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 May 2020 0.99 0.02 -0.03 -0.08 0.21 0.04% 0.52% 92.5%
Vanguard Developed Markets Index Admiral VTMGX Dec 2000 May 2020 1.04 -0.24 0.10 0.10 -0.14 -0.17% -2.04% 94.6%

Vanguard Total Stock Mkt Idx Adm

Factor regression results for Vanguard Total Stock Mkt Idx Adm
Ticker VTSAX
Time Period Dec 2000 - May 2020
Regression Basis 234 monthly samples
Coefficient of Determination (R2) 92.5%
Adjusted R2 92.4%
Regression F statistic 566.10 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.756 with p-value 0.028)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 10.648 with p-value 0.059)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.99 0.030 33.078 0.000 0.929...1.046
Size (SMB) 0.02 0.055 0.299 0.766 -0.092...0.125
Value (HML-DEV) -0.03 0.040 -0.644 0.520 -0.103...0.052
Momentum (MOM) -0.08 0.029 -2.651 0.009 -0.136...-0.020
Quality (QMJ) 0.21 0.074 2.852 0.005 0.065...0.357
Alpha (α) 4.31bps 0.001 0.454 0.651 -0.14%...0.23%
Annualized Alpha (α) 0.52%  

Vanguard Developed Markets Index Admiral

Factor regression results for Vanguard Developed Markets Index Admiral
Ticker VTMGX
Time Period Dec 2000 - May 2020
Regression Basis 234 monthly samples
Coefficient of Determination (R2) 94.6%
Adjusted R2 94.4%
Regression F statistic 792.74 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.177 with p-value 0.908)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 19.529 with p-value 0.002)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.04 0.028 36.820 0.000 0.985...1.097
Size (SMB) -0.24 0.052 -4.612 0.000 -0.344...-0.138
Value (HML-DEV) 0.10 0.037 2.677 0.008 0.026...0.174
Momentum (MOM) 0.10 0.028 3.521 0.001 0.043...0.153
Quality (QMJ) -0.14 0.070 -1.968 0.050 -0.276...0.000
Alpha (α) -16.96bps 0.001 -1.887 0.060 -0.35%...0.01%
Annualized Alpha (α) -2.04%  
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) 46.26 8.81 23.38 63.47 45.68  
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 May 2020 0.52% 45.68 0.15 -0.60 -4.94 9.65 54.25 92.5%
Vanguard Developed Markets Index Admiral VTMGX Dec 2000 May 2020 -2.04% 48.15 -2.12 2.34 6.21 -6.31 31.31 94.6%
Regression residuals
MonthVTSAXVTMGX
Dec 20000.00170.0037
Jan 20010.0091-0.0116
Feb 2001-0.00700.0005
Mar 20010.0019-0.0008
Apr 20010.00220.0027
May 20010.0199-0.0303
Jun 20010.0103-0.0120
Jul 20010.0023-0.0010
Aug 2001-0.01760.0223
Sep 2001-0.0001-0.0088
Oct 2001-0.00720.0129
Nov 20010.0156-0.0254
Dec 20010.00830.0059
Jan 20020.0107-0.0167
Feb 2002-0.01310.0147
Mar 2002-0.00410.0133
Apr 2002-0.02610.0296
May 2002-0.01650.0075
Jun 2002-0.02070.0232
Jul 2002-0.0044-0.0103
Aug 20020.0031-0.0099
Sep 2002-0.00750.0048
Oct 20020.0189-0.0110
Nov 20020.0140-0.0126
Dec 2002-0.01750.0115
Jan 20030.0011-0.0150
Feb 2003-0.0037-0.0033
Mar 20030.0110-0.0116
Apr 20030.00170.0069
May 2003-0.0005-0.0059
Jun 2003-0.00650.0051
Jul 20030.00210.0100
Aug 2003-0.0015-0.0045
Sep 2003-0.02550.0219
Oct 20030.0089-0.0016
Nov 2003-0.00450.0093
Dec 2003-0.01120.0118
Jan 20040.0093-0.0073
Feb 2004-0.00570.0043
Mar 2004-0.01580.0083
Apr 2004-0.00440.0030
May 20040.0037-0.0003
Jun 2004-0.00190.0021
Jul 2004-0.01120.0009
Aug 2004-0.0006-0.0003
Sep 2004-0.00310.0032
Oct 2004-0.00980.0093
Nov 2004-0.00600.0097
Dec 2004-0.00180.0061
Jan 2005-0.00850.0023
Feb 2005-0.01190.0079
Mar 2005-0.0016-0.0053
Apr 2005-0.00110.0066
May 20050.0185-0.0225
Jun 2005-0.0029-0.0036
Jul 20050.0029-0.0072
Aug 2005-0.01710.0185
Sep 2005-0.01250.0099
Oct 20050.00510.0022
Nov 20050.0082-0.0160
Dec 2005-0.02190.0213
Jan 2006-0.01320.0109
Feb 20060.0011-0.0042
Mar 2006-0.00800.0100
Apr 2006-0.01920.0144
May 2006-0.00260.0037
Jun 20060.0027-0.0008
Jul 2006-0.00430.0034
Aug 2006-0.00300.0023
Sep 20060.0106-0.0093
Oct 20060.00010.0004
Nov 2006-0.00600.0012
Dec 2006-0.00960.0019
Jan 20070.00680.0026
Feb 2007-0.01550.0078
Mar 2007-0.00910.0048
Apr 2007-0.0007-0.0054
May 20070.0058-0.0080
Jun 2007-0.01600.0082
Jul 2007-0.0196-0.0011
Aug 20070.0158-0.0021
Sep 2007-0.0124-0.0086
Oct 2007-0.02100.0015
Nov 2007-0.00460.0102
Dec 20070.0063-0.0118
Jan 20080.01630.0094
Feb 2008-0.0364-0.0117
Mar 20080.00500.0184
Apr 20080.0010-0.0078
May 2008-0.0009-0.0018
Jun 2008-0.0061-0.0018
Jul 20080.0155-0.0038
Aug 20080.0294-0.0181
Sep 20080.02530.0129
Oct 20080.01090.0029
Nov 2008-0.02340.0077
Dec 2008-0.03170.0391
Jan 2009-0.0043-0.0228
Feb 2009-0.01700.0066
Mar 20090.0138-0.0003
Apr 2009-0.0141-0.0008
May 2009-0.05000.0342
Jun 20090.0036-0.0018
Jul 2009-0.00150.0015
Aug 20090.00290.0084
Sep 2009-0.00340.0017
Oct 2009-0.01500.0000
Nov 20090.0193-0.0071
Dec 20090.0087-0.0087
Jan 20100.00070.0034
Feb 20100.0197-0.0149
Mar 20100.0076-0.0105
Apr 20100.0200-0.0261
May 20100.0054-0.0083
Jun 2010-0.03520.0200
Jul 2010-0.00210.0186
Aug 2010-0.01510.0022
Sep 20100.00160.0039
Oct 20100.00270.0024
Nov 20100.0252-0.0271
Dec 20100.00150.0052
Jan 20110.00510.0008
Feb 20110.00640.0000
Mar 20110.0051-0.0162
Apr 2011-0.01190.0245
May 20110.0030-0.0035
Jun 2011-0.00450.0072
Jul 2011-0.00810.0022
Aug 20110.0001-0.0058
Sep 20110.00500.0041
Oct 20110.0183-0.0207
Nov 20110.02350.0083
Dec 20110.0107-0.0201
Jan 2012-0.00390.0050
Feb 2012-0.0069-0.0003
Mar 20120.0233-0.0030
Apr 20120.0016-0.0099
May 20120.0215-0.0165
Jun 2012-0.00530.0197
Jul 2012-0.0000-0.0083
Aug 2012-0.00180.0078
Sep 2012-0.0041-0.0024
Oct 2012-0.01130.0092
Nov 2012-0.00610.0113
Dec 2012-0.00570.0139
Jan 20130.0062-0.0101
Feb 20130.0126-0.0125
Mar 20130.0183-0.0044
Apr 2013-0.00860.0134
May 20130.0234-0.0260
Jun 20130.00940.0057
Jul 20130.0055-0.0024
Aug 2013-0.01380.0093
Sep 2013-0.01330.0184
Oct 20130.0061-0.0064
Nov 20130.0114-0.0074
Dec 20130.0084-0.0044
Jan 20140.0048-0.0078
Feb 20140.00000.0053
Mar 20140.0011-0.0024
Apr 2014-0.00800.0082
May 20140.0026-0.0048
Jun 20140.0048-0.0089
Jul 2014-0.0045-0.0074
Aug 20140.0204-0.0167
Sep 20140.0087-0.0058
Oct 20140.0146-0.0018
Nov 20140.0058-0.0157
Dec 20140.0133-0.0182
Jan 2015-0.01000.0226
Feb 2015-0.00000.0037
Mar 20150.00030.0036
Apr 2015-0.02750.0088
May 20150.0138-0.0006
Jun 20150.00140.0034
Jul 20150.00860.0026
Aug 20150.00030.0013
Sep 20150.00270.0018
Oct 20150.0052-0.0110
Nov 20150.00980.0042
Dec 2015-0.00350.0007
Jan 2016-0.00310.0133
Feb 2016-0.0023-0.0176
Mar 2016-0.0008-0.0050
Apr 2016-0.00770.0006
May 20160.0133-0.0042
Jun 20160.0141-0.0117
Jul 2016-0.00560.0043
Aug 2016-0.00250.0058
Sep 2016-0.00430.0070
Oct 2016-0.0037-0.0053
Nov 20160.0282-0.0233
Dec 2016-0.00360.0038
Jan 2017-0.00450.0078
Feb 20170.0101-0.0120
Mar 2017-0.01410.0223
Apr 2017-0.00970.0131
May 2017-0.01600.0143
Jun 20170.00330.0009
Jul 2017-0.0045-0.0019
Aug 2017-0.0015-0.0029
Sep 20170.00080.0041
Oct 20170.0032-0.0010
Nov 20170.0073-0.0090
Dec 2017-0.00380.0002
Jan 20180.0032-0.0082
Feb 20180.0023-0.0033
Mar 2018-0.00640.0183
Apr 2018-0.00610.0020
May 20180.0185-0.0155
Jun 20180.0086-0.0060
Jul 20180.0081-0.0039
Aug 20180.0240-0.0236
Sep 2018-0.0011-0.0011
Oct 20180.0005-0.0027
Nov 20180.0034-0.0072
Dec 2018-0.02210.0215
Jan 20190.0070-0.0058
Feb 20190.0046-0.0031
Mar 20190.0052-0.0101
Apr 20190.0013-0.0005
May 2019-0.00460.0048
Jun 20190.0059-0.0069
Jul 20190.0110-0.0208
Aug 20190.00510.0021
Sep 2019-0.00630.0117
Oct 2019-0.00470.0089
Nov 20190.0122-0.0085
Dec 2019-0.00230.0011
Jan 20200.0134-0.0149
Feb 2020-0.00230.0077
Mar 2020-0.0113-0.0060
Apr 20200.0276-0.0274
May 20200.00750.0124