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.

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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) 77.2%
Adjusted R2 77.1%
Regression F statistic 821.19 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.899 with p-value 0.212)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 6.553 with p-value 0.010)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.13 0.040 28.656 0.000 1.055...1.211
Alpha (α) 14.25bps 0.002 0.784 0.434 -0.22%...0.50%
Annualized Alpha (α) 1.71%  
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) 57.09  
Name Ticker Start Date End Date Annual Alpha Rm-Rf Total R2
iShares S&P Small-Cap 600 Value ETF IJS Aug 2000 Nov 2020 1.71% 64.68 78.94 77.2%
Regression residuals
MonthIJS
Aug 2000-0.0123
Sep 20000.0534
Oct 20000.0154
Nov 20000.0739
Dec 20000.1087
Jan 20010.0363
Feb 20010.0665
Mar 20010.0272
Apr 2001-0.0271
May 20010.0164
Jun 20010.0378
Jul 20010.0175
Aug 20010.0591
Sep 2001-0.0447
Oct 20010.0135
Nov 2001-0.0130
Dec 20010.0471
Jan 20020.0349
Feb 20020.0190
Mar 20020.0364
Apr 20020.0963
May 2002-0.0235
Jun 20020.0328
Jul 2002-0.0680
Aug 2002-0.0127
Sep 20020.0354
Oct 2002-0.0658
Nov 2002-0.0152
Dec 20020.0354
Jan 2003-0.0139
Feb 2003-0.0216
Mar 2003-0.0163
Apr 2003-0.0074
May 20030.0233
Jun 20030.0100
Jul 20030.0203
Aug 20030.0210
Sep 2003-0.0233
Oct 20030.0198
Nov 20030.0255
Dec 2003-0.0237
Jan 2004-0.0048
Feb 20040.0071
Mar 20040.0309
Apr 2004-0.0208
May 20040.0005
Jun 20040.0302
Jul 2004-0.0039
Aug 2004-0.0010
Sep 20040.0263
Oct 2004-0.0092
Nov 20040.0367
Dec 2004-0.0262
Jan 2005-0.0043
Feb 20050.0046
Mar 2005-0.0048
Apr 2005-0.0252
May 20050.0164
Jun 20050.0290
Jul 20050.0102
Aug 2005-0.0093
Sep 2005-0.0094
Oct 2005-0.0154
Nov 20050.0037
Dec 2005-0.0123
Jan 20060.0481
Feb 20060.0013
Mar 20060.0269
Apr 2006-0.0115
May 2006-0.0108
Jun 2006-0.0010
Jul 2006-0.0275
Aug 2006-0.0016
Sep 2006-0.0145
Oct 20060.0131
Nov 2006-0.0012
Dec 2006-0.0121
Jan 2007-0.0003
Feb 20070.0078
Mar 2007-0.0044
Apr 2007-0.0270
May 20070.0041
Jun 2007-0.0056
Jul 2007-0.0258
Aug 2007-0.0027
Sep 2007-0.0380
Oct 2007-0.0144
Nov 2007-0.0216
Dec 2007-0.0013
Jan 20080.0285
Feb 2008-0.0013
Mar 20080.0157
Apr 2008-0.0289
May 20080.0149
Jun 20080.0084
Jul 20080.0345
Aug 20080.0276
Sep 20080.0536
Oct 2008-0.0056
Nov 2008-0.0306
Dec 20080.0446
Jan 2009-0.0489
Feb 2009-0.0173
Mar 2009-0.0272
Apr 20090.0720
May 2009-0.0538
Jun 20090.0088
Jul 20090.0210
Aug 2009-0.0044
Sep 2009-0.0057
Oct 2009-0.0328
Nov 2009-0.0354
Dec 20090.0483
Jan 20100.0113
Feb 20100.0077
Mar 20100.0050
Apr 20100.0421
May 20100.0025
Jun 2010-0.0212
Jul 2010-0.0129
Aug 2010-0.0266
Sep 2010-0.0003
Oct 2010-0.0051
Nov 20100.0164
Dec 20100.0109
Jan 2011-0.0264
Feb 20110.0010
Mar 20110.0153
Apr 2011-0.0237
May 2011-0.0047
Jun 20110.0025
Jul 2011-0.0025
Aug 2011-0.0134
Sep 2011-0.0211
Oct 20110.0234
Nov 20110.0080
Dec 20110.0103
Jan 20120.0203
Feb 2012-0.0344
Mar 2012-0.0077
Apr 2012-0.0109
May 2012-0.0031
Jun 2012-0.0001
Jul 2012-0.0172
Aug 20120.0104
Sep 2012-0.0011
Oct 2012-0.0012
Nov 20120.0062
Dec 20120.0206
Jan 2013-0.0110
Feb 20130.0003
Mar 2013-0.0060
Apr 2013-0.0178
May 20130.0097
Jun 20130.0108
Jul 20130.0002
Aug 2013-0.0049
Sep 20130.0218
Oct 2013-0.0140
Nov 20130.0057
Dec 2013-0.0203
Jan 20140.0010
Feb 2014-0.0078
Mar 20140.0071
Apr 2014-0.0222
May 2014-0.0185
Jun 20140.0075
Jul 2014-0.0290
Aug 2014-0.0048
Sep 2014-0.0385
Oct 20140.0413
Nov 2014-0.0255
Dec 20140.0249
Jan 2015-0.0194
Feb 2015-0.0124
Mar 20150.0215
Apr 2015-0.0264
May 2015-0.0093
Jun 20150.0201
Jul 2015-0.0459
Aug 20150.0208
Sep 2015-0.0044
Oct 2015-0.0236
Nov 20150.0169
Dec 2015-0.0278
Jan 20160.0053
Feb 20160.0201
Mar 20160.0137
Apr 20160.0093
May 2016-0.0173
Jun 20160.0073
Jul 20160.0042
Aug 20160.0040
Sep 20160.0042
Oct 2016-0.0162
Nov 20160.0768
Dec 20160.0098
Jan 2017-0.0359
Feb 2017-0.0288
Mar 2017-0.0102
Apr 2017-0.0092
May 2017-0.0366
Jun 20170.0187
Jul 2017-0.0158
Aug 2017-0.0313
Sep 20170.0550
Oct 2017-0.0219
Nov 20170.0000
Dec 2017-0.0180
Jan 2018-0.0525
Feb 2018-0.0016
Mar 20180.0377
Apr 20180.0115
May 20180.0258
Jun 2018-0.0003
Jul 2018-0.0130
Aug 2018-0.0106
Sep 2018-0.0341
Oct 2018-0.0157
Nov 2018-0.0167
Dec 2018-0.0189
Jan 20190.0237
Feb 2019-0.0004
Mar 2019-0.0549
Apr 2019-0.0052
May 2019-0.0247
Jun 2019-0.0052
Jul 2019-0.0038
Aug 2019-0.0252
Sep 20190.0363
Oct 2019-0.0062
Nov 2019-0.0194
Dec 2019-0.0058
Jan 2020-0.0645
Feb 2020-0.0120
Mar 2020-0.1086
Apr 2020-0.0172
May 2020-0.0393
Jun 20200.0064
Jul 2020-0.0411
Aug 2020-0.0373
Sep 2020-0.0122
Oct 20200.0589
Nov 20200.0493