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
Asset 1
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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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Total
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Factor Analysis Results

Factor Analysis Summary

Factor regression results
Name Ticker Start Date End Date Rm-Rf SMB HML-DEV MOM QMJ Alpha Annual Alpha R2
Vanguard Total Stock Mkt Idx Adm VTSAX Dec 2000 Dec 2019 0.97 -0.02 -0.04 -0.08 0.18 0.06% 0.74% 92.0%
Vanguard Developed Markets Index Admiral VTMGX Dec 2000 Dec 2019 1.05 -0.23 0.11 0.10 -0.11 -0.18% -2.18% 94.4%

Vanguard Total Stock Mkt Idx Adm

Factor regression results for Vanguard Total Stock Mkt Idx Adm
Ticker VTSAX
Time Period Dec 2000 - Dec 2019
Coefficient of Determination (R2) 92.0%
Adjusted R2 91.8%
Regression F statistic 512.45 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.757 with p-value 0.030)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 7.681 with p-value 0.175)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.97 0.032 30.116 0.000 0.905...1.031
Size (SMB) -0.02 0.057 -0.274 0.784 -0.128...0.097
Value (HML-DEV) -0.04 0.043 -0.939 0.349 -0.124...0.044
Momentum (MOM) -0.08 0.030 -2.799 0.006 -0.141...-0.024
Quality (QMJ) 0.18 0.079 2.296 0.023 0.026...0.336
Alpha (α) 6.18bps 0.001 0.617 0.538 -0.14%...0.26%
Annualized Alpha (α) 0.74%  

Vanguard Developed Markets Index Admiral

Factor regression results for Vanguard Developed Markets Index Admiral
Ticker VTMGX
Time Period Dec 2000 - Dec 2019
Coefficient of Determination (R2) 94.4%
Adjusted R2 94.3%
Regression F statistic 748.93 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.173 with p-value 0.901)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 14.764 with p-value 0.011)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.05 0.030 34.724 0.000 0.994...1.114
Size (SMB) -0.23 0.054 -4.186 0.000 -0.331...-0.119
Value (HML-DEV) 0.11 0.040 2.663 0.008 0.028...0.187
Momentum (MOM) 0.10 0.028 3.514 0.001 0.043...0.153
Quality (QMJ) -0.11 0.074 -1.453 0.148 -0.255...0.038
Alpha (α) -18.18bps 0.001 -1.923 0.056 -0.37%...0.00%
Annualized Alpha (α) -2.18%  
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
    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) 50.70 9.13 31.85 61.31 45.96  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML-DEV MOM QMJ Total R2
Vanguard Total Stock Mkt Idx Adm VTSAX Dec 2000 Dec 2019 0.74% 49.07 -0.14 -1.28 -5.07 8.31 57.07 92.0%
Vanguard Developed Markets Index Admiral VTMGX Dec 2000 Dec 2019 -2.18% 53.44 -2.06 3.43 6.01 -4.97 37.67 94.4%
Regression residuals
MonthVTSAXVTMGX
Dec 20000.00210.0037
Jan 20010.0100-0.0118
Feb 2001-0.0057-0.0002
Mar 20010.0017-0.0008
Apr 20010.00240.0025
May 20010.0211-0.0307
Jun 20010.0110-0.0123
Jul 20010.0024-0.0014
Aug 2001-0.01660.0218
Sep 2001-0.0018-0.0082
Oct 2001-0.00600.0122
Nov 20010.0160-0.0258
Dec 20010.00950.0052
Jan 20020.0120-0.0176
Feb 2002-0.01260.0141
Mar 2002-0.00280.0126
Apr 2002-0.02450.0288
May 2002-0.01640.0074
Jun 2002-0.02000.0226
Jul 2002-0.0055-0.0100
Aug 20020.0029-0.0098
Sep 2002-0.00740.0045
Oct 20020.0184-0.0108
Nov 20020.0137-0.0119
Dec 2002-0.01630.0107
Jan 20030.0008-0.0146
Feb 2003-0.0036-0.0035
Mar 20030.0112-0.0119
Apr 20030.00200.0071
May 20030.0007-0.0061
Jun 2003-0.00590.0050
Jul 20030.00260.0100
Aug 2003-0.0011-0.0045
Sep 2003-0.02470.0216
Oct 20030.0100-0.0018
Nov 2003-0.00360.0087
Dec 2003-0.01090.0116
Jan 20040.0100-0.0071
Feb 2004-0.00540.0041
Mar 2004-0.01500.0078
Apr 2004-0.00470.0028
May 20040.0036-0.0004
Jun 2004-0.00110.0018
Jul 2004-0.01130.0006
Aug 2004-0.0009-0.0002
Sep 2004-0.00260.0031
Oct 2004-0.00930.0089
Nov 2004-0.00470.0092
Dec 2004-0.00120.0057
Jan 2005-0.00830.0023
Feb 2005-0.01100.0073
Mar 2005-0.0017-0.0053
Apr 2005-0.00210.0070
May 20050.0188-0.0227
Jun 2005-0.0023-0.0038
Jul 20050.0036-0.0075
Aug 2005-0.01780.0185
Sep 2005-0.01330.0098
Oct 20050.00460.0025
Nov 20050.0083-0.0160
Dec 2005-0.02210.0216
Jan 2006-0.01190.0103
Feb 20060.0010-0.0040
Mar 2006-0.00740.0098
Apr 2006-0.01890.0142
May 2006-0.00330.0038
Jun 20060.0024-0.0008
Jul 2006-0.00470.0035
Aug 2006-0.00300.0024
Sep 20060.0105-0.0094
Oct 20060.00050.0003
Nov 2006-0.00570.0011
Dec 2006-0.00950.0019
Jan 20070.00720.0025
Feb 2007-0.01550.0079
Mar 2007-0.00900.0047
Apr 2007-0.0002-0.0057
May 20070.0060-0.0082
Jun 2007-0.01600.0080
Jul 2007-0.0201-0.0009
Aug 20070.0152-0.0021
Sep 2007-0.0128-0.0085
Oct 2007-0.02100.0015
Nov 2007-0.00570.0105
Dec 20070.0061-0.0118
Jan 20080.01500.0102
Feb 2008-0.0360-0.0119
Mar 20080.00510.0182
Apr 20080.0007-0.0077
May 2008-0.0003-0.0022
Jun 2008-0.0071-0.0013
Jul 20080.0152-0.0038
Aug 20080.0296-0.0185
Sep 20080.02380.0135
Oct 20080.00780.0043
Nov 2008-0.02460.0079
Dec 2008-0.03050.0383
Jan 2009-0.0045-0.0228
Feb 2009-0.01810.0070
Mar 20090.0140-0.0003
Apr 2009-0.0119-0.0019
May 2009-0.04840.0335
Jun 20090.0046-0.0024
Jul 2009-0.00070.0011
Aug 20090.00310.0086
Sep 2009-0.00210.0010
Oct 2009-0.0146-0.0006
Nov 20090.0194-0.0073
Dec 20090.0095-0.0092
Jan 20100.00100.0033
Feb 20100.0199-0.0151
Mar 20100.0086-0.0108
Apr 20100.0209-0.0263
May 20100.0038-0.0075
Jun 2010-0.03560.0199
Jul 2010-0.00140.0183
Aug 2010-0.01590.0025
Sep 20100.00370.0027
Oct 20100.00340.0020
Nov 20100.0254-0.0270
Dec 20100.00250.0049
Jan 20110.00500.0010
Feb 20110.00660.0000
Mar 20110.0058-0.0168
Apr 2011-0.01110.0239
May 20110.0029-0.0038
Jun 2011-0.00460.0070
Jul 2011-0.00820.0022
Aug 2011-0.0006-0.0060
Sep 20110.00370.0043
Oct 20110.0192-0.0210
Nov 20110.02360.0080
Dec 20110.0110-0.0203
Jan 2012-0.00350.0050
Feb 2012-0.0066-0.0004
Mar 20120.0236-0.0032
Apr 20120.0017-0.0101
May 20120.0208-0.0163
Jun 2012-0.00510.0196
Jul 2012-0.0000-0.0085
Aug 2012-0.00150.0076
Sep 2012-0.0039-0.0025
Oct 2012-0.01200.0098
Nov 2012-0.00610.0112
Dec 2012-0.00550.0140
Jan 20130.0071-0.0104
Feb 20130.0128-0.0126
Mar 20130.0188-0.0057
Apr 2013-0.00920.0147
May 20130.0236-0.0261
Jun 20130.00950.0054
Jul 20130.0064-0.0029
Aug 2013-0.01370.0093
Sep 2013-0.01230.0179
Oct 20130.0068-0.0069
Nov 20130.0120-0.0078
Dec 20130.0085-0.0044
Jan 20140.0042-0.0071
Feb 20140.00050.0050
Mar 20140.0014-0.0028
Apr 2014-0.00840.0081
May 20140.0024-0.0047
Jun 20140.0053-0.0092
Jul 2014-0.0053-0.0070
Aug 20140.0207-0.0169
Sep 20140.0076-0.0054
Oct 20140.0153-0.0026
Nov 20140.0054-0.0157
Dec 20140.0133-0.0182
Jan 2015-0.01100.0233
Feb 20150.00080.0031
Mar 20150.00030.0037
Apr 2015-0.02730.0087
May 20150.0140-0.0005
Jun 20150.00180.0031
Jul 20150.00800.0026
Aug 2015-0.00010.0015
Sep 20150.00260.0015
Oct 20150.0056-0.0115
Nov 20150.01000.0041
Dec 2015-0.00420.0010
Jan 2016-0.00360.0129
Feb 2016-0.0016-0.0183
Mar 20160.0007-0.0058
Apr 2016-0.00760.0009
May 20160.0131-0.0042
Jun 20160.0143-0.0119
Jul 2016-0.00480.0037
Aug 2016-0.00250.0058
Sep 2016-0.00440.0073
Oct 2016-0.0041-0.0052
Nov 20160.0294-0.0239
Dec 2016-0.00290.0033
Jan 2017-0.00440.0080
Feb 20170.0103-0.0123
Mar 2017-0.01410.0222
Apr 2017-0.00930.0125
May 2017-0.01610.0140
Jun 20170.00380.0008
Jul 2017-0.0045-0.0018
Aug 2017-0.0020-0.0027
Sep 20170.00200.0036
Oct 20170.0033-0.0011
Nov 20170.0079-0.0096
Dec 2017-0.00400.0004
Jan 20180.0035-0.0084
Feb 20180.0017-0.0030
Mar 2018-0.00630.0182
Apr 2018-0.00610.0021
May 20180.0192-0.0159
Jun 20180.0083-0.0059
Jul 20180.0079-0.0040
Aug 20180.0242-0.0238
Sep 2018-0.0019-0.0007
Oct 2018-0.0009-0.0021
Nov 20180.0033-0.0071
Dec 2018-0.02390.0223
Jan 20190.0082-0.0064
Feb 20190.0051-0.0034
Mar 20190.0042-0.0095
Apr 20190.0019-0.0011
May 2019-0.00590.0057
Jun 20190.0066-0.0074
Jul 20190.0110-0.0209
Aug 20190.00360.0029
Sep 2019-0.00570.0111
Oct 2019-0.00460.0088
Nov 20190.0121-0.0084
Dec 2019-0.00170.0008