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 - Jul 2020
Regression Basis 240 monthly samples
Coefficient of Determination (R2) 96.1%
Adjusted R2 96.1%
Regression F statistic 1,956.63 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.660 with p-value 0.004)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 14.263 with p-value 0.003)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.017 55.146 0.000 0.929...0.998
Size (SMB) 0.81 0.031 26.014 0.000 0.749...0.872
Value (HML) 0.52 0.024 21.490 0.000 0.470...0.565
Alpha (α) 3.43bps 0.001 0.460 0.646 -0.11%...0.18%
Annualized Alpha (α) 0.41%  
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) 52.03 18.29 4.64  
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 Jul 2020 0.41% 50.12 14.83 2.40 70.79 96.1%
Regression residuals
MonthIJS
Aug 20000.0135
Sep 20000.0242
Oct 20000.0135
Nov 20000.0210
Dec 20000.0659
Jan 20010.0148
Feb 2001-0.0103
Mar 2001-0.0203
Apr 20010.0075
May 2001-0.0187
Jun 2001-0.0079
Jul 20010.0214
Aug 20010.0160
Sep 2001-0.0180
Oct 2001-0.0011
Nov 2001-0.0062
Dec 20010.0082
Jan 20020.0067
Feb 20020.0121
Mar 20020.0047
Apr 20020.0201
May 2002-0.0074
Jun 2002-0.0136
Jul 2002-0.0200
Aug 2002-0.0041
Sep 2002-0.0088
Oct 20020.0003
Nov 2002-0.0212
Dec 20020.0150
Jan 2003-0.0235
Feb 2003-0.0134
Mar 2003-0.0098
Apr 2003-0.0023
May 2003-0.0018
Jun 2003-0.0036
Jul 2003-0.0112
Aug 2003-0.0056
Sep 2003-0.0308
Oct 20030.0004
Nov 20030.0030
Dec 2003-0.0035
Jan 2004-0.0330
Feb 20040.0196
Mar 20040.0144
Apr 20040.0074
May 20040.0073
Jun 20040.0090
Jul 2004-0.0001
Aug 20040.0080
Sep 20040.0068
Oct 2004-0.0050
Nov 20040.0047
Dec 2004-0.0197
Jan 2005-0.0058
Feb 20050.0044
Mar 2005-0.0043
Apr 20050.0056
May 20050.0045
Jun 2005-0.0038
Jul 2005-0.0032
Aug 2005-0.0094
Sep 2005-0.0068
Oct 2005-0.0090
Nov 20050.0097
Dec 2005-0.0102
Jan 20060.0046
Feb 20060.0062
Mar 2006-0.0014
Apr 2006-0.0118
May 2006-0.0042
Jun 2006-0.0022
Jul 2006-0.0100
Aug 20060.0044
Sep 20060.0006
Oct 20060.0058
Nov 2006-0.0046
Dec 2006-0.0170
Jan 20070.0029
Feb 2007-0.0047
Mar 2007-0.0006
Apr 20070.0027
May 20070.0107
Jun 2007-0.0083
Jul 20070.0066
Aug 20070.0125
Sep 2007-0.0032
Oct 20070.0013
Nov 2007-0.0013
Dec 2007-0.0007
Jan 20080.0072
Feb 20080.0013
Mar 20080.0082
Apr 2008-0.0018
May 20080.0001
Jun 2008-0.0028
Jul 2008-0.0159
Aug 2008-0.0061
Sep 20080.0158
Oct 20080.0000
Nov 20080.0123
Dec 20080.0207
Jan 2009-0.0045
Feb 20090.0026
Mar 2009-0.0288
Apr 20090.0231
May 2009-0.0238
Jun 20090.0034
Jul 2009-0.0092
Aug 2009-0.0306
Sep 2009-0.0223
Oct 20090.0197
Nov 2009-0.0036
Dec 20090.0046
Jan 20100.0020
Feb 2010-0.0115
Mar 2010-0.0059
Apr 2010-0.0083
May 20100.0021
Jun 20100.0095
Jul 2010-0.0001
Aug 20100.0009
Sep 20100.0014
Oct 20100.0069
Nov 2010-0.0069
Dec 2010-0.0017
Jan 2011-0.0061
Feb 2011-0.0100
Mar 20110.0044
Apr 2011-0.0018
May 20110.0106
Jun 20110.0035
Jul 20110.0119
Aug 20110.0149
Sep 20110.0028
Oct 20110.0169
Nov 20110.0118
Dec 20110.0091
Jan 20120.0185
Feb 2012-0.0121
Mar 2012-0.0011
Apr 2012-0.0045
May 2012-0.0096
Jun 2012-0.0009
Jul 20120.0077
Aug 20120.0059
Sep 2012-0.0072
Oct 2012-0.0134
Nov 20120.0089
Dec 2012-0.0068
Jan 2013-0.0083
Feb 20130.0071
Mar 2013-0.0032
Apr 20130.0026
May 2013-0.0112
Jun 20130.0012
Jul 2013-0.0070
Aug 20130.0035
Sep 20130.0118
Oct 20130.0006
Nov 20130.0006
Dec 2013-0.0088
Jan 20140.0004
Feb 20140.0010
Mar 2014-0.0020
Apr 20140.0076
May 20140.0019
Jun 2014-0.0080
Jul 20140.0029
Aug 20140.0036
Sep 2014-0.0034
Oct 20140.0213
Nov 20140.0122
Dec 2014-0.0054
Jan 2015-0.0009
Feb 20150.0045
Mar 2015-0.0015
Apr 2015-0.0098
May 2015-0.0062
Jun 2015-0.0001
Jul 20150.0129
Aug 2015-0.0062
Sep 20150.0103
Oct 20150.0069
Nov 2015-0.0081
Dec 20150.0060
Jan 20160.0130
Feb 20160.0170
Mar 20160.0136
Apr 2016-0.0105
May 2016-0.0015
Jun 20160.0106
Jul 2016-0.0037
Aug 2016-0.0210
Sep 2016-0.0032
Oct 2016-0.0043
Nov 2016-0.0012
Dec 2016-0.0057
Jan 2017-0.0089
Feb 20170.0043
Mar 2017-0.0020
Apr 2017-0.0023
May 20170.0067
Jun 2017-0.0034
Jul 20170.0010
Aug 2017-0.0054
Sep 20170.0081
Oct 2017-0.0017
Nov 20170.0120
Dec 2017-0.0053
Jan 2018-0.0102
Feb 2018-0.0033
Mar 20180.0033
Apr 20180.0010
May 20180.0047
Jun 20180.0041
Jul 20180.0089
Aug 20180.0085
Sep 2018-0.0069
Oct 2018-0.0069
Nov 2018-0.0075
Dec 2018-0.0050
Jan 20190.0179
Feb 20190.0043
Mar 2019-0.0054
Apr 20190.0062
May 2019-0.0133
Jun 20190.0106
Jul 20190.0150
Aug 20190.0173
Sep 20190.0124
Oct 20190.0068
Nov 2019-0.0095
Dec 2019-0.0156
Jan 2020-0.0055
Feb 2020-0.0117
Mar 2020-0.0151
Apr 2020-0.0092
May 2020-0.0232
Jun 20200.0013
Jul 2020-0.0050