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 May 2020 0.96 0.82 0.44 -0.02 0.01% 0.12% 97.5%
iShares Russell 2000 Value ETF IWN Apr 2006 May 2020 0.95 0.78 0.52 0.02 -0.06% -0.75% 98.2%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 May 2020 1.08 1.16 0.71 -0.49 0.03% 0.39% 91.6%
Vanguard Small-Cap Value ETF VBR Apr 2006 May 2020 1.01 0.56 0.37 -0.06 -0.03% -0.35% 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 - May 2020
Regression Basis 170 monthly samples
Coefficient of Determination (R2) 97.5%
Adjusted R2 97.4%
Regression F statistic 1,601.50 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.720 with p-value 0.031)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 26.454 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.019 50.517 0.000 0.927...1.002
Size (SMB) 0.82 0.035 23.561 0.000 0.754...0.892
Value (HML) 0.44 0.029 15.267 0.000 0.387...0.502
Momentum (MOM) -0.02 0.019 -0.903 0.368 -0.054...0.020
Alpha (α) 1.01bps 0.001 0.134 0.894 -0.14%...0.16%
Annualized Alpha (α) 0.12%  

iShares Russell 2000 Value ETF

Factor regression results for iShares Russell 2000 Value ETF
Ticker IWN
Time Period Apr 2006 - May 2020
Regression Basis 170 monthly samples
Coefficient of Determination (R2) 98.2%
Adjusted R2 98.2%
Regression F statistic 2,268.98 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.057 with p-value 0.636)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.662 with p-value 0.454)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.95 0.016 60.199 0.000 0.917...0.979
Size (SMB) 0.78 0.029 26.966 0.000 0.720...0.834
Value (HML) 0.52 0.024 21.490 0.000 0.469...0.564
Momentum (MOM) 0.02 0.016 1.348 0.180 -0.010...0.052
Alpha (α) -6.23bps 0.001 -0.995 0.321 -0.19%...0.06%
Annualized Alpha (α) -0.75%  

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 - May 2020
Regression Basis 170 monthly samples
Coefficient of Determination (R2) 91.6%
Adjusted R2 91.4%
Regression F statistic 450.80 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.937 with p-value 0.329)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 49.752 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.08 0.052 20.809 0.000 0.977...1.182
Size (SMB) 1.16 0.095 12.214 0.000 0.972...1.347
Value (HML) 0.71 0.079 8.952 0.000 0.553...0.865
Momentum (MOM) -0.49 0.051 -9.470 0.000 -0.588...-0.385
Alpha (α) 3.25bps 0.002 0.158 0.875 -0.37%...0.44%
Annualized Alpha (α) 0.39%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Apr 2006 - May 2020
Regression Basis 170 monthly samples
Coefficient of Determination (R2) 97.8%
Adjusted R2 97.7%
Regression F statistic 1,831.68 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.171 with p-value 0.862)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 13.552 with p-value 0.009)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.017 58.439 0.000 0.975...1.044
Size (SMB) 0.56 0.032 17.736 0.000 0.498...0.623
Value (HML) 0.37 0.026 14.207 0.000 0.322...0.427
Momentum (MOM) -0.06 0.017 -3.245 0.001 -0.089...-0.022
Alpha (α) -2.96bps 0.001 -0.431 0.667 -0.17%...0.11%
Annualized Alpha (α) -0.35%  
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) 69.94 -3.20 -35.85 6.72  
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 May 2020 0.12% 67.44 -2.63 -15.94 -0.11 49.76 97.5%
iShares Russell 2000 Value ETF IWN Apr 2006 May 2020 -0.75% 66.29 -2.49 -18.51 0.14 39.21 98.2%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 May 2020 0.39% 75.52 -3.71 -25.41 -3.27 46.38 91.6%
Vanguard Small-Cap Value ETF VBR Apr 2006 May 2020 -0.35% 70.61 -1.79 -13.43 -0.37 52.06 97.8%
Regression residuals
MonthIJSIWNRZVVBR
Apr 2006-0.0094-0.0097-0.0075-0.0130
May 2006-0.00230.0015-0.02500.0001
Jun 2006-0.00100.00620.01970.0094
Jul 2006-0.00750.00890.00260.0025
Aug 20060.00270.0088-0.0316-0.0037
Sep 20060.0008-0.0030-0.0016-0.0065
Oct 20060.00570.0050-0.00150.0003
Nov 2006-0.0046-0.0008-0.01110.0061
Dec 2006-0.0142-0.00880.0012-0.0135
Jan 20070.0031-0.00260.00750.0014
Feb 2007-0.0049-0.0069-0.00530.0026
Mar 2007-0.00010.0042-0.0082-0.0020
Apr 20070.0023-0.00810.0079-0.0063
May 20070.01090.0058-0.00860.0017
Jun 2007-0.0089-0.0089-0.0091-0.0067
Jul 20070.0052-0.01760.0208-0.0149
Aug 20070.01120.0190-0.01860.0126
Sep 2007-0.0033-0.00180.0003-0.0044
Oct 20070.00050.00170.00280.0061
Nov 2007-0.0014-0.0045-0.0009-0.0034
Dec 20070.0002-0.00740.0325-0.0023
Jan 20080.00890.01020.05550.0106
Feb 20080.00200.0023-0.01940.0122
Mar 20080.00890.00110.04350.0016
Apr 2008-0.00210.0124-0.05110.0115
May 2008-0.0005-0.0063-0.01610.0100
Jun 2008-0.0022-0.01450.0314-0.0210
Jul 2008-0.01260.0046-0.03160.0085
Aug 2008-0.00570.0020-0.0507-0.0086
Sep 20080.02080.03090.04140.0218
Oct 2008-0.0001-0.01530.0284-0.0180
Nov 20080.00970.01470.02480.0269
Dec 20080.01940.0115-0.05390.0052
Jan 2009-0.0125-0.0028-0.0654-0.0013
Feb 2009-0.0018-0.0078-0.0228-0.0097
Mar 2009-0.0279-0.01250.0240-0.0212
Apr 20090.0207-0.00090.14240.0264
May 2009-0.0255-0.0030-0.0271-0.0070
Jun 20090.0023-0.01250.0889-0.0066
Jul 2009-0.0060-0.00210.0241-0.0056
Aug 2009-0.0260-0.0115-0.0498-0.0005
Sep 2009-0.0227-0.0143-0.0105-0.0069
Oct 20090.01800.0160-0.05490.0064
Nov 2009-0.0033-0.0055-0.0168-0.0055
Dec 20090.00460.0030-0.01610.0091
Jan 20100.00160.00140.0113-0.0019
Feb 2010-0.0086-0.01270.0278-0.0005
Mar 2010-0.00360.00300.01140.0046
Apr 2010-0.0061-0.0041-0.01110.0057
May 20100.00060.0048-0.00850.0089
Jun 20100.00640.0040-0.03260.0009
Jul 20100.00020.00530.00700.0059
Aug 2010-0.00000.0041-0.00840.0057
Sep 2010-0.00100.0026-0.0033-0.0013
Oct 20100.00530.00660.02360.0014
Nov 2010-0.0073-0.00370.01160.0010
Dec 20100.0005-0.0052-0.0203-0.0117
Jan 2011-0.0051-0.0046-0.0258-0.0033
Feb 2011-0.00890.0004-0.00460.0004
Mar 20110.0038-0.00290.00750.0037
Apr 2011-0.00340.0048-0.00590.0058
May 20110.00940.01200.02930.0033
Jun 20110.0039-0.00520.00350.0002
Jul 20110.01140.00800.02750.0030
Aug 20110.01390.00280.01260.0050
Sep 20110.0023-0.00070.0079-0.0059
Oct 20110.01630.01240.00000.0107
Nov 20110.01250.00350.01450.0061
Dec 20110.01110.00350.0117-0.0006
Jan 20120.01620.0108-0.01160.0068
Feb 2012-0.0116-0.0135-0.0105-0.0095
Mar 20120.00010.0019-0.0087-0.0061
Apr 2012-0.0039-0.00080.00500.0058
May 2012-0.00850.00000.00340.0054
Jun 2012-0.00060.00560.0043-0.0006
Jul 20120.00860.00160.01570.0055
Aug 20120.00640.00150.0190-0.0042
Sep 2012-0.0062-0.00360.0022-0.0084
Oct 2012-0.0102-0.0086-0.03920.0033
Nov 20120.0083-0.00130.04470.0029
Dec 2012-0.00470.0022-0.0332-0.0016
Jan 2013-0.0080-0.0001-0.02180.0018
Feb 20130.00760.00150.01050.0066
Mar 2013-0.0029-0.0018-0.01510.0029
Apr 20130.00340.0018-0.0057-0.0031
May 2013-0.0098-0.02230.0177-0.0169
Jun 20130.0013-0.0012-0.0065-0.0059
Jul 2013-0.0065-0.0053-0.01600.0002
Aug 20130.0017-0.00630.0053-0.0054
Sep 20130.01130.00540.02540.0049
Oct 20130.0018-0.0011-0.00330.0016
Nov 20130.0013-0.00200.0225-0.0094
Dec 2013-0.0088-0.0002-0.00640.0033
Jan 2014-0.0006-0.00290.00060.0100
Feb 20140.00070.00110.00890.0037
Mar 20140.0015-0.0023-0.0222-0.0012
Apr 20140.00800.0050-0.00090.0082
May 20140.00300.00260.00720.0080
Jun 2014-0.00870.0000-0.01580.0030
Jul 20140.0038-0.00850.0158-0.0033
Aug 20140.00340.00390.00240.0093
Sep 2014-0.0035-0.01110.0083-0.0089
Oct 20140.01980.02250.00350.0061
Nov 20140.01080.00420.02140.0091
Dec 2014-0.0039-0.0030-0.0208-0.0026
Jan 2015-0.00250.0090-0.00080.0170
Feb 20150.0029-0.00490.0198-0.0025
Mar 2015-0.00140.00680.00280.0110
Apr 2015-0.0090-0.0113-0.0089-0.0130
May 2015-0.0057-0.00570.00630.0039
Jun 2015-0.0004-0.00140.0037-0.0106
Jul 20150.01230.00900.04320.0197
Aug 2015-0.0043-0.0082-0.0047-0.0010
Sep 20150.01210.01160.01760.0113
Oct 20150.0067-0.0012-0.0025-0.0026
Nov 2015-0.0081-0.0012-0.0117-0.0094
Dec 20150.00530.00150.02170.0006
Jan 20160.01550.0047-0.00700.0065
Feb 20160.01620.00440.01980.0110
Mar 20160.01350.00550.00100.0072
Apr 2016-0.0090-0.0077-0.0252-0.0076
May 2016-0.00240.0126-0.05030.0056
Jun 20160.01040.00690.02420.0063
Jul 2016-0.00510.0024-0.0120-0.0056
Aug 2016-0.0187-0.0057-0.0477-0.0184
Sep 2016-0.0041-0.00260.0061-0.0055
Oct 2016-0.00050.00080.00820.0007
Nov 20160.00380.0017-0.0193-0.0108
Dec 2016-0.00270.0060-0.0231-0.0039
Jan 2017-0.0105-0.0040-0.02470.0026
Feb 20170.00290.0057-0.01300.0011
Mar 2017-0.0045-0.0024-0.0259-0.0043
Apr 2017-0.0034-0.0025-0.0134-0.0039
May 20170.0044-0.0017-0.0073-0.0058
Jun 2017-0.00250.0028-0.0072-0.0011
Jul 20170.00180.0017-0.01720.0008
Aug 2017-0.0054-0.00250.02830.0029
Sep 20170.0095-0.00330.0020-0.0139
Oct 20170.0002-0.00670.0280-0.0013
Nov 20170.01200.00470.01450.0030
Dec 2017-0.0053-0.0103-0.0172-0.0005
Jan 2018-0.0100-0.0113-0.0000-0.0136
Feb 2018-0.0026-0.01250.0161-0.0061
Mar 20180.00290.0031-0.01270.0086
Apr 20180.00180.0034-0.0019-0.0082
May 20180.00330.00730.01870.0019
Jun 20180.00230.0025-0.0009-0.0014
Jul 20180.00940.0018-0.01570.0010
Aug 20180.00610.00140.0318-0.0001
Sep 2018-0.0074-0.0010-0.0011-0.0004
Oct 2018-0.00380.00200.0095-0.0018
Nov 2018-0.00730.0037-0.04980.0076
Dec 2018-0.0053-0.00450.00800.0019
Jan 20190.01580.0095-0.00160.0055
Feb 20190.00250.0041-0.00620.0036
Mar 2019-0.00750.00490.00790.0021
Apr 20190.00760.0016-0.0222-0.0020
May 2019-0.01330.0024-0.00580.0068
Jun 20190.0095-0.00250.0027-0.0021
Jul 20190.01640.00610.02960.0065
Aug 20190.01510.01050.04940.0068
Sep 20190.01640.00960.0172-0.0001
Oct 20190.00580.01320.00850.0019
Nov 2019-0.0109-0.0116-0.0201-0.0145
Dec 2019-0.0139-0.0072-0.0252-0.0131
Jan 2020-0.00900.0033-0.03880.0104
Feb 2020-0.0145-0.0065-0.0399-0.0111
Mar 2020-0.0231-0.01320.0249-0.0301
Apr 2020-0.0110-0.01740.0470-0.0202
May 2020-0.0258-0.0141-0.0147-0.0024