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
Asset 1
%
Asset 2
%
Asset 3
%
Asset 4
%
Asset 5
%
Asset 6
%
Asset 7
%
Asset 8
%
Asset 9
%
Asset 10
%
Total
%

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 - May 2020
Regression Basis 240 monthly samples
Coefficient of Determination (R2) 95.7%
Adjusted R2 95.7%
Regression F statistic 1,769.61 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.066 with p-value 0.693)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 11.487 with p-value 0.009)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.018 54.577 0.000 0.927...0.996
Size (SMB) 0.72 0.030 24.399 0.000 0.666...0.783
Value (HML) 0.35 0.023 14.874 0.000 0.303...0.395
Alpha (α) 4.50bps 0.001 0.600 0.549 -0.10%...0.19%
Annualized Alpha (α) 0.54%  
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) 49.50 22.68 5.17  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML Total R2
iShares Core S&P Small-Cap ETF IJR Jun 2000 May 2020 0.54% 47.59 16.43 1.80 70.32 95.7%
Regression residuals
MonthIJR
Jun 2000-0.0562
Jul 2000-0.0174
Aug 20000.0307
Sep 20000.0069
Oct 20000.0337
Nov 2000-0.0221
Dec 20000.0634
Jan 2001-0.0189
Feb 2001-0.0068
Mar 2001-0.0058
Apr 20010.0104
May 2001-0.0200
Jun 2001-0.0031
Jul 20010.0224
Aug 20010.0137
Sep 2001-0.0168
Oct 20010.0040
Nov 2001-0.0128
Dec 20010.0122
Jan 20020.0070
Feb 2002-0.0012
Mar 20020.0008
Apr 20020.0231
May 2002-0.0138
Jun 2002-0.0163
Jul 2002-0.0126
Aug 20020.0081
Sep 20020.0161
Oct 2002-0.0081
Nov 2002-0.0218
Dec 20020.0126
Jan 2003-0.0140
Feb 2003-0.0107
Mar 2003-0.0061
Apr 2003-0.0024
May 2003-0.0159
Jun 2003-0.0022
Jul 2003-0.0079
Aug 20030.0004
Sep 2003-0.0222
Oct 20030.0012
Nov 20030.0034
Dec 2003-0.0155
Jan 2004-0.0194
Feb 20040.0124
Mar 20040.0130
Apr 20040.0015
May 20040.0122
Jun 20040.0146
Jul 2004-0.0042
Aug 2004-0.0042
Sep 20040.0116
Oct 20040.0054
Nov 20040.0076
Dec 2004-0.0171
Jan 20050.0062
Feb 20050.0056
Mar 2005-0.0047
Apr 2005-0.0030
May 20050.0087
Jun 2005-0.0009
Jul 20050.0015
Aug 2005-0.0058
Sep 20050.0007
Oct 2005-0.0114
Nov 20050.0109
Dec 2005-0.0104
Jan 20060.0056
Feb 2006-0.0022
Mar 20060.0040
Apr 2006-0.0094
May 2006-0.0027
Jun 2006-0.0035
Jul 2006-0.0147
Aug 2006-0.0067
Sep 2006-0.0037
Oct 20060.0034
Nov 2006-0.0014
Dec 2006-0.0156
Jan 20070.0014
Feb 2007-0.0010
Mar 20070.0070
Apr 20070.0038
May 20070.0080
Jun 2007-0.0034
Jul 20070.0106
Aug 20070.0139
Sep 20070.0047
Oct 20070.0037
Nov 2007-0.0055
Dec 2007-0.0049
Jan 2008-0.0016
Feb 20080.0092
Mar 2008-0.0004
Apr 20080.0130
May 20080.0029
Jun 20080.0036
Jul 2008-0.0139
Aug 2008-0.0050
Sep 20080.0066
Oct 2008-0.0063
Nov 2008-0.0013
Dec 20080.0085
Jan 2009-0.0009
Feb 20090.0021
Mar 2009-0.0322
Apr 20090.0284
May 2009-0.0142
Jun 20090.0036
Jul 2009-0.0107
Aug 2009-0.0293
Sep 2009-0.0099
Oct 20090.0139
Nov 2009-0.0091
Dec 20090.0112
Jan 2010-0.0034
Feb 2010-0.0118
Mar 20100.0007
Apr 2010-0.0074
May 20100.0117
Jun 20100.0119
Jul 2010-0.0030
Aug 2010-0.0022
Sep 20100.0027
Oct 20100.0055
Nov 20100.0082
Dec 2010-0.0086
Jan 2011-0.0035
Feb 2011-0.0047
Mar 20110.0112
Apr 20110.0092
May 20110.0155
Jun 20110.0003
Jul 20110.0046
Aug 20110.0099
Sep 2011-0.0001
Oct 20110.0154
Nov 20110.0109
Dec 20110.0039
Jan 20120.0053
Feb 2012-0.0088
Mar 2012-0.0002
Apr 2012-0.0005
May 2012-0.0016
Jun 2012-0.0026
Jul 20120.0040
Aug 20120.0064
Sep 2012-0.0126
Oct 2012-0.0112
Nov 20120.0041
Dec 2012-0.0037
Jan 2013-0.0020
Feb 20130.0045
Mar 2013-0.0025
Apr 2013-0.0016
May 2013-0.0052
Jun 20130.0021
Jul 2013-0.0017
Aug 20130.0097
Sep 20130.0078
Oct 20130.0021
Nov 20130.0047
Dec 2013-0.0090
Jan 2014-0.0044
Feb 2014-0.0022
Mar 2014-0.0020
Apr 20140.0008
May 2014-0.0042
Jun 20140.0024
Jul 2014-0.0057
Aug 20140.0008
Sep 2014-0.0016
Oct 20140.0199
Nov 2014-0.0012
Dec 20140.0034
Jan 20150.0098
Feb 20150.0035
Mar 20150.0060
Apr 2015-0.0140
May 2015-0.0005
Jun 20150.0071
Jul 20150.0209
Aug 2015-0.0071
Sep 20150.0112
Oct 20150.0004
Nov 2015-0.0035
Dec 20150.0025
Jan 20160.0104
Feb 20160.0070
Mar 20160.0039
Apr 2016-0.0138
May 20160.0067
Jun 20160.0073
Jul 2016-0.0040
Aug 2016-0.0115
Sep 2016-0.0061
Oct 2016-0.0081
Nov 20160.0094
Dec 20160.0024
Jan 2017-0.0081
Feb 20170.0018
Mar 2017-0.0010
Apr 2017-0.0009
May 2017-0.0006
Jun 20170.0001
Jul 20170.0021
Aug 2017-0.0075
Sep 20170.0089
Oct 2017-0.0001
Nov 20170.0086
Dec 2017-0.0080
Jan 2018-0.0033
Feb 2018-0.0023
Mar 20180.0126
Apr 2018-0.0041
May 20180.0103
Jun 20180.0037
Jul 20180.0139
Aug 20180.0190
Sep 2018-0.0116
Oct 2018-0.0114
Nov 20180.0024
Dec 2018-0.0082
Jan 20190.0033
Feb 20190.0035
Mar 2019-0.0087
Apr 20190.0035
May 2019-0.0057
Jun 20190.0058
Jul 20190.0126
Aug 20190.0118
Sep 20190.0007
Oct 20190.0040
Nov 2019-0.0086
Dec 2019-0.0098
Jan 20200.0035
Feb 2020-0.0120
Mar 2020-0.0118
Apr 2020-0.0183
May 2020-0.0101