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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Asset 2
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Asset 4
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Asset 5
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Asset 9
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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 Jul 2020 0.96 0.82 0.45 -0.02 0.01% 0.08% 97.5%
iShares Russell 2000 Value ETF IWN Apr 2006 Jul 2020 0.94 0.78 0.52 0.02 -0.07% -0.83% 98.2%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Jul 2020 1.09 1.15 0.71 -0.48 0.05% 0.59% 91.5%
Vanguard Small-Cap Value ETF VBR Apr 2006 Jul 2020 1.01 0.56 0.38 -0.06 -0.04% -0.45% 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 - Jul 2020
Regression Basis 172 monthly samples
Coefficient of Determination (R2) 97.5%
Adjusted R2 97.4%
Regression F statistic 1,611.14 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.764 with p-value 0.056)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 26.658 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.019 51.237 0.000 0.926...1.000
Size (SMB) 0.82 0.035 23.842 0.000 0.755...0.891
Value (HML) 0.45 0.029 15.393 0.000 0.388...0.502
Momentum (MOM) -0.02 0.019 -0.960 0.339 -0.055...0.019
Alpha (α) 0.68bps 0.001 0.090 0.929 -0.14%...0.16%
Annualized Alpha (α) 0.08%  

iShares Russell 2000 Value ETF

Factor regression results for iShares Russell 2000 Value ETF
Ticker IWN
Time Period Apr 2006 - Jul 2020
Regression Basis 172 monthly samples
Coefficient of Determination (R2) 98.2%
Adjusted R2 98.1%
Regression F statistic 2,257.27 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.056 with p-value 0.634)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.449 with p-value 0.486)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.94 0.016 60.616 0.000 0.914...0.975
Size (SMB) 0.78 0.029 27.190 0.000 0.721...0.834
Value (HML) 0.52 0.024 21.556 0.000 0.469...0.564
Momentum (MOM) 0.02 0.015 1.197 0.233 -0.012...0.049
Alpha (α) -6.95bps 0.001 -1.111 0.268 -0.19%...0.05%
Annualized Alpha (α) -0.83%  

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 - Jul 2020
Regression Basis 172 monthly samples
Coefficient of Determination (R2) 91.5%
Adjusted R2 91.3%
Regression F statistic 451.39 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.926 with p-value 0.303)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 48.898 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.09 0.051 21.311 0.000 0.990...1.192
Size (SMB) 1.15 0.094 12.192 0.000 0.961...1.332
Value (HML) 0.71 0.079 9.027 0.000 0.556...0.867
Momentum (MOM) -0.48 0.051 -9.380 0.000 -0.576...-0.376
Alpha (α) 4.95bps 0.002 0.241 0.810 -0.36%...0.46%
Annualized Alpha (α) 0.59%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Apr 2006 - Jul 2020
Regression Basis 172 monthly samples
Coefficient of Determination (R2) 97.8%
Adjusted R2 97.7%
Regression F statistic 1,826.56 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.159 with p-value 0.846)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 13.988 with p-value 0.007)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.017 59.045 0.000 0.975...1.042
Size (SMB) 0.56 0.031 17.761 0.000 0.495...0.619
Value (HML) 0.38 0.026 14.350 0.000 0.325...0.429
Momentum (MOM) -0.06 0.017 -3.278 0.001 -0.089...-0.022
Alpha (α) -3.77bps 0.001 -0.550 0.583 -0.17%...0.10%
Annualized Alpha (α) -0.45%  
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) 73.90 -2.83 -37.22 10.62  
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 Jul 2020 0.08% 71.15 -2.32 -16.56 -0.19 52.75 97.5%
iShares Russell 2000 Value ETF IWN Apr 2006 Jul 2020 -0.83% 69.79 -2.20 -19.23 0.20 41.61 98.2%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Jul 2020 0.59% 80.63 -3.24 -26.46 -5.05 50.82 91.5%
Vanguard Small-Cap Value ETF VBR Apr 2006 Jul 2020 -0.45% 74.52 -1.57 -14.03 -0.59 54.55 97.8%
Regression residuals
MonthIJSIWNRZVVBR
Apr 2006-0.0094-0.0096-0.0081-0.0131
May 2006-0.00240.0014-0.0248-0.0000
Jun 2006-0.00100.00630.01940.0094
Jul 2006-0.00750.00890.00210.0024
Aug 20060.00270.0088-0.0314-0.0035
Sep 20060.0009-0.0029-0.0020-0.0064
Oct 20060.00580.0052-0.00180.0005
Nov 2006-0.0045-0.0006-0.01110.0062
Dec 2006-0.0141-0.00870.0006-0.0135
Jan 20070.0031-0.00240.00700.0015
Feb 2007-0.0049-0.0069-0.00500.0026
Mar 2007-0.00000.0044-0.0087-0.0019
Apr 20070.0023-0.00790.0071-0.0063
May 20070.01090.0059-0.00910.0019
Jun 2007-0.0089-0.0089-0.0090-0.0066
Jul 20070.0052-0.01760.0205-0.0149
Aug 20070.01120.0191-0.01890.0128
Sep 2007-0.0032-0.0015-0.0011-0.0043
Oct 20070.00060.00190.00190.0063
Nov 2007-0.0015-0.0045-0.0011-0.0034
Dec 20070.0003-0.00720.0318-0.0022
Jan 20080.00880.00980.05670.0105
Feb 20080.00200.0025-0.01990.0123
Mar 20080.00900.00120.04310.0017
Apr 2008-0.00200.0127-0.05200.0116
May 2008-0.0004-0.0061-0.01640.0103
Jun 2008-0.0022-0.01440.0310-0.0209
Jul 2008-0.01260.0045-0.03080.0086
Aug 2008-0.00580.0018-0.0503-0.0085
Sep 20080.02080.03080.04220.0217
Oct 2008-0.0002-0.01550.0291-0.0181
Nov 20080.00980.01480.02490.0270
Dec 20080.01940.0115-0.05320.0055
Jan 2009-0.0127-0.0031-0.0644-0.0011
Feb 2009-0.0018-0.0077-0.0225-0.0095
Mar 2009-0.0279-0.01250.0228-0.0213
Apr 20090.0207-0.00130.14550.0267
May 2009-0.0256-0.0032-0.0271-0.0070
Jun 20090.0024-0.01230.0884-0.0064
Jul 2009-0.0063-0.00230.0234-0.0057
Aug 2009-0.0261-0.0116-0.0496-0.0006
Sep 2009-0.0225-0.0140-0.0101-0.0066
Oct 20090.01790.0160-0.05580.0063
Nov 2009-0.0031-0.0052-0.0177-0.0054
Dec 20090.00470.0032-0.01610.0094
Jan 20100.00150.00110.0122-0.0019
Feb 2010-0.0084-0.01230.0273-0.0003
Mar 2010-0.00350.00320.01040.0047
Apr 2010-0.0060-0.0040-0.01130.0059
May 20100.00060.0047-0.00780.0090
Jun 20100.00620.0038-0.03210.0009
Jul 20100.00030.00570.00590.0061
Aug 20100.00000.0041-0.00830.0057
Sep 2010-0.00080.0030-0.0041-0.0009
Oct 20100.00550.00690.02310.0016
Nov 2010-0.0073-0.00370.01150.0012
Dec 20100.0007-0.0049-0.0207-0.0115
Jan 2011-0.0050-0.0044-0.0263-0.0033
Feb 2011-0.00870.0007-0.00490.0006
Mar 20110.0038-0.00280.00730.0039
Apr 2011-0.00330.0050-0.00630.0059
May 20110.00940.01200.02920.0034
Jun 20110.0038-0.00520.00320.0002
Jul 20110.01140.00800.02740.0030
Aug 20110.01370.00260.01250.0048
Sep 20110.0020-0.00110.0084-0.0061
Oct 20110.01650.0127-0.00090.0110
Nov 20110.01260.00370.01410.0062
Dec 20110.01120.00360.0111-0.0007
Jan 20120.01630.0108-0.01110.0071
Feb 2012-0.0116-0.0134-0.0115-0.0095
Mar 20120.00020.0021-0.0094-0.0060
Apr 2012-0.0038-0.00060.00450.0059
May 2012-0.00850.00000.00340.0054
Jun 2012-0.00050.00580.0037-0.0004
Jul 20120.00870.00180.01460.0054
Aug 20120.00660.00180.0190-0.0040
Sep 2012-0.0061-0.00340.0018-0.0083
Oct 2012-0.0102-0.0086-0.03950.0032
Nov 20120.0084-0.00120.04480.0031
Dec 2012-0.00470.0022-0.0330-0.0016
Jan 2013-0.00770.0004-0.02200.0022
Feb 20130.00770.00170.01010.0067
Mar 2013-0.0029-0.0017-0.01610.0029
Apr 20130.00360.0022-0.0062-0.0029
May 2013-0.0095-0.02200.0179-0.0166
Jun 20130.0013-0.0012-0.0065-0.0058
Jul 2013-0.0062-0.0049-0.01650.0005
Aug 20130.0017-0.00630.0054-0.0052
Sep 20130.01140.00570.02520.0053
Oct 20130.0019-0.0008-0.00400.0017
Nov 20130.0010-0.00220.0217-0.0095
Dec 2013-0.0086-0.0001-0.00680.0035
Jan 2014-0.0007-0.00290.00090.0101
Feb 20140.00130.00200.00870.0043
Mar 20140.0015-0.0022-0.0225-0.0013
Apr 20140.00850.0055-0.00020.0086
May 20140.00250.00220.00590.0076
Jun 2014-0.00850.0004-0.01520.0035
Jul 20140.0037-0.00860.0152-0.0035
Aug 20140.00360.00420.00170.0095
Sep 2014-0.0035-0.01110.0075-0.0089
Oct 20140.01980.02250.00340.0064
Nov 20140.01080.00430.02030.0091
Dec 2014-0.0038-0.0029-0.0207-0.0024
Jan 2015-0.00240.0092-0.00110.0172
Feb 20150.0029-0.00480.0194-0.0023
Mar 2015-0.00130.00690.00270.0112
Apr 2015-0.0091-0.0115-0.0087-0.0131
May 2015-0.0060-0.00580.00500.0038
Jun 2015-0.0002-0.00110.0042-0.0102
Jul 20150.01250.00960.04120.0198
Aug 2015-0.0044-0.0084-0.0039-0.0011
Sep 20150.01230.01180.01700.0113
Oct 20150.0067-0.0010-0.0034-0.0025
Nov 2015-0.0082-0.0012-0.0124-0.0094
Dec 20150.00540.00170.02100.0006
Jan 20160.01540.0047-0.00710.0063
Feb 20160.01610.00430.02020.0111
Mar 20160.01380.00580.00090.0074
Apr 2016-0.0091-0.0078-0.0247-0.0076
May 2016-0.00210.0128-0.04960.0060
Jun 20160.01040.00700.02320.0063
Jul 2016-0.00500.0025-0.0123-0.0055
Aug 2016-0.0190-0.0059-0.0481-0.0186
Sep 2016-0.0043-0.00280.0061-0.0055
Oct 2016-0.00030.00110.00800.0006
Nov 20160.00380.0016-0.0185-0.0106
Dec 2016-0.00290.0059-0.0236-0.0040
Jan 2017-0.0107-0.0041-0.02570.0025
Feb 20170.00330.0062-0.01310.0014
Mar 2017-0.0044-0.0023-0.0256-0.0040
Apr 2017-0.0034-0.0023-0.0140-0.0038
May 20170.0048-0.0012-0.0077-0.0055
Jun 2017-0.00240.0029-0.0074-0.0010
Jul 20170.00150.0015-0.01840.0006
Aug 2017-0.0059-0.00290.02680.0026
Sep 20170.0098-0.00300.0026-0.0135
Oct 2017-0.0005-0.00710.0258-0.0017
Nov 20170.01230.00500.01410.0032
Dec 2017-0.0051-0.0101-0.0173-0.0004
Jan 2018-0.0100-0.0109-0.0017-0.0134
Feb 2018-0.0032-0.01310.0151-0.0065
Mar 20180.00290.0029-0.01210.0088
Apr 20180.00160.0033-0.0019-0.0082
May 20180.00270.00690.01750.0018
Jun 20180.00200.0022-0.0010-0.0014
Jul 20180.00950.0020-0.01640.0011
Aug 20180.00650.00210.03100.0004
Sep 2018-0.0073-0.0008-0.0013-0.0003
Oct 2018-0.00380.00180.0097-0.0020
Nov 2018-0.00720.0039-0.04970.0078
Dec 2018-0.0052-0.00450.00860.0019
Jan 20190.01590.0096-0.00120.0058
Feb 20190.00250.0041-0.00630.0038
Mar 2019-0.00730.00520.00700.0022
Apr 20190.00770.0017-0.0225-0.0019
May 2019-0.01320.0025-0.00600.0069
Jun 20190.0097-0.00220.0026-0.0018
Jul 20190.01620.00590.02850.0063
Aug 20190.01550.01110.04930.0072
Sep 20190.01650.00950.0174-0.0002
Oct 20190.00560.01320.00810.0020
Nov 2019-0.0111-0.0117-0.0206-0.0146
Dec 2019-0.0144-0.0076-0.0268-0.0135
Jan 2020-0.00850.0040-0.03990.0108
Feb 2020-0.0145-0.0066-0.0387-0.0109
Mar 2020-0.0230-0.01310.0255-0.0298
Apr 2020-0.0111-0.01730.0449-0.0202
May 2020-0.0266-0.0147-0.0172-0.0028
Jun 2020-0.0004-0.00350.0117-0.0110
Jul 2020-0.0040-0.00980.0357-0.0032