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 Dec 2019 0.96 0.82 0.39 -0.03 0.05% 0.62% 97.4%
iShares Russell 2000 Value ETF IWN Apr 2006 Dec 2019 0.95 0.78 0.49 0.01 -0.04% -0.49% 98.0%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Dec 2019 1.06 1.17 0.71 -0.48 0.06% 0.74% 90.6%
Vanguard Small-Cap Value ETF VBR Apr 2006 Dec 2019 1.00 0.56 0.33 -0.07 -0.00% -0.01% 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 - Dec 2019
Coefficient of Determination (R2) 97.4%
Adjusted R2 97.3%
Regression F statistic 1,470.91 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.935 with p-value 0.326)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 33.811 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.019 50.440 0.000 0.925...1.000
Size (SMB) 0.82 0.034 24.530 0.000 0.758...0.891
Value (HML) 0.39 0.030 12.883 0.000 0.329...0.448
Momentum (MOM) -0.03 0.018 -1.465 0.145 -0.062...0.009
Alpha (α) 5.20bps 0.001 0.716 0.475 -0.09%...0.20%
Annualized Alpha (α) 0.62%  

iShares Russell 2000 Value ETF

Factor regression results for iShares Russell 2000 Value ETF
Ticker IWN
Time Period Apr 2006 - Dec 2019
Coefficient of Determination (R2) 98.0%
Adjusted R2 98.0%
Regression F statistic 1,995.56 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.192 with p-value 0.887)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 9.716 with p-value 0.045)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.95 0.016 58.819 0.000 0.919...0.983
Size (SMB) 0.78 0.028 27.414 0.000 0.724...0.837
Value (HML) 0.49 0.026 18.992 0.000 0.435...0.536
Momentum (MOM) 0.01 0.015 0.951 0.343 -0.016...0.045
Alpha (α) -4.11bps 0.001 -0.667 0.506 -0.16%...0.08%
Annualized Alpha (α) -0.49%  

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 - Dec 2019
Coefficient of Determination (R2) 90.6%
Adjusted R2 90.4%
Regression F statistic 386.31 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.959 with p-value 0.384)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 49.885 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.054 19.620 0.000 0.953...1.166
Size (SMB) 1.17 0.095 12.275 0.000 0.979...1.355
Value (HML) 0.71 0.085 8.345 0.000 0.544...0.881
Momentum (MOM) -0.48 0.051 -9.452 0.000 -0.586...-0.383
Alpha (α) 6.16bps 0.002 0.300 0.765 -0.34%...0.47%
Annualized Alpha (α) 0.74%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Apr 2006 - Dec 2019
Coefficient of Determination (R2) 97.7%
Adjusted R2 97.7%
Regression F statistic 1,709.95 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.328 with p-value 0.982)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 12.839 with p-value 0.012)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.00 0.017 58.559 0.000 0.970...1.038
Size (SMB) 0.56 0.030 18.594 0.000 0.502...0.621
Value (HML) 0.33 0.027 12.214 0.000 0.278...0.385
Momentum (MOM) -0.07 0.016 -4.076 0.000 -0.099...-0.034
Alpha (α) -0.08bps 0.001 -0.012 0.990 -0.13%...0.13%
Annualized Alpha (α) -0.01%  
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) 73.52 -2.02 -18.34 1.28  
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 Dec 2019 0.62% 70.76 -1.67 -7.13 -0.03 67.13 97.4%
iShares Russell 2000 Value ETF IWN Apr 2006 Dec 2019 -0.49% 69.92 -1.58 -8.91 0.02 55.35 98.0%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Dec 2019 0.74% 77.88 -2.36 -13.07 -0.62 67.99 90.6%
Vanguard Small-Cap Value ETF VBR Apr 2006 Dec 2019 -0.01% 73.80 -1.14 -6.07 -0.09 66.43 97.7%
Regression residuals
MonthIJSIWNRZVVBR
Apr 2006-0.0083-0.0090-0.0076-0.0120
May 2006-0.00180.0019-0.02600.0003
Jun 2006-0.00090.00640.01930.0096
Jul 2006-0.00640.00960.00240.0033
Aug 20060.00110.0078-0.0313-0.0050
Sep 20060.0004-0.0033-0.0014-0.0067
Oct 20060.00540.0047-0.00110.0002
Nov 2006-0.0050-0.0011-0.01100.0058
Dec 2006-0.0127-0.00790.0011-0.0122
Jan 20070.0026-0.00290.00730.0011
Feb 2007-0.0056-0.0072-0.00610.0019
Mar 2007-0.00040.0041-0.0084-0.0021
Apr 20070.0014-0.00860.0087-0.0069
May 20070.01050.0054-0.00820.0016
Jun 2007-0.0100-0.0095-0.0100-0.0076
Jul 20070.0032-0.01850.0200-0.0165
Aug 20070.00950.0181-0.01870.0114
Sep 2007-0.0042-0.00230.0008-0.0048
Oct 2007-0.00080.00100.00280.0054
Nov 2007-0.0025-0.0047-0.0020-0.0043
Dec 20070.0001-0.00730.0319-0.0021
Jan 20080.00970.01080.05400.0107
Feb 20080.00150.0023-0.02040.0120
Mar 20080.00880.00110.04290.0016
Apr 2008-0.00300.0118-0.05030.0111
May 2008-0.0014-0.0069-0.01630.0096
Jun 2008-0.0029-0.01440.0292-0.0215
Jul 2008-0.01030.0058-0.03240.0102
Aug 2008-0.00570.0018-0.0509-0.0086
Sep 20080.02380.03300.03910.0238
Oct 2008-0.0017-0.01520.0247-0.0196
Nov 20080.00660.01350.02320.0243
Dec 20080.01830.0107-0.05400.0043
Jan 2009-0.0195-0.0063-0.0669-0.0071
Feb 2009-0.0061-0.0096-0.0250-0.0132
Mar 2009-0.0272-0.01270.0257-0.0207
Apr 20090.0202-0.00210.14430.0253
May 2009-0.0271-0.0042-0.0259-0.0084
Jun 20090.0009-0.01330.0884-0.0075
Jul 2009-0.0039-0.00140.0252-0.0038
Aug 2009-0.0229-0.0100-0.04950.0018
Sep 2009-0.0230-0.0147-0.0101-0.0071
Oct 20090.01550.0149-0.05530.0045
Nov 2009-0.0037-0.0059-0.0158-0.0055
Dec 20090.00440.0026-0.01640.0092
Jan 20100.00070.00100.0104-0.0029
Feb 2010-0.0069-0.01190.02790.0011
Mar 2010-0.00240.00340.01220.0059
Apr 2010-0.0046-0.0035-0.01150.0071
May 2010-0.00130.0041-0.01030.0071
Jun 20100.00310.0025-0.0337-0.0019
Jul 2010-0.00010.00490.00810.0061
Aug 2010-0.00160.0036-0.00930.0043
Sep 2010-0.00290.0010-0.0018-0.0023
Oct 20100.00360.00550.02400.0003
Nov 2010-0.0080-0.00420.01110.0006
Dec 20100.0020-0.0047-0.0194-0.0103
Jan 2011-0.0050-0.0045-0.0255-0.0031
Feb 2011-0.00850.0005-0.00430.0010
Mar 20110.0028-0.00350.00710.0031
Apr 2011-0.00520.0038-0.00540.0046
May 20110.00780.01120.02890.0020
Jun 20110.0034-0.00540.0028-0.0001
Jul 20110.01030.00760.02690.0021
Aug 20110.01200.00210.01140.0032
Sep 20110.0007-0.00110.0065-0.0074
Oct 20110.01580.01150.00180.0108
Nov 20110.01230.00350.01410.0061
Dec 20110.01190.00400.01150.0001
Jan 20120.01440.0094-0.01080.0054
Feb 2012-0.0119-0.0138-0.0098-0.0095
Mar 20120.00040.0019-0.0083-0.0057
Apr 2012-0.0043-0.00090.00450.0057
May 2012-0.00870.00030.00170.0052
Jun 2012-0.00080.00530.0048-0.0005
Jul 20120.00840.00160.01570.0055
Aug 20120.00660.00150.0192-0.0040
Sep 2012-0.0058-0.00350.0024-0.0080
Oct 2012-0.0085-0.0075-0.03990.0046
Nov 20120.0074-0.00180.04460.0023
Dec 2012-0.00340.0028-0.0334-0.0006
Jan 2013-0.0080-0.0004-0.02090.0021
Feb 20130.00730.00130.01050.0065
Mar 2013-0.0032-0.0021-0.01470.0029
Apr 20130.00340.0019-0.0056-0.0030
May 2013-0.0089-0.02200.0178-0.0161
Jun 20130.0008-0.0014-0.0071-0.0063
Jul 2013-0.0063-0.0055-0.01530.0006
Aug 2013-0.0003-0.00730.0046-0.0070
Sep 20130.01050.00480.02560.0046
Oct 20130.0021-0.0010-0.00260.0021
Nov 20130.0011-0.00230.0228-0.0094
Dec 2013-0.0093-0.0006-0.00610.0031
Jan 2014-0.0021-0.0035-0.00040.0088
Feb 20140.00030.00080.00950.0038
Mar 20140.0037-0.0011-0.02230.0004
Apr 20140.00790.0051-0.00090.0081
May 20140.00260.00240.00740.0078
Jun 2014-0.0095-0.0006-0.01580.0026
Jul 20140.0034-0.00850.0154-0.0037
Aug 20140.00280.00340.00290.0091
Sep 2014-0.0045-0.01150.0080-0.0097
Oct 20140.01840.02150.00350.0052
Nov 20140.00890.00310.02180.0078
Dec 2014-0.0031-0.0026-0.0214-0.0019
Jan 2015-0.00460.0081-0.00160.0155
Feb 20150.0013-0.00610.0208-0.0036
Mar 2015-0.00180.00650.00200.0108
Apr 2015-0.0090-0.0114-0.0087-0.0132
May 2015-0.0063-0.00600.00610.0037
Jun 2015-0.0010-0.00170.0029-0.0110
Jul 20150.01060.00830.04340.0189
Aug 2015-0.0035-0.0075-0.0063-0.0007
Sep 20150.01250.01210.01680.0117
Oct 20150.0060-0.0018-0.0010-0.0029
Nov 2015-0.0086-0.0015-0.0122-0.0097
Dec 20150.00380.00090.0212-0.0005
Jan 20160.01630.0056-0.00830.0070
Feb 20160.01510.00380.01950.0100
Mar 20160.01340.00500.00220.0072
Apr 2016-0.0082-0.0074-0.0253-0.0072
May 2016-0.00360.0119-0.05020.0049
Jun 20160.00960.00650.02380.0058
Jul 2016-0.00640.0014-0.0116-0.0065
Aug 2016-0.0176-0.0051-0.0481-0.0176
Sep 2016-0.0055-0.00340.0058-0.0065
Oct 20160.00150.00220.00770.0022
Nov 20160.00760.0034-0.0192-0.0077
Dec 2016-0.00120.0068-0.0231-0.0026
Jan 2017-0.0125-0.0052-0.02440.0011
Feb 20170.00140.0048-0.01230.0001
Mar 2017-0.0068-0.0037-0.0261-0.0060
Apr 2017-0.0048-0.0033-0.0134-0.0049
May 20170.0021-0.0029-0.0071-0.0075
Jun 2017-0.00220.0029-0.0076-0.0008
Jul 20170.00150.0015-0.01700.0007
Aug 2017-0.0067-0.00310.02820.0021
Sep 20170.0106-0.00290.0018-0.0129
Oct 20170.0002-0.00660.0282-0.0010
Nov 20170.01160.00430.01490.0028
Dec 2017-0.0057-0.0106-0.0172-0.0009
Jan 2018-0.0107-0.01180.0010-0.0137
Feb 2018-0.0034-0.01270.0150-0.0067
Mar 20180.00220.0027-0.01380.0080
Apr 20180.00160.0033-0.0023-0.0082
May 20180.00150.00610.01860.0008
Jun 20180.00030.0013-0.0011-0.0030
Jul 20180.00930.0019-0.01470.0011
Aug 20180.00400.00010.0322-0.0014
Sep 2018-0.0085-0.0015-0.0011-0.0013
Oct 2018-0.00250.00320.0079-0.0012
Nov 2018-0.00770.0035-0.04970.0074
Dec 2018-0.0064-0.00460.00600.0007
Jan 20190.01430.0082-0.00020.0045
Feb 20190.00060.0029-0.00590.0023
Mar 2019-0.00990.00370.00820.0004
Apr 20190.00810.0017-0.0216-0.0015
May 2019-0.01440.0022-0.00750.0059
Jun 20190.0085-0.00340.0040-0.0027
Jul 20190.01630.00610.02970.0066
Aug 20190.01260.00940.04880.0050
Sep 20190.01910.01100.01720.0018
Oct 20190.00420.01230.00870.0009
Nov 2019-0.0125-0.0127-0.0195-0.0157
Dec 2019-0.0136-0.0071-0.0253-0.0127