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 Feb 2020 0.97 0.82 0.40 -0.02 0.03% 0.40% 97.4%
iShares Russell 2000 Value ETF IWN Apr 2006 Feb 2020 0.95 0.78 0.49 0.02 -0.05% -0.56% 98.1%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Feb 2020 1.07 1.17 0.75 -0.48 0.01% 0.17% 90.7%
Vanguard Small-Cap Value ETF VBR Apr 2006 Feb 2020 1.01 0.55 0.33 -0.06 -0.01% -0.10% 97.7%

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 - Feb 2020
Regression Basis 167 monthly samples
Coefficient of Determination (R2) 97.4%
Adjusted R2 97.3%
Regression F statistic 1,492.36 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.868 with p-value 0.187)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 33.540 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.97 0.019 51.183 0.000 0.930...1.004
Size (SMB) 0.82 0.034 24.497 0.000 0.757...0.889
Value (HML) 0.40 0.030 13.385 0.000 0.342...0.460
Momentum (MOM) -0.02 0.018 -1.300 0.195 -0.060...0.012
Alpha (α) 3.36bps 0.001 0.462 0.645 -0.11%...0.18%
Annualized Alpha (α) 0.40%  

iShares Russell 2000 Value ETF

Factor regression results for iShares Russell 2000 Value ETF
Ticker IWN
Time Period Apr 2006 - Feb 2020
Regression Basis 167 monthly samples
Coefficient of Determination (R2) 98.1%
Adjusted R2 98.0%
Regression F statistic 2,067.00 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.191 with p-value 0.888)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 9.727 with p-value 0.045)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.95 0.016 60.333 0.000 0.923...0.985
Size (SMB) 0.78 0.028 27.656 0.000 0.722...0.833
Value (HML) 0.49 0.025 19.460 0.000 0.438...0.537
Momentum (MOM) 0.02 0.015 1.065 0.288 -0.014...0.046
Alpha (α) -4.66bps 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 - Feb 2020
Regression Basis 167 monthly samples
Coefficient of Determination (R2) 90.7%
Adjusted R2 90.5%
Regression F statistic 396.05 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.922 with p-value 0.296)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 48.288 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.07 0.053 20.029 0.000 0.964...1.175
Size (SMB) 1.17 0.095 12.293 0.000 0.979...1.354
Value (HML) 0.75 0.085 8.813 0.000 0.579...0.913
Momentum (MOM) -0.48 0.051 -9.303 0.000 -0.580...-0.377
Alpha (α) 1.41bps 0.002 0.069 0.945 -0.39%...0.42%
Annualized Alpha (α) 0.17%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Apr 2006 - Feb 2020
Regression Basis 167 monthly samples
Coefficient of Determination (R2) 97.7%
Adjusted R2 97.7%
Regression F statistic 1,742.86 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.354 with p-value 0.989)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 14.350 with p-value 0.006)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.017 59.758 0.000 0.977...1.043
Size (SMB) 0.55 0.030 18.432 0.000 0.494...0.613
Value (HML) 0.33 0.027 12.401 0.000 0.279...0.385
Momentum (MOM) -0.06 0.016 -3.891 0.000 -0.095...-0.031
Alpha (α) -0.86bps 0.001 -0.131 0.896 -0.14%...0.12%
Annualized Alpha (α) -0.10%  
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) 67.70 -3.28 -24.25 4.47  
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 Feb 2020 0.40% 65.48 -2.70 -9.72 -0.11 56.32 97.4%
iShares Russell 2000 Value ETF IWN Apr 2006 Feb 2020 -0.56% 64.60 -2.55 -11.82 0.07 45.63 98.1%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Feb 2020 0.17% 72.40 -3.83 -18.08 -2.14 49.77 90.7%
Vanguard Small-Cap Value ETF VBR Apr 2006 Feb 2020 -0.10% 68.38 -1.82 -8.05 -0.28 57.37 97.7%
Regression residuals
MonthIJSIWNRZVVBR
Apr 2006-0.0085-0.0092-0.0082-0.0122
May 2006-0.00160.0021-0.02560.0005
Jun 2006-0.00080.00640.01950.0096
Jul 2006-0.00660.00960.00210.0031
Aug 20060.00140.0078-0.0303-0.0049
Sep 20060.0005-0.0033-0.0010-0.0068
Oct 20060.00540.0046-0.00110.0002
Nov 2006-0.0049-0.0011-0.01070.0059
Dec 2006-0.0130-0.00810.0003-0.0124
Jan 20070.0028-0.00280.00780.0012
Feb 2007-0.0052-0.0070-0.00530.0023
Mar 2007-0.00030.0041-0.0081-0.0022
Apr 20070.0014-0.00880.0091-0.0072
May 20070.01050.0054-0.00800.0015
Jun 2007-0.0095-0.0093-0.0088-0.0073
Jul 20070.0038-0.01840.0218-0.0165
Aug 20070.00990.0181-0.01750.0115
Sep 2007-0.0042-0.00250.0012-0.0052
Oct 2007-0.00060.00090.00370.0052
Nov 2007-0.0020-0.0046-0.0007-0.0042
Dec 20070.0002-0.00730.0322-0.0022
Jan 20080.01000.01110.05440.0113
Feb 20080.00180.0024-0.01970.0121
Mar 20080.00890.00110.04320.0017
Apr 2008-0.00290.0117-0.05000.0108
May 2008-0.0012-0.0068-0.01570.0097
Jun 2008-0.0024-0.01420.0305-0.0211
Jul 2008-0.01060.0059-0.03340.0106
Aug 2008-0.00560.0020-0.0508-0.0083
Sep 20080.02360.03320.03840.0243
Oct 2008-0.0006-0.01480.0273-0.0189
Nov 20080.00760.01370.02600.0245
Dec 20080.01870.0109-0.05330.0047
Jan 2009-0.0175-0.0057-0.0618-0.0063
Feb 2009-0.0047-0.0091-0.0214-0.0126
Mar 2009-0.0276-0.01280.0248-0.0208
Apr 20090.0204-0.00180.14420.0261
May 2009-0.0268-0.0042-0.0250-0.0084
Jun 20090.0012-0.01320.0894-0.0074
Jul 2009-0.0045-0.00160.0235-0.0039
Aug 2009-0.0236-0.0101-0.05130.0018
Sep 2009-0.0230-0.0147-0.0100-0.0070
Oct 20090.01620.0149-0.05330.0044
Nov 2009-0.0038-0.0061-0.0158-0.0060
Dec 20090.00440.0027-0.01640.0095
Jan 20100.00120.00120.0115-0.0024
Feb 2010-0.0074-0.01200.02670.0010
Mar 2010-0.00280.00320.01110.0056
Apr 2010-0.0049-0.0034-0.01230.0073
May 2010-0.00040.0045-0.00830.0077
Jun 20100.00410.0028-0.0310-0.0015
Jul 2010-0.00030.00480.00790.0057
Aug 2010-0.00100.0037-0.00770.0045
Sep 2010-0.00280.0009-0.0014-0.0025
Oct 20100.00390.00550.02490.0002
Nov 2010-0.0077-0.00410.01170.0008
Dec 20100.0015-0.0049-0.0206-0.0105
Jan 2011-0.0051-0.0046-0.0255-0.0034
Feb 2011-0.00860.0005-0.00470.0009
Mar 20110.0030-0.00340.00780.0033
Apr 2011-0.00480.0038-0.00440.0045
May 20110.00830.01130.03020.0021
Jun 20110.0037-0.00530.00350.0000
Jul 20110.01070.00770.02800.0022
Aug 20110.01270.00230.01330.0035
Sep 20110.0015-0.00090.0083-0.0071
Oct 20110.01550.01130.00130.0105
Nov 20110.01240.00350.01450.0061
Dec 20110.01180.00390.0111-0.0000
Jan 20120.01480.0096-0.00990.0056
Feb 2012-0.0119-0.0139-0.0098-0.0098
Mar 20120.00030.0018-0.0086-0.0059
Apr 2012-0.0041-0.00090.00500.0056
May 2012-0.00840.00040.00260.0055
Jun 2012-0.00080.00530.0047-0.0006
Jul 20120.00850.00150.01600.0052
Aug 20120.00650.00150.0192-0.0040
Sep 2012-0.0059-0.00350.0022-0.0080
Oct 2012-0.0087-0.0075-0.04060.0047
Nov 20120.0077-0.00180.04530.0024
Dec 2012-0.00360.0028-0.0340-0.0005
Jan 2013-0.0081-0.0004-0.02120.0019
Feb 20130.00740.00130.01070.0064
Mar 2013-0.0032-0.0022-0.01460.0027
Apr 20130.00340.0018-0.0055-0.0032
May 2013-0.0090-0.02200.0173-0.0160
Jun 20130.0011-0.0013-0.0065-0.0061
Jul 2013-0.0065-0.0055-0.01570.0004
Aug 20130.0003-0.00710.0062-0.0067
Sep 20130.01060.00480.02590.0046
Oct 20130.0020-0.0012-0.00300.0018
Nov 20130.0011-0.00230.0228-0.0094
Dec 2013-0.0092-0.0007-0.00580.0030
Jan 2014-0.0016-0.00330.00100.0091
Feb 20140.00030.00070.00950.0035
Mar 20140.0033-0.0012-0.02340.0003
Apr 20140.00800.0050-0.00050.0079
May 20140.00260.00230.00770.0076
Jun 2014-0.0093-0.0005-0.01540.0028
Jul 20140.0036-0.00860.0161-0.0038
Aug 20140.00290.00330.00310.0089
Sep 2014-0.0042-0.01150.0090-0.0098
Oct 20140.01880.02170.00430.0055
Nov 20140.00930.00300.02300.0075
Dec 2014-0.0031-0.0026-0.0216-0.0017
Jan 2015-0.00400.00830.00010.0156
Feb 20150.0015-0.00610.0215-0.0037
Mar 2015-0.00160.00670.00250.0111
Apr 2015-0.0089-0.0113-0.0084-0.0132
May 2015-0.0062-0.00600.00650.0036
Jun 2015-0.0007-0.00150.0036-0.0107
Jul 20150.01090.00810.04440.0183
Aug 2015-0.0033-0.0073-0.0059-0.0002
Sep 20150.01260.01210.01700.0116
Oct 20150.0059-0.0020-0.0010-0.0033
Nov 2015-0.0084-0.0014-0.0117-0.0094
Dec 20150.00420.00090.0226-0.0006
Jan 20160.01640.0056-0.00800.0071
Feb 20160.01550.00390.02040.0103
Mar 20160.01330.00500.00190.0071
Apr 2016-0.0083-0.0073-0.0256-0.0069
May 2016-0.00330.0119-0.04940.0048
Jun 20160.00980.00650.02450.0058
Jul 2016-0.00610.0015-0.0109-0.0064
Aug 2016-0.0177-0.0051-0.0485-0.0174
Sep 2016-0.0051-0.00320.0067-0.0063
Oct 20160.00120.00210.00690.0020
Nov 20160.00680.0034-0.0217-0.0074
Dec 2016-0.00150.0067-0.0240-0.0027
Jan 2017-0.0121-0.0051-0.02320.0010
Feb 20170.00170.0048-0.0115-0.0002
Mar 2017-0.0062-0.0036-0.0245-0.0058
Apr 2017-0.0045-0.0032-0.0125-0.0048
May 20170.0026-0.0029-0.0056-0.0077
Jun 2017-0.00220.0029-0.0076-0.0007
Jul 20170.00150.0015-0.01680.0005
Aug 2017-0.0064-0.00310.02910.0019
Sep 20170.0104-0.00280.0011-0.0126
Oct 20170.0001-0.00680.0282-0.0013
Nov 20170.01160.00430.01510.0027
Dec 2017-0.0056-0.0106-0.0167-0.0009
Jan 2018-0.0108-0.01200.0011-0.0143
Feb 2018-0.0030-0.01260.0160-0.0065
Mar 20180.00260.0029-0.01290.0086
Apr 20180.00180.0034-0.0020-0.0081
May 20180.00190.00620.01960.0010
Jun 20180.00090.00150.0003-0.0027
Jul 20180.00910.0015-0.01510.0007
Aug 20180.00430.00010.0333-0.0016
Sep 2018-0.0082-0.0015-0.0002-0.0014
Oct 2018-0.00240.00330.0081-0.0009
Nov 2018-0.00760.0035-0.04940.0074
Dec 2018-0.0057-0.00430.00780.0011
Jan 20190.01450.00820.00020.0045
Feb 20190.00090.0029-0.00480.0024
Mar 2019-0.00940.00360.00980.0001
Apr 20190.00790.0016-0.0220-0.0017
May 2019-0.01390.0024-0.00600.0061
Jun 20190.0084-0.00350.0042-0.0030
Jul 20190.01630.00600.02980.0064
Aug 20190.01320.00940.05070.0049
Sep 20190.01860.01090.01570.0019
Oct 20190.00460.01240.00960.0009
Nov 2019-0.0122-0.0126-0.0186-0.0157
Dec 2019-0.0136-0.0071-0.0253-0.0127
Jan 2020-0.01160.0017-0.03660.0078
Feb 2020-0.0163-0.0074-0.0392-0.0130