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) 77.0%
Adjusted R2 76.9%
Regression F statistic 798.14 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.946 with p-value 0.336)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 7.879 with p-value 0.005)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.13 0.040 28.251 0.000 1.050...1.207
Alpha (α) 12.06bps 0.002 0.667 0.506 -0.24%...0.48%
Annualized Alpha (α) 1.45%  
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.
  • CAPM: Ra = Rrf + Bmkt × ( Rmkt - Rrf ) + α
  • Symbols:
    Ra
    Asset return
    Rrf
    Risk free return
    Bmkt
    Market loading factor (exposure to market risk, CAPM beta)
    Rmkt
    Market return
    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  
Name Ticker Start Date End Date Annual Alpha Rm-Rf Total R2
iShares S&P Small-Cap 600 Value ETF IJS Aug 2000 Jul 2020 1.45% 58.72 70.79 77.0%
Regression residuals
MonthIJS
Aug 2000-0.0117
Sep 20000.0534
Oct 20000.0155
Nov 20000.0737
Dec 20000.1090
Jan 20010.0366
Feb 20010.0663
Mar 20010.0271
Apr 2001-0.0265
May 20010.0166
Jun 20010.0380
Jul 20010.0176
Aug 20010.0590
Sep 2001-0.0449
Oct 20010.0138
Nov 2001-0.0125
Dec 20010.0474
Jan 20020.0351
Feb 20020.0191
Mar 20020.0368
Apr 20020.0963
May 2002-0.0233
Jun 20020.0326
Jul 2002-0.0682
Aug 2002-0.0125
Sep 20020.0351
Oct 2002-0.0653
Nov 2002-0.0147
Dec 20020.0353
Jan 2003-0.0138
Feb 2003-0.0214
Mar 2003-0.0160
Apr 2003-0.0068
May 20030.0238
Jun 20030.0103
Jul 20030.0207
Aug 20030.0213
Sep 2003-0.0231
Oct 20030.0203
Nov 20030.0258
Dec 2003-0.0233
Jan 2004-0.0045
Feb 20040.0074
Mar 20040.0310
Apr 2004-0.0207
May 20040.0008
Jun 20040.0306
Jul 2004-0.0039
Aug 2004-0.0008
Sep 20040.0266
Oct 2004-0.0089
Nov 20040.0372
Dec 2004-0.0258
Jan 2005-0.0042
Feb 20050.0049
Mar 2005-0.0047
Apr 2005-0.0251
May 20050.0168
Jun 20050.0292
Jul 20050.0106
Aug 2005-0.0091
Sep 2005-0.0092
Oct 2005-0.0152
Nov 20050.0040
Dec 2005-0.0121
Jan 20060.0485
Feb 20060.0015
Mar 20060.0272
Apr 2006-0.0113
May 2006-0.0107
Jun 2006-0.0008
Jul 2006-0.0274
Aug 2006-0.0013
Sep 2006-0.0142
Oct 20060.0134
Nov 2006-0.0009
Dec 2006-0.0119
Jan 2007-0.0000
Feb 20070.0079
Mar 2007-0.0041
Apr 2007-0.0266
May 20070.0045
Jun 2007-0.0055
Jul 2007-0.0257
Aug 2007-0.0025
Sep 2007-0.0376
Oct 2007-0.0141
Nov 2007-0.0216
Dec 2007-0.0012
Jan 20080.0285
Feb 2008-0.0013
Mar 20080.0158
Apr 2008-0.0285
May 20080.0152
Jun 20080.0082
Jul 20080.0347
Aug 20080.0278
Sep 20080.0534
Oct 2008-0.0062
Nov 2008-0.0308
Dec 20080.0449
Jan 2009-0.0490
Feb 2009-0.0176
Mar 2009-0.0266
Apr 20090.0726
May 2009-0.0533
Jun 20090.0091
Jul 20090.0216
Aug 2009-0.0041
Sep 2009-0.0053
Oct 2009-0.0327
Nov 2009-0.0349
Dec 20090.0486
Jan 20100.0114
Feb 20100.0081
Mar 20100.0055
Apr 20100.0424
May 20100.0023
Jun 2010-0.0213
Jul 2010-0.0124
Aug 2010-0.0266
Sep 20100.0003
Oct 2010-0.0047
Nov 20100.0167
Dec 20100.0114
Jan 2011-0.0261
Feb 20110.0014
Mar 20110.0157
Apr 2011-0.0233
May 2011-0.0045
Jun 20110.0026
Jul 2011-0.0023
Aug 2011-0.0135
Sep 2011-0.0212
Oct 20110.0241
Nov 20110.0083
Dec 20110.0106
Jan 20120.0208
Feb 2012-0.0339
Mar 2012-0.0074
Apr 2012-0.0107
May 2012-0.0032
Jun 20120.0003
Jul 2012-0.0170
Aug 20120.0107
Sep 2012-0.0008
Oct 2012-0.0011
Nov 20120.0064
Dec 20120.0209
Jan 2013-0.0105
Feb 20130.0005
Mar 2013-0.0056
Apr 2013-0.0175
May 20130.0101
Jun 20130.0109
Jul 20130.0006
Aug 2013-0.0048
Sep 20130.0222
Oct 2013-0.0136
Nov 20130.0061
Dec 2013-0.0200
Jan 20140.0011
Feb 2014-0.0074
Mar 20140.0073
Apr 2014-0.0220
May 2014-0.0182
Jun 20140.0078
Jul 2014-0.0289
Aug 2014-0.0044
Sep 2014-0.0384
Oct 20140.0417
Nov 2014-0.0252
Dec 20140.0251
Jan 2015-0.0193
Feb 2015-0.0118
Mar 20150.0217
Apr 2015-0.0261
May 2015-0.0090
Jun 20150.0203
Jul 2015-0.0456
Aug 20150.0208
Sep 2015-0.0042
Oct 2015-0.0230
Nov 20150.0172
Dec 2015-0.0276
Jan 20160.0053
Feb 20160.0202
Mar 20160.0142
Apr 20160.0096
May 2016-0.0170
Jun 20160.0075
Jul 20160.0046
Aug 20160.0043
Sep 20160.0045
Oct 2016-0.0160
Nov 20160.0773
Dec 20160.0101
Jan 2017-0.0356
Feb 2017-0.0284
Mar 2017-0.0099
Apr 2017-0.0089
May 2017-0.0364
Jun 20170.0190
Jul 2017-0.0155
Aug 2017-0.0311
Sep 20170.0553
Oct 2017-0.0216
Nov 20170.0004
Dec 2017-0.0178
Jan 2018-0.0520
Feb 2018-0.0015
Mar 20180.0378
Apr 20180.0118
May 20180.0262
Jun 2018-0.0000
Jul 2018-0.0127
Aug 2018-0.0102
Sep 2018-0.0339
Oct 2018-0.0158
Nov 2018-0.0164
Dec 2018-0.0192
Jan 20190.0243
Feb 2019-0.0000
Mar 2019-0.0546
Apr 2019-0.0048
May 2019-0.0248
Jun 2019-0.0046
Jul 2019-0.0035
Aug 2019-0.0251
Sep 20190.0366
Oct 2019-0.0059
Nov 2019-0.0190
Dec 2019-0.0055
Jan 2020-0.0643
Feb 2020-0.0121
Mar 2020-0.1089
Apr 2020-0.0164
May 2020-0.0388
Jun 20200.0068
Jul 2020-0.0407