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

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%  
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
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%
Regression residuals
MonthIJS
Aug 20000.0137
Sep 20000.0218
Oct 20000.0124
Nov 20000.0185
Dec 20000.0655
Jan 20010.0157
Feb 2001-0.0097
Mar 2001-0.0200
Apr 20010.0075
May 2001-0.0200
Jun 2001-0.0088
Jul 20010.0213
Aug 20010.0164
Sep 2001-0.0166
Oct 2001-0.0016
Nov 2001-0.0070
Dec 20010.0068
Jan 20020.0061
Feb 20020.0123
Mar 20020.0049
Apr 20020.0192
May 2002-0.0068
Jun 2002-0.0126
Jul 2002-0.0191
Aug 2002-0.0041
Sep 2002-0.0089
Oct 2002-0.0018
Nov 2002-0.0225
Dec 20020.0143
Jan 2003-0.0239
Feb 2003-0.0132
Mar 2003-0.0096
Apr 2003-0.0030
May 2003-0.0022
Jun 2003-0.0033
Jul 2003-0.0117
Aug 2003-0.0045
Sep 2003-0.0305
Oct 2003-0.0004
Nov 20030.0028
Dec 2003-0.0018
Jan 2004-0.0341
Feb 20040.0186
Mar 20040.0141
Apr 20040.0074
May 20040.0068
Jun 20040.0094
Jul 20040.0036
Aug 20040.0073
Sep 20040.0057
Oct 2004-0.0051
Nov 20040.0070
Dec 2004-0.0180
Jan 2005-0.0052
Feb 20050.0045
Mar 2005-0.0074
Apr 20050.0038
May 20050.0040
Jun 2005-0.0048
Jul 2005-0.0014
Aug 2005-0.0092
Sep 2005-0.0067
Oct 2005-0.0096
Nov 20050.0090
Dec 2005-0.0094
Jan 20060.0051
Feb 20060.0068
Mar 2006-0.0009
Apr 2006-0.0104
May 2006-0.0036
Jun 2006-0.0027
Jul 2006-0.0092
Aug 20060.0047
Sep 2006-0.0004
Oct 20060.0071
Nov 2006-0.0041
Dec 2006-0.0149
Jan 20070.0052
Feb 2007-0.0044
Mar 20070.0013
Apr 20070.0049
May 20070.0117
Jun 2007-0.0082
Jul 20070.0083
Aug 20070.0117
Sep 2007-0.0013
Oct 20070.0026
Nov 2007-0.0002
Dec 20070.0003
Jan 20080.0061
Feb 20080.0012
Mar 20080.0082
Apr 2008-0.0021
May 20080.0013
Jun 20080.0004
Jul 2008-0.0147
Aug 2008-0.0059
Sep 20080.0157
Oct 2008-0.0004
Nov 20080.0130
Dec 20080.0190
Jan 2009-0.0052
Feb 20090.0016
Mar 2009-0.0287
Apr 20090.0220
May 2009-0.0251
Jun 20090.0034
Jul 2009-0.0070
Aug 2009-0.0293
Sep 2009-0.0222
Oct 20090.0195
Nov 2009-0.0035
Dec 20090.0046
Jan 20100.0022
Feb 2010-0.0124
Mar 2010-0.0068
Apr 2010-0.0088
May 20100.0020
Jun 20100.0097
Jul 2010-0.0001
Aug 20100.0014
Sep 20100.0018
Oct 20100.0072
Nov 2010-0.0069
Dec 2010-0.0021
Jan 2011-0.0056
Feb 2011-0.0119
Mar 20110.0052
Apr 2011-0.0017
May 20110.0104
Jun 20110.0042
Jul 20110.0104
Aug 20110.0157
Sep 20110.0035
Oct 20110.0151
Nov 20110.0114
Dec 20110.0085
Jan 20120.0181
Feb 2012-0.0129
Mar 2012-0.0022
Apr 2012-0.0040
May 2012-0.0090
Jun 2012-0.0024
Jul 20120.0068
Aug 20120.0057
Sep 2012-0.0078
Oct 2012-0.0136
Nov 20120.0091
Dec 2012-0.0070
Jan 2013-0.0086
Feb 20130.0064
Mar 2013-0.0034
Apr 20130.0026
May 2013-0.0120
Jun 20130.0005
Jul 2013-0.0078
Aug 20130.0034
Sep 20130.0118
Oct 2013-0.0000
Nov 20130.0005
Dec 2013-0.0097
Jan 20140.0002
Feb 20140.0003
Mar 2014-0.0023
Apr 20140.0069
May 20140.0020
Jun 2014-0.0087
Jul 20140.0034
Aug 20140.0032
Sep 2014-0.0030
Oct 20140.0213
Nov 20140.0120
Dec 2014-0.0064
Jan 2015-0.0003
Feb 20150.0045
Mar 2015-0.0016
Apr 2015-0.0097
May 2015-0.0073
Jun 2015-0.0005
Jul 20150.0133
Aug 2015-0.0060
Sep 20150.0101
Oct 20150.0075
Nov 2015-0.0082
Dec 20150.0062
Jan 20160.0134
Feb 20160.0171
Mar 20160.0137
Apr 2016-0.0112
May 2016-0.0021
Jun 20160.0107
Jul 2016-0.0031
Aug 2016-0.0209
Sep 2016-0.0045
Oct 2016-0.0041
Nov 2016-0.0021
Dec 2016-0.0058
Jan 2017-0.0084
Feb 20170.0038
Mar 2017-0.0010
Apr 2017-0.0012
May 20170.0069
Jun 2017-0.0041
Jul 20170.0020
Aug 2017-0.0048
Sep 20170.0071
Oct 2017-0.0017
Nov 20170.0113
Dec 2017-0.0060
Jan 2018-0.0104
Feb 2018-0.0036
Mar 20180.0026
Apr 20180.0013
May 20180.0050
Jun 20180.0040
Jul 20180.0082
Aug 20180.0079
Sep 2018-0.0057
Oct 2018-0.0067
Nov 2018-0.0083
Dec 2018-0.0030
Jan 20190.0177
Feb 20190.0036
Mar 2019-0.0047
Apr 20190.0061
May 2019-0.0135
Jun 20190.0100
Jul 20190.0143
Aug 20190.0175
Sep 20190.0116
Oct 20190.0071
Nov 2019-0.0090
Dec 2019-0.0164
Jan 2020-0.0050
Feb 2020-0.0115
Mar 2020-0.0129
Apr 2020-0.0089
May 2020-0.0228
Jun 20200.0013
Jul 2020-0.0059
Aug 2020-0.0058
Sep 2020-0.0040
Oct 2020-0.0005
Nov 20200.0147