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
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Asset 2
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Asset 4
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Asset 5
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Asset 6
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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 Aug 2019 0.97 0.83 0.38 -0.03 0.05% 0.59% 97.5%
iShares Russell 2000 Value ETF IWN Apr 2006 Aug 2019 0.95 0.78 0.48 0.01 -0.05% -0.54% 98.1%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Aug 2019 1.06 1.17 0.70 -0.49 0.07% 0.83% 90.7%
Vanguard Small-Cap Value ETF VBR Apr 2006 Aug 2019 1.01 0.56 0.33 -0.07 0.01% 0.16% 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 - Aug 2019
Coefficient of Determination (R2) 97.5%
Adjusted R2 97.4%
Regression F statistic 1,511.02 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.005 with p-value 0.500)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 30.699 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.97 0.019 51.286 0.000 0.928...1.003
Size (SMB) 0.83 0.033 25.026 0.000 0.763...0.894
Value (HML) 0.38 0.030 12.402 0.000 0.317...0.437
Momentum (MOM) -0.03 0.018 -1.479 0.141 -0.062...0.009
Alpha (α) 4.95bps 0.001 0.684 0.495 -0.09%...0.19%
Annualized Alpha (α) 0.59%  

iShares Russell 2000 Value ETF

Factor regression results for iShares Russell 2000 Value ETF
Ticker IWN
Time Period Apr 2006 - Aug 2019
Coefficient of Determination (R2) 98.1%
Adjusted R2 98.1%
Regression F statistic 2,039.18 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.236 with p-value 0.930)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 10.833 with p-value 0.029)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.95 0.016 59.588 0.000 0.921...0.984
Size (SMB) 0.78 0.028 27.850 0.000 0.728...0.839
Value (HML) 0.48 0.026 18.580 0.000 0.428...0.530
Momentum (MOM) 0.01 0.015 0.943 0.347 -0.016...0.044
Alpha (α) -4.54bps 0.001 -0.739 0.461 -0.17%...0.08%
Annualized Alpha (α) -0.54%  

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 - Aug 2019
Coefficient of Determination (R2) 90.7%
Adjusted R2 90.4%
Regression F statistic 378.13 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.965 with p-value 0.398)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 49.681 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.054 19.523 0.000 0.955...1.170
Size (SMB) 1.17 0.096 12.236 0.000 0.983...1.361
Value (HML) 0.70 0.088 7.997 0.000 0.529...0.876
Momentum (MOM) -0.49 0.052 -9.390 0.000 -0.588...-0.384
Alpha (α) 6.92bps 0.002 0.331 0.741 -0.34%...0.48%
Annualized Alpha (α) 0.83%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Apr 2006 - Aug 2019
Coefficient of Determination (R2) 97.8%
Adjusted R2 97.7%
Regression F statistic 1,730.71 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.387 with p-value 0.993)
Heteroskedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 13.141 with p-value 0.011)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.017 58.989 0.000 0.972...1.040
Size (SMB) 0.56 0.030 18.763 0.000 0.504...0.622
Value (HML) 0.33 0.028 11.912 0.000 0.273...0.382
Momentum (MOM) -0.07 0.016 -4.206 0.000 -0.100...-0.036
Alpha (α) 1.33bps 0.001 0.203 0.839 -0.12%...0.14%
Annualized Alpha (α) 0.16%  
Notes on results:
  • Time frame for factor analysis is the full available data range unless a specific date interval is specified.
  • 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
  • Resources:

Factor Performance Attribution in Basis Points

Factor regression results
Monthly Factor Premiums (BPS) 69.04 -2.68 -21.62 8.38  
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 Aug 2019 0.59% 66.65 -2.22 -8.14 -0.22 61.01 97.5%
iShares Russell 2000 Value ETF IWN Apr 2006 Aug 2019 -0.54% 65.77 -2.10 -10.36 0.12 48.89 98.1%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Aug 2019 0.83% 73.38 -3.14 -15.19 -4.07 57.90 90.7%
Vanguard Small-Cap Value ETF VBR Apr 2006 Aug 2019 0.16% 69.46 -1.51 -7.09 -0.57 61.62 97.8%
Regression residuals
MonthIJSIWNRZVVBR
Apr 2006-0.0079-0.0088-0.0074-0.0121
May 2006-0.00120.0023-0.02550.0003
Jun 2006-0.00070.00650.01930.0095
Jul 2006-0.00590.01000.00280.0033
Aug 20060.00080.0076-0.0317-0.0053
Sep 20060.0004-0.0033-0.0015-0.0069
Oct 20060.00530.0047-0.0013-0.0000
Nov 2006-0.0051-0.0011-0.01120.0056
Dec 2006-0.0123-0.00770.0014-0.0122
Jan 20070.0025-0.00290.00720.0009
Feb 2007-0.0056-0.0072-0.00620.0018
Mar 2007-0.00040.0041-0.0085-0.0022
Apr 20070.0012-0.00870.0084-0.0071
May 20070.01040.0054-0.00840.0014
Jun 2007-0.0101-0.0095-0.0102-0.0077
Jul 20070.0030-0.01850.0199-0.0166
Aug 20070.00930.0180-0.01900.0112
Sep 2007-0.0044-0.00240.0005-0.0049
Oct 2007-0.00120.00080.00250.0052
Nov 2007-0.0023-0.0046-0.0019-0.0043
Dec 20070.0001-0.00730.0318-0.0022
Jan 20080.01040.01120.05450.0106
Feb 20080.00150.0024-0.02040.0120
Mar 20080.00880.00110.04280.0016
Apr 2008-0.00310.0118-0.05060.0108
May 2008-0.0017-0.0070-0.01670.0093
Jun 2008-0.0030-0.01440.0292-0.0213
Jul 2008-0.00960.0061-0.03200.0101
Aug 2008-0.00570.0018-0.0511-0.0089
Sep 20080.02490.03370.04000.0241
Oct 2008-0.0014-0.01500.0251-0.0193
Nov 20080.00620.01330.02300.0243
Dec 20080.01810.0106-0.05440.0040
Jan 2009-0.0206-0.0069-0.0679-0.0075
Feb 2009-0.0067-0.0099-0.0254-0.0133
Mar 2009-0.0270-0.01260.0255-0.0211
Apr 20090.0205-0.00210.14390.0245
May 2009-0.0271-0.0042-0.0262-0.0088
Jun 20090.0004-0.01350.0880-0.0077
Jul 2009-0.0036-0.00120.0252-0.0040
Aug 2009-0.0220-0.0095-0.04890.0018
Sep 2009-0.0231-0.0148-0.0104-0.0074
Oct 20090.01530.0148-0.05550.0044
Nov 2009-0.0037-0.0059-0.0160-0.0057
Dec 20090.00410.0025-0.01680.0090
Jan 20100.00090.00110.0104-0.0030
Feb 2010-0.0067-0.01170.02800.0011
Mar 2010-0.00240.00340.01210.0058
Apr 2010-0.0045-0.0034-0.01150.0070
May 2010-0.00130.0041-0.01040.0071
Jun 20100.00280.0024-0.0340-0.0021
Jul 2010-0.00030.00490.00780.0058
Aug 2010-0.00150.0036-0.00930.0043
Sep 2010-0.00370.0006-0.0027-0.0028
Oct 20100.00320.00530.02350.0000
Nov 2010-0.0083-0.00430.01080.0004
Dec 20100.0023-0.0045-0.0193-0.0105
Jan 2011-0.0049-0.0044-0.0254-0.0033
Feb 2011-0.00850.0005-0.00450.0008
Mar 20110.0025-0.00370.00670.0029
Apr 2011-0.00550.0036-0.00590.0043
May 20110.00760.01110.02860.0018
Jun 20110.0034-0.00530.0028-0.0002
Jul 20110.01030.00760.02680.0019
Aug 20110.01200.00220.01140.0032
Sep 20110.0010-0.00100.0067-0.0075
Oct 20110.01530.01130.00110.0104
Nov 20110.01220.00350.01400.0061
Dec 20110.01220.00420.01160.0000
Jan 20120.01410.0092-0.01130.0050
Feb 2012-0.0119-0.0137-0.0099-0.0097
Mar 20120.00050.0020-0.0084-0.0058
Apr 2012-0.0042-0.00080.00450.0056
May 2012-0.00860.00040.00190.0053
Jun 2012-0.00080.00530.0046-0.0007
Jul 20120.00850.00170.01580.0054
Aug 20120.00670.00150.0192-0.0042
Sep 2012-0.0057-0.00340.0023-0.0082
Oct 2012-0.0079-0.0072-0.03950.0046
Nov 20120.0073-0.00190.04430.0021
Dec 2012-0.00300.0030-0.0333-0.0008
Jan 2013-0.0080-0.0004-0.02120.0018
Feb 20130.00730.00140.01040.0064
Mar 2013-0.0034-0.0022-0.01490.0027
Apr 20130.00360.0020-0.0055-0.0031
May 2013-0.0087-0.02180.0178-0.0162
Jun 20130.0008-0.0014-0.0072-0.0064
Jul 2013-0.0065-0.0055-0.01560.0004
Aug 2013-0.0006-0.00740.0043-0.0072
Sep 20130.01010.00470.02520.0044
Oct 20130.0022-0.0009-0.00270.0019
Nov 20130.0010-0.00230.0225-0.0096
Dec 2013-0.0094-0.0006-0.00630.0029
Jan 2014-0.0023-0.0036-0.00060.0087
Feb 20140.00020.00070.00920.0035
Mar 20140.0044-0.0007-0.02190.0003
Apr 20140.00820.0053-0.00070.0080
May 20140.00260.00240.00730.0077
Jun 2014-0.0098-0.0007-0.01620.0024
Jul 20140.0036-0.00840.0155-0.0038
Aug 20140.00270.00330.00260.0088
Sep 2014-0.0044-0.01140.0080-0.0098
Oct 20140.01800.02130.00300.0049
Nov 20140.00860.00300.02150.0075
Dec 2014-0.0029-0.0025-0.0213-0.0020
Jan 2015-0.00490.0080-0.00190.0153
Feb 20150.0009-0.00630.0202-0.0040
Mar 2015-0.00200.00640.00170.0106
Apr 2015-0.0087-0.0111-0.0086-0.0134
May 2015-0.0065-0.00610.00590.0036
Jun 2015-0.0012-0.00170.0027-0.0111
Jul 20150.01030.00820.04310.0188
Aug 2015-0.0030-0.0072-0.0059-0.0007
Sep 20150.01280.01230.01700.0118
Oct 20150.0059-0.0019-0.0012-0.0032
Nov 2015-0.0089-0.0017-0.0125-0.0099
Dec 20150.00370.00090.0212-0.0006
Jan 20160.01690.0060-0.00770.0071
Feb 20160.01500.00370.01930.0098
Mar 20160.01330.00500.00190.0068
Apr 2016-0.0079-0.0072-0.0252-0.0073
May 2016-0.00380.0118-0.05050.0047
Jun 20160.00940.00640.02360.0057
Jul 2016-0.00670.0013-0.0121-0.0069
Aug 2016-0.0172-0.0049-0.0479-0.0177
Sep 2016-0.0057-0.00350.0054-0.0067
Oct 20160.00230.00260.00830.0023
Nov 20160.00830.0037-0.0189-0.0078
Dec 2016-0.00080.0070-0.0229-0.0027
Jan 2017-0.0129-0.0053-0.02480.0008
Feb 20170.00120.0048-0.0127-0.0002
Mar 2017-0.0072-0.0039-0.0266-0.0063
Apr 2017-0.0051-0.0034-0.0138-0.0051
May 20170.0017-0.0030-0.0075-0.0077
Jun 2017-0.00210.0030-0.0075-0.0009
Jul 20170.00140.0015-0.01720.0005
Aug 2017-0.0069-0.00320.02800.0019
Sep 20170.0107-0.00280.0017-0.0131
Oct 20170.0002-0.00660.0282-0.0010
Nov 20170.01170.00440.01490.0027
Dec 2017-0.0057-0.0105-0.0172-0.0010
Jan 2018-0.0107-0.01170.0010-0.0138
Feb 2018-0.0033-0.01260.0151-0.0067
Mar 20180.00210.0026-0.01400.0078
Apr 20180.00170.0034-0.0023-0.0084
May 20180.00080.00580.01790.0005
Jun 20180.00000.0012-0.0014-0.0033
Jul 20180.00940.0019-0.01480.0010
Aug 20180.0033-0.00020.0315-0.0017
Sep 2018-0.0086-0.0015-0.0012-0.0014
Oct 2018-0.00160.00370.0086-0.0010
Nov 2018-0.00770.0035-0.04980.0072
Dec 2018-0.0062-0.00440.00630.0008
Jan 20190.01390.0079-0.00090.0039
Feb 20190.00010.0026-0.00640.0020
Mar 2019-0.01030.00350.00780.0002
Apr 20190.00830.0019-0.0215-0.0016
May 2019-0.01440.0023-0.00740.0060
Jun 20190.0081-0.00350.0036-0.0030
Jul 20190.01640.00620.02970.0065
Aug 20190.01220.00930.04840.0050