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 3
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Asset 4
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Asset 5
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Asset 6
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Asset 7
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Asset 8
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Asset 9
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Asset 10
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Factor Analysis Results

Factor Analysis Summary

Factor regression results
Name Ticker Start Date End Date Rm-Rf SMB HML Alpha Annual Alpha R2
Bogle Investment Mgmt Sm Cp Gr Instl BOGIX Aug 2000 Nov 2020 1.06 0.73 0.24 0.00% 0.05% 90.9%
iShares S&P Small-Cap 600 Value ETF IJS Aug 2000 Nov 2020 0.97 0.81 0.53 0.04% 0.52% 96.4%
iShares Core S&P Small-Cap ETF IJR Aug 2000 Nov 2020 0.96 0.78 0.34 0.07% 0.90% 96.4%
iShares S&P Small-Cap 600 Growth ETF IJT Aug 2000 Nov 2020 0.97 0.71 0.16 0.08% 0.94% 93.7%

Bogle Investment Mgmt Sm Cp Gr Instl

Factor regression results for Bogle Investment Mgmt Sm Cp Gr Instl
Ticker BOGIX
Time Period Aug 2000 - Nov 2020
Regression Basis 244 monthly samples
Coefficient of Determination (R2) 90.9%
Adjusted R2 90.8%
Regression F statistic 798.75 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.996 with p-value 0.485)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 0.472 with p-value 0.925)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.028 38.244 0.000 1.009...1.119
Size (SMB) 0.73 0.050 14.618 0.000 0.630...0.826
Value (HML) 0.24 0.039 6.307 0.000 0.168...0.321
Alpha (α) 0.39bps 0.001 0.033 0.974 -0.23%...0.24%
Annualized Alpha (α) 0.05%  

iShares S&P Small-Cap 600 Value ETF

Factor regression results for iShares S&P Small-Cap 600 Value ETF
Ticker IJS
Time Period Aug 2000 - Nov 2020
Regression Basis 244 monthly samples
Coefficient of Determination (R2) 96.4%
Adjusted R2 96.3%
Regression F statistic 2,124.05 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.679 with p-value 0.006)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 14.232 with p-value 0.003)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.97 0.017 57.306 0.000 0.935...1.001
Size (SMB) 0.81 0.030 26.950 0.000 0.755...0.874
Value (HML) 0.53 0.024 22.649 0.000 0.487...0.580
Alpha (α) 4.37bps 0.001 0.599 0.550 -0.10%...0.19%
Annualized Alpha (α) 0.52%  

iShares Core S&P Small-Cap ETF

Factor regression results for iShares Core S&P Small-Cap ETF
Ticker IJR
Time Period Aug 2000 - Nov 2020
Regression Basis 244 monthly samples
Coefficient of Determination (R2) 96.4%
Adjusted R2 96.3%
Regression F statistic 2,131.70 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.143 with p-value 0.868)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 12.466 with p-value 0.006)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.016 59.422 0.000 0.925...0.988
Size (SMB) 0.78 0.029 27.026 0.000 0.722...0.835
Value (HML) 0.34 0.022 15.311 0.000 0.300...0.388
Alpha (α) 7.48bps 0.001 1.076 0.283 -0.06%...0.21%
Annualized Alpha (α) 0.90%  

iShares S&P Small-Cap 600 Growth ETF

Factor regression results for iShares S&P Small-Cap 600 Growth ETF
Ticker IJT
Time Period Aug 2000 - Nov 2020
Regression Basis 244 monthly samples
Coefficient of Determination (R2) 93.7%
Adjusted R2 93.6%
Regression F statistic 1,191.89 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.146 with p-value 0.871)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 2.952 with p-value 0.399)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.97 0.021 46.237 0.000 0.925...1.007
Size (SMB) 0.71 0.037 19.063 0.000 0.639...0.786
Value (HML) 0.16 0.029 5.467 0.000 0.102...0.217
Alpha (α) 7.86bps 0.001 0.871 0.385 -0.10%...0.26%
Annualized Alpha (α) 0.94%  
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.
  • 3-factor model: Ra = Rrf + Bmkt × ( Rmkt - Rrf ) + Bsmb × SMB + Bhml × HML + 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
    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) 57.09 20.25 5.30  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML Total R2
Bogle Investment Mgmt Sm Cp Gr Instl BOGIX Aug 2000 Nov 2020 0.05% 60.73 14.73 1.30 77.15 90.9%
iShares S&P Small-Cap 600 Value ETF IJS Aug 2000 Nov 2020 0.52% 55.25 16.49 2.83 78.94 96.4%
iShares Core S&P Small-Cap ETF IJR Aug 2000 Nov 2020 0.90% 54.61 15.77 1.82 79.68 96.4%
iShares S&P Small-Cap 600 Growth ETF IJT Aug 2000 Nov 2020 0.94% 55.14 14.43 0.84 78.27 93.7%
Regression residuals
MonthBOGIXIJSIJRIJT
Aug 20000.03450.01370.03040.0630
Sep 20000.03100.02180.00780.0047
Oct 20000.03600.01240.03540.0313
Nov 2000-0.00600.0185-0.0199-0.0320
Dec 20000.04300.06550.06430.0459
Jan 2001-0.05400.0157-0.0229-0.0774
Feb 20010.0188-0.0097-0.0048-0.0041
Mar 20010.0068-0.0200-0.0051-0.0024
Apr 20010.02300.00750.00960.0233
May 2001-0.0043-0.0200-0.0217-0.0189
Jun 2001-0.0041-0.0088-0.0078-0.0108
Jul 20010.02900.02130.02540.0201
Aug 20010.01020.01640.01260.0152
Sep 20010.0401-0.0166-0.0129-0.0009
Oct 2001-0.0149-0.0016-0.0017-0.0005
Nov 2001-0.0436-0.0070-0.0126-0.0173
Dec 2001-0.00890.00680.00890.0050
Jan 20020.01480.00610.0065-0.0009
Feb 20020.00330.0123-0.0005-0.0091
Mar 2002-0.00810.0049-0.0009-0.0007
Apr 20020.02220.01920.01970.0110
May 2002-0.0070-0.0068-0.0117-0.0122
Jun 20020.0104-0.0126-0.0184-0.0236
Jul 2002-0.0017-0.0191-0.01090.0024
Aug 20020.0198-0.00410.01080.0277
Sep 20020.0117-0.00890.01440.0275
Oct 2002-0.0394-0.0018-0.00700.0000
Nov 2002-0.0466-0.0225-0.0251-0.0237
Dec 20020.01510.01430.01190.0040
Jan 20030.0113-0.0239-0.0154-0.0142
Feb 2003-0.0018-0.0132-0.0107-0.0065
Mar 2003-0.0116-0.0096-0.00690.0024
Apr 2003-0.0034-0.0030-0.0029-0.0116
May 20030.0052-0.0022-0.0178-0.0257
Jun 20030.0024-0.0033-0.0033-0.0087
Jul 20030.0219-0.0117-0.0111-0.0034
Aug 2003-0.0001-0.0045-0.00030.0039
Sep 2003-0.0026-0.0305-0.0225-0.0207
Oct 20030.0140-0.0004-0.00010.0030
Nov 20030.01590.00280.00250.0026
Dec 2003-0.0184-0.0018-0.0130-0.0201
Jan 20040.0176-0.0341-0.0206-0.0128
Feb 2004-0.00630.01860.01270.0107
Mar 2004-0.00990.01410.01160.0068
Apr 2004-0.02210.00740.00100.0011
May 2004-0.00300.00680.01190.0093
Jun 20040.00400.00940.01390.0191
Jul 20040.00140.00360.0003-0.0008
Aug 2004-0.02570.0073-0.0040-0.0173
Sep 20040.02340.00570.00930.0166
Oct 2004-0.0239-0.00510.00540.0136
Nov 2004-0.00340.00700.00800.0053
Dec 2004-0.0083-0.0180-0.0155-0.0134
Jan 20050.0009-0.00520.00760.0257
Feb 20050.01780.00450.00610.0067
Mar 2005-0.0070-0.0074-0.0062-0.0106
Apr 20050.00740.0038-0.0027-0.0078
May 20050.00200.00400.00700.0133
Jun 2005-0.0014-0.0048-0.0024-0.0026
Jul 20050.0076-0.00140.00120.0039
Aug 20050.0138-0.0092-0.00520.0003
Sep 20050.0177-0.00670.00100.0099
Oct 20050.0181-0.0096-0.0114-0.0152
Nov 20050.01780.00900.00960.0084
Dec 20050.0014-0.0094-0.0098-0.0088
Jan 20060.02580.00510.0033-0.0041
Feb 20060.00720.0068-0.0018-0.0044
Mar 2006-0.0017-0.00090.00270.0064
Apr 20060.0240-0.0104-0.0073-0.0057
May 2006-0.0303-0.0036-0.0007-0.0019
Jun 2006-0.0110-0.0027-0.0038-0.0036
Jul 2006-0.0278-0.0092-0.0121-0.0085
Aug 2006-0.01070.0047-0.0077-0.0235
Sep 20060.0006-0.0004-0.0039-0.0076
Oct 2006-0.00080.00710.0034-0.0049
Nov 2006-0.0064-0.0041-0.00140.0055
Dec 20060.0052-0.0149-0.0133-0.0138
Jan 20070.00090.00520.00250.0013
Feb 2007-0.0029-0.0044-0.00190.0045
Mar 20070.00290.00130.00760.0133
Apr 20070.00100.00490.00640.0024
May 2007-0.00100.01170.00800.0092
Jun 20070.0199-0.0082-0.00420.0000
Jul 2007-0.00580.00830.01180.0117
Aug 2007-0.02900.01170.01300.0211
Sep 20070.0161-0.00130.00670.0117
Oct 20070.00180.00260.00400.0060
Nov 2007-0.0305-0.0002-0.0038-0.0103
Dec 20070.01100.0003-0.0046-0.0012
Jan 2008-0.03000.0061-0.0021-0.0046
Feb 20080.00880.00120.00890.0108
Mar 2008-0.03780.0082-0.00080.0018
Apr 2008-0.0159-0.00210.01350.0152
May 2008-0.00710.00130.00210.0038
Jun 2008-0.00630.00040.00410.0175
Jul 20080.0142-0.0147-0.0137-0.0174
Aug 2008-0.0378-0.0059-0.0066-0.0076
Sep 2008-0.05620.01570.00740.0125
Oct 2008-0.0164-0.0004-0.0068-0.0282
Nov 2008-0.01920.0130-0.0013-0.0035
Dec 20080.02090.01900.0055-0.0025
Jan 20090.0370-0.0052-0.0048-0.0112
Feb 20090.00610.0016-0.0006-0.0025
Mar 2009-0.0293-0.0287-0.0313-0.0252
Apr 20090.00040.02200.02580.0254
May 20090.0526-0.0251-0.0132-0.0103
Jun 20090.03920.00340.00170.0032
Jul 2009-0.0120-0.0070-0.0089-0.0074
Aug 2009-0.0121-0.0293-0.0263-0.0231
Sep 2009-0.0062-0.0222-0.0107-0.0023
Oct 2009-0.00700.01950.01470.0133
Nov 20090.0018-0.0035-0.0075-0.0154
Dec 20090.00390.00460.00790.0173
Jan 2010-0.00340.0022-0.0039-0.0120
Feb 2010-0.0089-0.0124-0.0123-0.0103
Mar 2010-0.0211-0.0068-0.00010.0041
Apr 2010-0.0069-0.0088-0.0097-0.0084
May 20100.01620.00200.01020.0194
Jun 2010-0.00490.00970.01130.0141
Jul 20100.0092-0.0001-0.0029-0.0088
Aug 20100.00530.0014-0.0011-0.0018
Sep 20100.02760.00180.00090.0012
Oct 2010-0.00060.00720.00500.0053
Nov 20100.0080-0.00690.00570.0142
Dec 2010-0.0065-0.0021-0.0083-0.0120
Jan 20110.0123-0.0056-0.0017-0.0015
Feb 2011-0.0029-0.0119-0.0065-0.0019
Mar 20110.01330.00520.00990.0192
Apr 20110.0193-0.00170.00910.0177
May 2011-0.00460.01040.01470.0204
Jun 20110.01170.00420.0003-0.0040
Jul 20110.01540.01040.0038-0.0017
Aug 2011-0.00920.01570.01090.0061
Sep 2011-0.02700.00350.00060.0006
Oct 20110.01040.01510.01320.0113
Nov 2011-0.00820.01140.01030.0093
Dec 2011-0.01540.00850.0037-0.0015
Jan 20120.02860.01810.0041-0.0097
Feb 20120.0142-0.0129-0.0082-0.0053
Mar 2012-0.0116-0.0022-0.00020.0021
Apr 20120.0019-0.0040-0.00060.0029
May 2012-0.0266-0.0090-0.00220.0060
Jun 20120.0022-0.0024-0.0039-0.0009
Jul 20120.00550.00680.0046-0.0040
Aug 20120.01440.00570.00630.0071
Sep 20120.0049-0.0078-0.0130-0.0184
Oct 20120.0138-0.0136-0.0106-0.0039
Nov 20120.01700.00910.0037-0.0060
Dec 2012-0.0004-0.0070-0.00410.0020
Jan 20130.0019-0.0086-0.00180.0024
Feb 2013-0.00390.00640.00400.0016
Mar 20130.0109-0.0034-0.0029-0.0023
Apr 2013-0.00950.0026-0.0002-0.0050
May 20130.0024-0.0120-0.00600.0011
Jun 2013-0.00230.00050.0008-0.0024
Jul 20130.0113-0.0078-0.00280.0042
Aug 2013-0.00090.00340.00870.0127
Sep 20130.00480.01180.00630.0032
Oct 2013-0.0156-0.00000.00280.0036
Nov 20130.00730.00050.00380.0093
Dec 20130.0195-0.0097-0.0092-0.0139
Jan 20140.00190.0002-0.0058-0.0108
Feb 20140.00190.0003-0.0023-0.0041
Mar 2014-0.0006-0.0023-0.00070.0025
Apr 20140.00480.00690.0027-0.0055
May 20140.01370.0020-0.0036-0.0086
Jun 2014-0.0003-0.00870.00030.0086
Jul 2014-0.00080.0034-0.0036-0.0105
Aug 20140.02950.00320.0002-0.0039
Sep 2014-0.0088-0.0030-0.00010.0023
Oct 2014-0.04710.02130.01720.0160
Nov 2014-0.00720.0120-0.0009-0.0149
Dec 2014-0.0241-0.00640.00160.0081
Jan 20150.0241-0.00030.00950.0208
Feb 20150.00680.00450.00300.0015
Mar 20150.0045-0.00160.00400.0108
Apr 20150.0020-0.0097-0.0123-0.0169
May 2015-0.0144-0.0073-0.00230.0031
Jun 2015-0.0208-0.00050.00500.0118
Jul 20150.00900.01330.02250.0298
Aug 2015-0.0014-0.0060-0.0076-0.0082
Sep 2015-0.04000.01010.01190.0135
Oct 20150.01090.00750.0021-0.0034
Nov 2015-0.0025-0.0082-0.0059-0.0044
Dec 2015-0.00310.00620.00330.0005
Jan 2016-0.02240.01340.01200.0111
Feb 20160.02070.01710.0061-0.0049
Mar 20160.01560.01370.0042-0.0045
Apr 20160.0044-0.0112-0.0142-0.0168
May 2016-0.0079-0.00210.00610.0144
Jun 2016-0.02410.01070.00650.0025
Jul 20160.0136-0.0031-0.0050-0.0069
Aug 2016-0.0216-0.0209-0.0119-0.0035
Sep 20160.0230-0.0045-0.0087-0.0116
Oct 2016-0.0136-0.0041-0.0052-0.0084
Nov 2016-0.0014-0.00210.00730.0186
Dec 2016-0.0190-0.00580.00270.0104
Jan 20170.0152-0.0084-0.0079-0.0065
Feb 2017-0.00700.00380.0024-0.0013
Mar 2017-0.0108-0.0010-0.0016-0.0026
Apr 20170.0019-0.0012-0.0010-0.0011
May 2017-0.02390.00690.0004-0.0074
Jun 20170.0010-0.0041-0.00140.0025
Jul 20170.04040.00200.00320.0043
Aug 20170.0168-0.0048-0.0074-0.0120
Sep 2017-0.02410.00710.00680.0065
Oct 20170.0175-0.00170.00030.0021
Nov 2017-0.04030.01130.00840.0054
Dec 20170.0159-0.0060-0.0077-0.0103
Jan 2018-0.0010-0.0104-0.00170.0040
Feb 20180.0015-0.0036-0.0039-0.0030
Mar 2018-0.02660.00260.00940.0173
Apr 2018-0.00840.0013-0.0049-0.0104
May 20180.01710.00500.00670.0107
Jun 2018-0.01500.00400.00230.0013
Jul 2018-0.01660.00820.01470.0186
Aug 20180.02980.00790.01780.0298
Sep 20180.0112-0.0057-0.0103-0.0178
Oct 2018-0.0092-0.0067-0.0088-0.0106
Nov 2018-0.0438-0.00830.00200.0122
Dec 2018-0.0019-0.0030-0.0069-0.0100
Jan 20190.01500.01770.0021-0.0136
Feb 2019-0.00540.00360.0013-0.0008
Mar 2019-0.0001-0.0047-0.0075-0.0126
Apr 2019-0.00770.00610.00480.0023
May 20190.0016-0.0135-0.00620.0015
Jun 20190.00020.01000.00580.0019
Jul 20190.02070.01430.01290.0103
Aug 20190.00100.01750.01230.0083
Sep 2019-0.01980.01160.0018-0.0103
Oct 20190.00910.00710.00340.0005
Nov 20190.0052-0.0090-0.0091-0.0096
Dec 2019-0.0265-0.0164-0.0108-0.0068
Jan 2020-0.0034-0.00500.00450.0138
Feb 20200.0230-0.0115-0.0139-0.0131
Mar 2020-0.0152-0.0129-0.0113-0.0153
Apr 2020-0.0187-0.0089-0.0191-0.0265
May 20200.0139-0.0228-0.0124-0.0068
Jun 20200.00800.0013-0.0017-0.0022
Jul 20200.0359-0.00590.00820.0168
Aug 2020-0.0392-0.0058-0.0229-0.0389
Sep 20200.0162-0.0040-0.0043-0.0036
Oct 2020-0.0010-0.0005-0.0032-0.0022
Nov 2020-0.03050.01470.01200.0092