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 FF-MKT-RF FF-SMB FF-HML FF-MOM FF-RMW Alpha Annual Alpha R2
iShares S&P Small-Cap 600 Value ETF IJS Aug 2000 Nov 2020 1.01 0.86 0.48 -0.02 0.22 -0.07% -0.89% 96.9%
iShares Core S&P Small-Cap ETF IJR Aug 2000 Nov 2020 1.01 0.82 0.32 0.05 0.15 -0.03% -0.40% 96.9%

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) 96.9%
Adjusted R2 96.8%
Regression F statistic 1,472.48 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.710 with p-value 0.011)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 9.054 with p-value 0.107)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
FF-MKT-RF Market 1.01 0.018 55.217 0.000 0.971...1.043
FF-SMB Size 0.86 0.029 29.448 0.000 0.805...0.921
FF-HML Value 0.48 0.024 20.124 0.000 0.433...0.527
FF-MOM Momentum -0.02 0.015 -1.085 0.279 -0.047...0.014
FF-RMW Profitability 0.22 0.036 6.145 0.000 0.150...0.291
Alpha Alpha -7.39bps 0.001 -1.043 0.298 -0.21%...0.07%
Annualized Alpha Annualized Alpha -0.89%  

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) 96.9%
Adjusted R2 96.8%
Regression F statistic 1,480.30 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.114 with p-value 0.810)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 23.020 with p-value 0.000)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
FF-MKT-RF Market 1.01 0.017 58.171 0.000 0.976...1.045
FF-SMB Size 0.82 0.028 29.375 0.000 0.765...0.875
FF-HML Value 0.32 0.023 13.895 0.000 0.271...0.360
FF-MOM Momentum 0.05 0.015 3.082 0.002 0.016...0.074
FF-RMW Profitability 0.15 0.034 4.517 0.000 0.087...0.222
Alpha Alpha -3.30bps 0.001 -0.488 0.626 -0.17%...0.10%
Annualized Alpha Annualized Alpha -0.40%  
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.
  • Symbols:
    MKT-RF
    Market factor (excess return over the risk free rate)
    SMB
    Size factor (Small Minus Big)
    HML
    Value factor (High Minus Low)
    MOM
    Momentum factor (Up Minus Down)
    RMW
    Profitability factor (Robust Minus Weak)
    CMA
    Conservative investment factor (Conservative Minus Aggressive)
    ST-REV
    Short-term reversal factor
    LT-REV
    Long-term reversal factor
    QMJ
    Quality factor (Quality Minus Junk)
    BAB
    Bet Against Beta factor
    TRM
    Term factor (fixed income)
    CDT
    Credit factor (fixed income)
    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 14.80 41.14  
Name Ticker Start Date End Date Annual Alpha FF-MKT-RF FF-SMB FF-HML FF-MOM FF-RMW Total R2
iShares S&P Small-Cap 600 Value ETF IJS Aug 2000 Nov 2020 -0.89% 57.49 17.47 2.54 -0.25 9.07 78.94 96.9%
iShares Core S&P Small-Cap ETF IJR Aug 2000 Nov 2020 -0.40% 57.69 16.60 1.67 0.67 6.35 79.68 96.9%
Regression residuals
MonthIJSIJR
Aug 20000.01960.0299
Sep 20000.02430.0094
Oct 2000-0.00200.0287
Nov 20000.0024-0.0276
Dec 20000.06580.0599
Jan 20010.0171-0.0083
Feb 2001-0.0153-0.0140
Mar 2001-0.0183-0.0071
Apr 20010.00890.0137
May 2001-0.0185-0.0223
Jun 2001-0.0134-0.0108
Jul 20010.01300.0171
Aug 20010.01250.0083
Sep 2001-0.0167-0.0166
Oct 2001-0.00420.0011
Nov 2001-0.0005-0.0050
Dec 20010.00530.0072
Jan 2002-0.00050.0000
Feb 2002-0.0004-0.0125
Mar 20020.0065-0.0001
Apr 20020.01330.0120
May 2002-0.0069-0.0127
Jun 2002-0.0180-0.0238
Jul 2002-0.0218-0.0115
Aug 2002-0.00250.0110
Sep 2002-0.00940.0116
Oct 20020.0022-0.0024
Nov 2002-0.0091-0.0079
Dec 20020.00700.0029
Jan 2003-0.0204-0.0130
Feb 2003-0.0135-0.0107
Mar 2003-0.0143-0.0110
Apr 20030.00360.0051
May 20030.0082-0.0060
Jun 2003-0.0046-0.0039
Jul 2003-0.0052-0.0071
Aug 20030.00020.0027
Sep 2003-0.0315-0.0226
Oct 20030.0017-0.0024
Nov 20030.00340.0016
Dec 2003-0.0021-0.0109
Jan 2004-0.0251-0.0165
Feb 20040.01540.0111
Mar 20040.01140.0101
Apr 2004-0.0000-0.0001
May 20040.01040.0135
Jun 20040.00720.0106
Jul 2004-0.0015-0.0007
Aug 20040.0070-0.0031
Sep 20040.00860.0079
Oct 2004-0.00430.0068
Nov 20040.00740.0051
Dec 2004-0.0161-0.0132
Jan 2005-0.00650.0058
Feb 20050.00330.0031
Mar 2005-0.0048-0.0040
Apr 20050.00590.0006
May 20050.00460.0063
Jun 2005-0.0056-0.0045
Jul 2005-0.00090.0006
Aug 2005-0.0014-0.0005
Sep 2005-0.00520.0002
Oct 2005-0.0052-0.0068
Nov 20050.00940.0090
Dec 2005-0.0080-0.0090
Jan 20060.00470.0005
Feb 20060.00910.0012
Mar 2006-0.00140.0012
Apr 2006-0.0114-0.0084
May 2006-0.00120.0042
Jun 2006-0.0035-0.0049
Jul 2006-0.0084-0.0098
Aug 20060.0069-0.0044
Sep 2006-0.0014-0.0042
Oct 20060.00620.0022
Nov 2006-0.0045-0.0013
Dec 2006-0.0106-0.0109
Jan 20070.00420.0016
Feb 2007-0.00240.0010
Mar 20070.00090.0060
Apr 20070.00270.0046
May 20070.00760.0048
Jun 2007-0.0084-0.0038
Jul 20070.01030.0133
Aug 20070.01450.0151
Sep 20070.00040.0051
Oct 20070.00290.0014
Nov 2007-0.0000-0.0024
Dec 20070.0007-0.0075
Jan 20080.00590.0039
Feb 20080.00200.0072
Mar 20080.0080-0.0028
Apr 2008-0.00690.0095
May 2008-0.0022-0.0025
Jun 2008-0.0059-0.0048
Jul 2008-0.0097-0.0075
Aug 2008-0.0110-0.0084
Sep 20080.01950.0120
Oct 20080.0024-0.0041
Nov 20080.0066-0.0067
Dec 20080.01690.0064
Jan 2009-0.0083-0.0024
Feb 20090.00070.0001
Mar 2009-0.0258-0.0251
Apr 20090.01050.0340
May 2009-0.0240-0.0062
Jun 20090.00570.0005
Jul 2009-0.0071-0.0083
Aug 2009-0.0201-0.0161
Sep 2009-0.0277-0.0127
Oct 20090.01320.0104
Nov 2009-0.0056-0.0102
Dec 20090.00030.0024
Jan 20100.00640.0031
Feb 2010-0.0099-0.0137
Mar 2010-0.0055-0.0031
Apr 2010-0.0106-0.0137
May 20100.00220.0129
Jun 20100.01170.0167
Jul 2010-0.0022-0.0070
Aug 20100.00380.0026
Sep 2010-0.0035-0.0058
Oct 20100.00270.0004
Nov 2010-0.00860.0030
Dec 20100.0051-0.0034
Jan 2011-0.00230.0007
Feb 2011-0.0075-0.0054
Mar 20110.00110.0051
Apr 2011-0.00470.0067
May 20110.00650.0131
Jun 20110.0009-0.0023
Jul 20110.00690.0025
Aug 20110.01180.0106
Sep 20110.00330.0046
Oct 20110.01530.0112
Nov 20110.00920.0069
Dec 20110.00870.0027
Jan 20120.01900.0081
Feb 2012-0.0116-0.0079
Mar 20120.00030.0001
Apr 2012-0.0049-0.0028
May 2012-0.0102-0.0049
Jun 2012-0.0002-0.0028
Jul 20120.00730.0034
Aug 20120.00900.0094
Sep 2012-0.0043-0.0106
Oct 2012-0.0058-0.0048
Nov 20120.00840.0031
Dec 2012-0.00170.0008
Jan 2013-0.0058-0.0001
Feb 20130.00890.0050
Mar 2013-0.0052-0.0061
Apr 20130.00440.0008
May 2013-0.0071-0.0025
Jun 20130.00250.0023
Jul 2013-0.0062-0.0041
Aug 20130.00280.0094
Sep 20130.01130.0034
Oct 2013-0.0052-0.0018
Nov 2013-0.00010.0024
Dec 2013-0.0083-0.0087
Jan 20140.01020.0014
Feb 20140.0002-0.0045
Mar 2014-0.00310.0005
Apr 20140.00230.0022
May 20140.0034-0.0035
Jun 2014-0.00610.0011
Jul 20140.0054-0.0010
Aug 20140.0036-0.0007
Sep 2014-0.00260.0011
Oct 20140.01950.0154
Nov 20140.0085-0.0039
Dec 2014-0.00250.0036
Jan 2015-0.00260.0072
Feb 20150.00400.0031
Mar 2015-0.00140.0028
Apr 2015-0.0074-0.0064
May 2015-0.0027-0.0026
Jun 2015-0.00090.0035
Jul 20150.01510.0184
Aug 2015-0.0031-0.0028
Sep 20150.01080.0106
Oct 20150.00390.0003
Nov 2015-0.0031-0.0037
Dec 20150.00780.0038
Jan 20160.01360.0132
Feb 20160.00960.0034
Mar 20160.00980.0026
Apr 2016-0.0036-0.0057
May 20160.00060.0067
Jun 20160.00830.0029
Jul 2016-0.0084-0.0078
Aug 2016-0.0153-0.0064
Sep 2016-0.0004-0.0054
Oct 20160.0003-0.0018
Nov 2016-0.00160.0078
Dec 2016-0.00600.0021
Jan 2017-0.0081-0.0070
Feb 20170.00270.0022
Mar 2017-0.0041-0.0028
Apr 2017-0.0062-0.0047
May 20170.0049-0.0013
Jun 20170.00130.0024
Jul 20170.00500.0042
Aug 2017-0.0038-0.0082
Sep 20170.00970.0082
Oct 2017-0.0018-0.0024
Nov 20170.00410.0033
Dec 2017-0.0064-0.0070
Jan 2018-0.0081-0.0032
Feb 2018-0.0023-0.0039
Mar 20180.00340.0113
Apr 20180.0072-0.0008
May 20180.00600.0047
Jun 20180.00100.0018
Jul 20180.00580.0135
Aug 20180.00630.0134
Sep 2018-0.0057-0.0097
Oct 2018-0.0005-0.0011
Nov 2018-0.00620.0041
Dec 20180.0026-0.0009
Jan 20190.01380.0021
Feb 20190.0009-0.0016
Mar 2019-0.0063-0.0093
Apr 20190.00360.0037
May 2019-0.0077-0.0041
Jun 20190.00540.0023
Jul 20190.01700.0132
Aug 20190.01860.0103
Sep 20190.01080.0045
Oct 20190.00570.0022
Nov 2019-0.0077-0.0073
Dec 2019-0.0162-0.0101
Jan 2020-0.00170.0048
Feb 2020-0.0062-0.0074
Mar 2020-0.0072-0.0066
Apr 2020-0.0216-0.0283
May 2020-0.0291-0.0181
Jun 2020-0.0012-0.0034
Jul 2020-0.00660.0024
Aug 2020-0.0184-0.0335
Sep 20200.0002-0.0016
Oct 20200.00230.0006
Nov 20200.01360.0145