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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Asset 2
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Asset 3
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Asset 5
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Factor Analysis Results

iShares Core S&P Small-Cap ETF

Factor regression results for iShares Core S&P Small-Cap ETF
Ticker IJR
Time Period Jun 2000 - Dec 2019
Coefficient of Determination (R2) 95.3%
Adjusted R2 95.2%
Regression F statistic 1,565.01 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.094 with p-value 0.764)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 12.142 with p-value 0.007)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.018 52.399 0.000 0.925...0.998
Size (SMB) 0.72 0.030 24.193 0.000 0.666...0.784
Value (HML) 0.34 0.025 13.425 0.000 0.287...0.385
Alpha (α) 6.80bps 0.001 0.896 0.371 -0.08%...0.22%
Annualized Alpha (α) 0.82%  
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) 51.58 24.06 18.33  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML Total R2
iShares Core S&P Small-Cap ETF IJR Jun 2000 Dec 2019 0.82% 49.60 17.44 6.16 79.99 95.3%
Regression residuals
MonthIJR
Jun 2000-0.0577
Jul 2000-0.0166
Aug 20000.0304
Sep 20000.0074
Oct 20000.0342
Nov 2000-0.0209
Dec 20000.0642
Jan 2001-0.0197
Feb 2001-0.0053
Mar 2001-0.0051
Apr 20010.0095
May 2001-0.0199
Jun 2001-0.0034
Jul 20010.0229
Aug 20010.0138
Sep 2001-0.0168
Oct 20010.0027
Nov 2001-0.0128
Dec 20010.0121
Jan 20020.0073
Feb 2002-0.0011
Mar 20020.0007
Apr 20020.0234
May 2002-0.0138
Jun 2002-0.0165
Jul 2002-0.0133
Aug 20020.0082
Sep 20020.0161
Oct 2002-0.0090
Nov 2002-0.0222
Dec 20020.0127
Jan 2003-0.0145
Feb 2003-0.0111
Mar 2003-0.0065
Apr 2003-0.0025
May 2003-0.0161
Jun 2003-0.0024
Jul 2003-0.0084
Aug 20030.0004
Sep 2003-0.0225
Oct 20030.0012
Nov 20030.0034
Dec 2003-0.0155
Jan 2004-0.0193
Feb 20040.0122
Mar 20040.0128
Apr 20040.0009
May 20040.0119
Jun 20040.0146
Jul 2004-0.0040
Aug 2004-0.0042
Sep 20040.0112
Oct 20040.0050
Nov 20040.0075
Dec 2004-0.0174
Jan 20050.0062
Feb 20050.0056
Mar 2005-0.0046
Apr 2005-0.0033
May 20050.0083
Jun 2005-0.0008
Jul 20050.0011
Aug 2005-0.0058
Sep 20050.0006
Oct 2005-0.0116
Nov 20050.0104
Dec 2005-0.0107
Jan 20060.0056
Feb 2006-0.0025
Mar 20060.0038
Apr 2006-0.0093
May 2006-0.0027
Jun 2006-0.0037
Jul 2006-0.0146
Aug 2006-0.0071
Sep 2006-0.0040
Oct 20060.0032
Nov 2006-0.0016
Dec 2006-0.0154
Jan 20070.0010
Feb 2007-0.0013
Mar 20070.0067
Apr 20070.0035
May 20070.0078
Jun 2007-0.0038
Jul 20070.0099
Aug 20070.0134
Sep 20070.0042
Oct 20070.0032
Nov 2007-0.0059
Dec 2007-0.0052
Jan 2008-0.0013
Feb 20080.0089
Mar 2008-0.0007
Apr 20080.0126
May 20080.0025
Jun 20080.0031
Jul 2008-0.0133
Aug 2008-0.0051
Sep 20080.0072
Oct 2008-0.0069
Nov 2008-0.0023
Dec 20080.0082
Jan 2009-0.0025
Feb 20090.0010
Mar 2009-0.0320
Apr 20090.0289
May 2009-0.0144
Jun 20090.0030
Jul 2009-0.0103
Aug 2009-0.0285
Sep 2009-0.0100
Oct 20090.0131
Nov 2009-0.0093
Dec 20090.0109
Jan 2010-0.0036
Feb 2010-0.0116
Mar 20100.0008
Apr 2010-0.0073
May 20100.0112
Jun 20100.0111
Jul 2010-0.0033
Aug 2010-0.0026
Sep 20100.0021
Oct 20100.0049
Nov 20100.0078
Dec 2010-0.0084
Jan 2011-0.0036
Feb 2011-0.0048
Mar 20110.0107
Apr 20110.0086
May 20110.0150
Jun 20110.0000
Jul 20110.0042
Aug 20110.0094
Sep 2011-0.0005
Oct 20110.0151
Nov 20110.0106
Dec 20110.0039
Jan 20120.0049
Feb 2012-0.0091
Mar 2012-0.0003
Apr 2012-0.0008
May 2012-0.0019
Jun 2012-0.0028
Jul 20120.0038
Aug 20120.0063
Sep 2012-0.0127
Oct 2012-0.0110
Nov 20120.0037
Dec 2012-0.0035
Jan 2013-0.0021
Feb 20130.0042
Mar 2013-0.0028
Apr 2013-0.0017
May 2013-0.0051
Jun 20130.0019
Jul 2013-0.0018
Aug 20130.0092
Sep 20130.0074
Oct 20130.0020
Nov 20130.0045
Dec 2013-0.0093
Jan 2014-0.0049
Feb 2014-0.0025
Mar 2014-0.0016
Apr 20140.0007
May 2014-0.0045
Jun 20140.0021
Jul 2014-0.0059
Aug 20140.0004
Sep 2014-0.0020
Oct 20140.0194
Nov 2014-0.0019
Dec 20140.0034
Jan 20150.0091
Feb 20150.0030
Mar 20150.0058
Apr 2015-0.0140
May 2015-0.0009
Jun 20150.0068
Jul 20150.0201
Aug 2015-0.0070
Sep 20150.0110
Oct 20150.0001
Nov 2015-0.0038
Dec 20150.0019
Jan 20160.0104
Feb 20160.0067
Mar 20160.0038
Apr 2016-0.0136
May 20160.0062
Jun 20160.0069
Jul 2016-0.0044
Aug 2016-0.0113
Sep 2016-0.0066
Oct 2016-0.0078
Nov 20160.0102
Dec 20160.0026
Jan 2017-0.0087
Feb 20170.0013
Mar 2017-0.0017
Apr 2017-0.0014
May 2017-0.0013
Jun 20170.0001
Jul 20170.0018
Aug 2017-0.0081
Sep 20170.0091
Oct 2017-0.0004
Nov 20170.0084
Dec 2017-0.0082
Jan 2018-0.0037
Feb 2018-0.0027
Mar 20180.0124
Apr 2018-0.0043
May 20180.0097
Jun 20180.0032
Jul 20180.0139
Aug 20180.0182
Sep 2018-0.0120
Oct 2018-0.0111
Nov 20180.0022
Dec 2018-0.0086
Jan 20190.0029
Feb 20190.0029
Mar 2019-0.0094
Apr 20190.0035
May 2019-0.0062
Jun 20190.0055
Jul 20190.0124
Aug 20190.0109
Sep 20190.0013
Oct 20190.0035
Nov 2019-0.0091
Dec 2019-0.0098