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

Factor Analysis Summary

Factor regression results
Name Ticker Start Date End Date Rm-Rf SMB HML MOM Alpha Annual Alpha R2
iShares S&P Small-Cap 600 Value ETF IJS Apr 2006 Nov 2020 0.97 0.83 0.46 -0.02 0.02% 0.24% 97.6%
iShares Russell 2000 Value ETF IWN Apr 2006 Nov 2020 0.95 0.79 0.53 0.01 -0.05% -0.56% 98.3%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Nov 2020 1.11 1.10 0.70 -0.46 0.03% 0.34% 91.4%
Vanguard Small-Cap Value ETF VBR Apr 2006 Nov 2020 1.00 0.57 0.39 -0.06 -0.02% -0.19% 97.8%

iShares S&P Small-Cap 600 Value ETF

Factor regression results for iShares S&P Small-Cap 600 Value ETF
Ticker IJS
Time Period Apr 2006 - Nov 2020
Regression Basis 176 monthly samples
Coefficient of Determination (R2) 97.6%
Adjusted R2 97.6%
Regression F statistic 1,774.80 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.753 with p-value 0.046)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 25.088 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.97 0.018 53.630 0.000 0.930...1.001
Size (SMB) 0.83 0.033 24.973 0.000 0.765...0.896
Value (HML) 0.46 0.028 16.118 0.000 0.403...0.515
Momentum (MOM) -0.02 0.018 -1.071 0.286 -0.055...0.016
Alpha (α) 2.00bps 0.001 0.272 0.786 -0.13%...0.17%
Annualized Alpha (α) 0.24%  

iShares Russell 2000 Value ETF

Factor regression results for iShares Russell 2000 Value ETF
Ticker IWN
Time Period Apr 2006 - Nov 2020
Regression Basis 176 monthly samples
Coefficient of Determination (R2) 98.3%
Adjusted R2 98.2%
Regression F statistic 2,449.57 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.001 with p-value 0.489)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.787 with p-value 0.775)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.95 0.015 63.070 0.000 0.920...0.979
Size (SMB) 0.79 0.028 28.366 0.000 0.734...0.843
Value (HML) 0.53 0.024 22.132 0.000 0.480...0.574
Momentum (MOM) 0.01 0.015 0.952 0.342 -0.015...0.044
Alpha (α) -4.70bps 0.001 -0.765 0.445 -0.17%...0.07%
Annualized Alpha (α) -0.56%  

Invesco S&P SmallCap 600 Pure Value ETF

Factor regression results for Invesco S&P SmallCap 600 Pure Value ETF
Ticker RZV
Time Period Apr 2006 - Nov 2020
Regression Basis 176 monthly samples
Coefficient of Determination (R2) 91.4%
Adjusted R2 91.2%
Regression F statistic 457.19 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.871 with p-value 0.186)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 52.266 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.11 0.051 21.929 0.000 1.010...1.210
Size (SMB) 1.10 0.093 11.789 0.000 0.918...1.287
Value (HML) 0.70 0.080 8.703 0.000 0.539...0.855
Momentum (MOM) -0.46 0.051 -9.073 0.000 -0.563...-0.362
Alpha (α) 2.83bps 0.002 0.137 0.891 -0.38%...0.44%
Annualized Alpha (α) 0.34%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Apr 2006 - Nov 2020
Regression Basis 176 monthly samples
Coefficient of Determination (R2) 97.8%
Adjusted R2 97.8%
Regression F statistic 1,935.90 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.185 with p-value 0.885)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 14.604 with p-value 0.006)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.00 0.017 60.337 0.000 0.968...1.034
Size (SMB) 0.57 0.031 18.645 0.000 0.511...0.632
Value (HML) 0.39 0.026 14.931 0.000 0.340...0.444
Momentum (MOM) -0.06 0.017 -3.349 0.001 -0.089...-0.023
Alpha (α) -1.58bps 0.001 -0.233 0.816 -0.15%...0.12%
Annualized Alpha (α) -0.19%  
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
    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) 80.40 2.38 -37.18 3.68  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
iShares S&P Small-Cap 600 Value ETF IJS Apr 2006 Nov 2020 0.24% 77.63 1.98 -17.07 -0.07 64.46 97.6%
iShares Russell 2000 Value ETF IWN Apr 2006 Nov 2020 -0.56% 76.32 1.88 -19.60 0.05 53.95 98.3%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Nov 2020 0.34% 89.25 2.62 -25.92 -1.70 67.08 91.4%
Vanguard Small-Cap Value ETF VBR Apr 2006 Nov 2020 -0.19% 80.49 1.36 -14.58 -0.21 65.49 97.8%
Regression residuals
MonthIJSIWNRZVVBR
Apr 2006-0.0080-0.0081-0.0058-0.0121
May 2006-0.00190.0020-0.02340.0001
Jun 2006-0.00150.00580.01900.0088
Jul 2006-0.00680.01000.00290.0032
Aug 20060.00270.0087-0.0307-0.0033
Sep 2006-0.0000-0.0039-0.0037-0.0069
Oct 20060.00690.00620.00070.0014
Nov 2006-0.0041-0.0004-0.00980.0065
Dec 2006-0.0123-0.00650.0040-0.0120
Jan 20070.0050-0.00030.01010.0032
Feb 2007-0.0048-0.0069-0.00320.0024
Mar 20070.00140.0062-0.0065-0.0006
Apr 20070.0045-0.00580.0086-0.0041
May 20070.01140.0068-0.00800.0028
Jun 2007-0.0089-0.0090-0.0083-0.0069
Jul 20070.0067-0.01590.0208-0.0137
Aug 20070.01050.0180-0.02070.0122
Sep 2007-0.00140.0005-0.0011-0.0023
Oct 20070.00180.00310.00180.0073
Nov 2007-0.0003-0.0033-0.0004-0.0029
Dec 20070.0013-0.00610.0326-0.0017
Jan 20080.00760.00850.05830.0088
Feb 20080.00210.0024-0.02060.0118
Mar 20080.00920.00120.04350.0013
Apr 2008-0.00230.0123-0.05430.0119
May 20080.0007-0.0052-0.01400.0108
Jun 20080.0007-0.01110.0348-0.0197
Jul 2008-0.01180.0056-0.02480.0088
Aug 2008-0.00580.0015-0.0471-0.0089
Sep 20080.02070.03110.04530.0204
Oct 2008-0.0003-0.01570.0280-0.0200
Nov 20080.01040.01550.02250.0270
Dec 20080.01780.0093-0.05280.0039
Jan 2009-0.0138-0.0046-0.0676-0.0022
Feb 2009-0.0027-0.0091-0.0252-0.0112
Mar 2009-0.0281-0.01290.0248-0.0206
Apr 20090.0186-0.00400.15180.0261
May 2009-0.0265-0.0051-0.0286-0.0074
Jun 20090.0023-0.01260.0883-0.0068
Jul 2009-0.0042-0.00040.0293-0.0039
Aug 2009-0.0249-0.0104-0.04460.0003
Sep 2009-0.0226-0.0145-0.0081-0.0066
Oct 20090.01780.0158-0.05920.0064
Nov 2009-0.0029-0.0050-0.0192-0.0045
Dec 20090.00440.0027-0.01360.0088
Jan 20100.00140.00100.0143-0.0024
Feb 2010-0.0092-0.01310.0272-0.0010
Mar 2010-0.00430.00230.00960.0043
Apr 2010-0.0065-0.0047-0.00890.0049
May 20100.00020.0043-0.00750.0080
Jun 20100.00620.0036-0.03300.0008
Jul 20100.00040.00560.00520.0067
Aug 20100.00050.0046-0.00870.0059
Sep 2010-0.00050.0028-0.0038-0.0000
Oct 20100.00580.00690.02280.0021
Nov 2010-0.0075-0.00390.01290.0007
Dec 20100.0003-0.0054-0.0196-0.0114
Jan 2011-0.0045-0.0038-0.0264-0.0026
Feb 2011-0.0104-0.0013-0.0067-0.0008
Mar 20110.0044-0.00230.00880.0041
Apr 2011-0.00320.0049-0.00730.0063
May 20110.00890.01150.02840.0031
Jun 20110.0044-0.00460.00430.0005
Jul 20110.01020.00650.02500.0017
Aug 20110.01440.00330.01230.0050
Sep 20110.0024-0.00040.0087-0.0061
Oct 20110.01480.0104-0.00270.0103
Nov 20110.01220.00330.01310.0058
Dec 20110.01050.00310.0104-0.0012
Jan 20120.01580.0098-0.01000.0070
Feb 2012-0.0121-0.0141-0.0135-0.0095
Mar 2012-0.00060.0010-0.0110-0.0066
Apr 2012-0.0036-0.00010.00450.0061
May 2012-0.00820.00080.00410.0051
Jun 2012-0.00190.00410.0021-0.0014
Jul 20120.00800.00110.01170.0050
Aug 20120.00630.00140.0198-0.0041
Sep 2012-0.0066-0.00410.0020-0.0086
Oct 2012-0.0104-0.0086-0.03840.0028
Nov 20120.0086-0.00120.04530.0032
Dec 2012-0.00500.0018-0.0307-0.0021
Jan 2013-0.0080-0.0002-0.02220.0023
Feb 20130.00700.00090.00880.0062
Mar 2013-0.0030-0.0020-0.01640.0030
Apr 20130.00370.0023-0.0071-0.0027
May 2013-0.0103-0.02300.0189-0.0174
Jun 20130.0006-0.0021-0.0065-0.0067
Jul 2013-0.0070-0.0058-0.01700.0001
Aug 20130.0016-0.00660.0052-0.0057
Sep 20130.01140.00550.02540.0052
Oct 20130.0015-0.0014-0.00540.0017
Nov 20130.0010-0.00250.0223-0.0096
Dec 2013-0.0093-0.0011-0.00840.0030
Jan 2014-0.0009-0.00330.00090.0095
Feb 20140.00070.00110.00720.0041
Mar 20140.0012-0.0024-0.0213-0.0016
Apr 20140.00780.0049-0.00190.0083
May 20140.00280.00230.00500.0080
Jun 2014-0.0092-0.0007-0.01510.0027
Jul 20140.0042-0.00800.0144-0.0030
Aug 20140.00310.00350.00070.0094
Sep 2014-0.0031-0.01060.0061-0.0085
Oct 20140.01960.02210.00490.0061
Nov 20140.01070.00390.01790.0094
Dec 2014-0.0047-0.0040-0.0198-0.0037
Jan 2015-0.00190.0097-0.00150.0173
Feb 20150.0028-0.00520.0187-0.0019
Mar 2015-0.00160.00650.00390.0105
Apr 2015-0.0090-0.0115-0.0079-0.0128
May 2015-0.0069-0.00680.00290.0030
Jun 2015-0.0007-0.00180.0049-0.0111
Jul 20150.01310.01030.03700.0208
Aug 2015-0.0044-0.0084-0.0011-0.0020
Sep 20150.01210.01190.01560.0110
Oct 20150.0073-0.0006-0.0037-0.0012
Nov 2015-0.0085-0.0016-0.0110-0.0099
Dec 20150.00560.00190.01910.0008
Jan 20160.01580.0054-0.00650.0062
Feb 20160.01600.00400.02150.0109
Mar 20160.01380.00550.00200.0079
Apr 2016-0.0098-0.0088-0.0231-0.0084
May 2016-0.00260.0121-0.05140.0057
Jun 20160.01050.00710.02290.0062
Jul 2016-0.00470.0026-0.0104-0.0050
Aug 2016-0.0190-0.0060-0.0455-0.0189
Sep 2016-0.0056-0.00450.0053-0.0068
Oct 2016-0.00000.00170.00800.0008
Nov 20160.00270.0005-0.0141-0.0119
Dec 2016-0.00300.0059-0.0222-0.0041
Jan 2017-0.0102-0.0039-0.02620.0031
Feb 20170.00280.0056-0.01530.0016
Mar 2017-0.0035-0.0017-0.0243-0.0034
Apr 2017-0.0025-0.0015-0.0128-0.0030
May 20170.0051-0.0011-0.0099-0.0050
Jun 2017-0.00320.0019-0.0066-0.0019
Jul 20170.00260.0025-0.01790.0015
Aug 2017-0.0053-0.00220.02600.0032
Sep 20170.0088-0.00420.0049-0.0147
Oct 2017-0.0003-0.00700.0243-0.0014
Nov 20170.01150.00410.01300.0030
Dec 2017-0.0057-0.0109-0.0183-0.0008
Jan 2018-0.0097-0.0109-0.0046-0.0127
Feb 2018-0.0035-0.01340.0147-0.0073
Mar 20180.00180.0018-0.01050.0074
Apr 20180.00170.0033-0.0006-0.0083
May 20180.00290.00670.01900.0017
Jun 20180.00190.0017-0.0008-0.0017
Jul 20180.00890.0013-0.01840.0009
Aug 20180.00620.00130.02860.0002
Sep 2018-0.00640.0004-0.00110.0007
Oct 2018-0.00360.00230.0103-0.0025
Nov 2018-0.00800.0030-0.05070.0074
Dec 2018-0.0036-0.00240.01070.0026
Jan 20190.01550.00860.00020.0060
Feb 20190.00170.0030-0.00750.0034
Mar 2019-0.00670.00580.00480.0032
Apr 20190.00770.0015-0.0227-0.0017
May 2019-0.01340.0024-0.00770.0060
Jun 20190.0094-0.00310.0014-0.0017
Jul 20190.01570.00540.02640.0060
Aug 20190.01590.01140.04630.0074
Sep 20190.01570.00880.0194-0.0009
Oct 20190.00590.01320.00790.0023
Nov 2019-0.0107-0.0116-0.0199-0.0140
Dec 2019-0.0152-0.0086-0.0266-0.0140
Jan 2020-0.00790.0046-0.04320.0116
Feb 2020-0.0146-0.0068-0.0379-0.0117
Mar 2020-0.0210-0.01110.0218-0.0287
Apr 2020-0.0108-0.01760.0457-0.0189
May 2020-0.0263-0.0149-0.0176-0.0021
Jun 2020-0.0006-0.00410.0123-0.0112
Jul 2020-0.0047-0.01050.0319-0.0029
Aug 2020-0.0075-0.00090.0454-0.0167
Sep 2020-0.00520.00060.01700.0107
Oct 20200.00130.0021-0.04250.0102
Nov 20200.01360.0198-0.03890.0028