0047
Nov 1991-0.0016
Dec 1991-0.0157
Jan 19920.0098
Feb 19920.0090
Mar 1992-0.0027
Apr 1992-0.0010
May 19920.0053
Jun 1992-0.0058
Jul 1992-0.0008
Aug 19920.0009
Sep 1992-0.0014
Oct 19920.0042
Nov 1992-0.0038
Dec 19920.0026
Jan 19930.0092
Feb 19930.0041
Mar 19930.0047
Apr 19930.0095
May 1993-0.0019
Jun 1993-0.0032
Jul 19930.0044
Aug 19930.0022
Sep 19930.0044
Oct 1993-0.0033
Nov 1993-0.0014
Dec 19930.0031
Jan 19940.0057
Feb 19940.0006
Mar 19940.0052
Apr 19940.0057
May 19940.0028
Jun 1994-0.0003
Jul 19940.0013
Aug 19940.0009
Sep 1994-0.0030
Oct 1994-0.0017
Nov 1994-0.0005
Dec 19940.0129
Jan 1995-0.0082
Feb 1995-0.0006
Mar 19950.0003
Apr 1995-0.0013
May 19950.0006
Jun 1995-0.0048
Jul 19950.0006
Aug 1995-0.0022
Sep 1995-0.0057
Oct 19950.0002
Nov 19950.0042
Dec 19950.0088
Jan 1996-0.0057
Feb 19960.0044
Mar 1996-0.0052
Apr 1996-0.0040
May 1996-0.0125
Jun 1996-0.0037
Jul 19960.0010
Aug 19960.0082
Sep 1996-0.0063
Oct 19960.0011
Nov 19960.0044
Dec 19960.0128
Jan 1997-0.0177
Feb 1997-0.0040
Mar 19970.0038
Apr 19970.0018
May 19970.0023
Jun 1997-0.0026
Jul 1997-0.0031
Aug 19970.0026
Sep 1997-0.0048
Oct 1997-0.0051
Nov 1997-0.0007
Dec 19970.0143
Jan 1998-0.0102
Feb 1998-0.0013
Mar 1998-0.0058
Apr 1998-0.0048
May 1998-0.0033
Jun 1998-0.0073
Jul 1998-0.0163
Aug 19980.0079
Sep 19980.0165
Oct 1998-0.0064
Nov 1998-0.0159
Dec 19980.0102
Jan 1999-0.0180
Feb 1999-0.0004
Mar 19990.0116
Apr 19990.0049
May 19990.0099
Jun 1999-0.0107
Jul 1999-0.0086
Aug 1999-0.0113
Sep 19990.0065
Oct 1999-0.0052
Nov 1999-0.0187
Dec 1999-0.0040
Jan 2000-0.0015
Feb 20000.0075
Mar 2000-0.0161
Apr 20000.0381
May 20000.0121
Jun 2000-0.0279
Jul 2000-0.0097
Aug 20000.0089
Sep 20000.0184
Oct 2000-0.0038
Nov 2000-0.0015
Dec 20000.0411
Jan 2001-0.0246
Feb 20010.0056
Mar 20010.0017
Apr 20010.0014
May 2001-0.0142
Jun 20010.0083
Jul 2001-0.0158
Aug 20010.0085
Sep 20010.0017
Oct 2001-0.0064
Nov 20010.0026
Dec 20010.0026
Jan 2002-0.0090
Feb 2002-0.0053
Mar 20020.0035
Apr 20020.0069
May 2002-0.0068
Jun 2002-0.0024
Jul 2002-0.0174
Aug 20020.0015
Sep 20020.0094
Oct 2002-0.0124
Nov 20020.0081
Dec 2002-0.0038
Jan 2003-0.0057
Feb 2003-0.0030
Mar 2003-0.0036
Apr 20030.0022
May 2003-0.0003
Jun 2003-0.0081
Jul 2003-0.0047
Aug 20030.0049
Sep 2003-0.0072
Oct 2003-0.0023
Nov 20030.0060
Dec 2003-0.0007
Jan 2004-0.0007
Feb 20040.0059
Mar 20040.0082
Apr 2004-0.0127
May 20040.0117
Jun 20040.0006
Jul 20040.0038
Aug 20040.0048
Sep 20040.0007
Oct 20040.0063
Nov 2004-0.0039
Dec 20040.0014
Jan 2005-0.0002
Feb 20050.0019
Mar 20050.0065
Apr 20050.0112
May 20050.0022
Jun 20050.0012
Jul 2005-0.0004
Aug 20050.0016
Sep 20050.0024
Oct 2005-0.0013
Nov 20050.0013
Dec 20050.0018
Jan 2006-0.0008
Feb 20060.0031
Mar 2006-0.0025
Apr 2006-0.0051
May 20060.0066
Jun 20060.0036
Jul 2006-0.0011
Aug 2006-0.0036
Sep 2006-0.0028
Oct 20060.0006
Nov 20060.0039
Dec 2006-0.0062
Jan 20070.0052
Feb 20070.0060
Mar 20070.0008
Apr 20070.0033
May 20070.0040
Jun 2007-0.0042
Jul 20070.0023
Aug 20070.0054
Sep 20070.0062
Oct 20070.0069
Nov 20070.0025
Dec 2007-0.0009
Jan 20080.0039
Feb 20080.0095
Mar 2008-0.0015
Apr 20080.0144
May 20080.0071
Jun 2008-0.0125
Jul 2008-0.0054
Aug 2008-0.0128
Sep 2008-0.0042
Oct 2008-0.0112
Nov 2008-0.0016
Dec 20080.0126
Jan 20090.0016
Feb 2009-0.0023
Mar 2009-0.0022
Apr 20090.0213
May 20090.0043
Jun 2009-0.0079
Jul 2009-0.0025
Aug 20090.0105
Sep 2009-0.0002
Oct 2009-0.0011
Nov 2009-0.0018
Dec 20090.0019
Jan 20100.0004
Feb 20100.0030
Mar 20100.0019
Apr 2010-0.0049
May 20100.0045
Jun 20100.0043
Jul 20100.0000
Aug 20100.0097
Sep 2010-0.0058
Oct 2010-0.0034
Nov 2010-0.0030
Dec 20100.0000
Jan 20110.0082
Feb 20110.0059
Mar 2011-0.0005
Apr 20110.0055
May 2011-0.0014
Jun 2011-0.0027
Jul 2011-0.0022
Aug 20110.0043
Sep 2011-0.0016
Oct 20110.0100
Nov 20110.0010
Dec 2011-0.0025
Jan 20120.0033
Feb 20120.0006
Mar 2012-0.0042
Apr 20120.0044
May 2012-0.0033
Jun 2012-0.0010
Jul 20120.0054
Aug 20120.0063
Sep 2012-0.0049
Oct 20120.0105
Nov 20120.0024
Dec 20120.0045
Jan 20130.0031
Feb 20130.0043
Mar 2013-0.0006
Apr 20130.0042
May 2013-0.0072
Jun 2013-0.0067
Jul 2013-0.0045
Aug 2013-0.0014
Sep 2013-0.0009
Oct 20130.0004
Nov 2013-0.0148
Dec 20130.0026
Jan 20140.0131
Feb 20140.0030
Mar 2014-0.0004
Apr 20140.0101
May 20140.0067
Jun 20140.0008
Jul 20140.0060
Aug 20140.0052
Sep 2014-0.0022
Oct 2014-0.0090
Nov 20140.0028
Dec 2014-0.0083
Jan 20150.0192
Feb 2015-0.0047
Mar 20150.0010
Apr 20150.0015
May 20150.0021
Jun 2015-0.0139
Jul 20150.0193
Aug 20150.0010
Sep 20150.0087
Oct 2015-0.0056
Nov 2015-0.0113
Dec 20150.0057
Jan 20160.0089
Feb 20160.0018
Mar 20160.0031
Apr 2016-0.0002
May 20160.0089
Jun 2016-0.0001
Jul 2016-0.0097
Aug 2016-0.0113
Sep 2016-0.0101
Oct 20160.0109
Nov 2016-0.0196
Dec 2016-0.0042
Jan 20170.0082
Feb 20170.0049
Mar 2017-0.0087
Apr 2017-0.0060
May 20170.0034
Jun 2017-0.0037
Jul 20170.0055
Aug 20170.0042
Sep 2017-0.0198
Oct 20170.0076
Nov 2017-0.0001
Dec 20170.0006
Jan 2018-0.0034
Feb 2018-0.0054
Mar 20180.0076
Apr 2018-0.0065
May 2018-0.0119
Jun 2018-0.0045
Jul 2018-0.0009
Aug 20180.0055
Sep 20180.0033
Oct 20180.0117
Nov 20180.0099
Dec 20180.0116
Jan 20190.0068
Feb 2019-0.0007
Mar 20190.0079
Apr 20190.0017
May 20190.0114
Jun 2019-0.0048
Jul 20190.0144
Aug 20190.0135
Sep 2019-0.0073
Oct 2019-0.0066
Nov 2019-0.0012
Dec 2019-0.0154
Jan 20200.0183
Feb 20200.0003
Mar 2020-0.0083
Apr 2020-0.0164
May 20200.0071
Jun 2020-0.0134
Jul 20200.0101
Aug 2020-0.0310
Sep 20200.0125
Oct 20200.0045
Nov 2020-0.0205