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
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Asset 2
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Asset 3
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Asset 4
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Asset 5
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Asset 6
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Asset 7
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Asset 8
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Asset 9
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Asset 10
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Factor Analysis Results

Factor Analysis Summary

Factor regression results
Name Ticker Start Date End Date AQR-MKT-RF AQR-SMB AQR-HML AQR-QMJ Alpha Annual Alpha R2
DFA US Small Cap I DFSTX Jun 2000 Mar 2019 1.12 0.93 0.27 0.27 -0.14% -1.68% 97.2%
iShares Core S&P Small-Cap ETF IJR Jun 2000 Mar 2019 1.13 0.87 0.33 0.43 -0.18% -2.22% 94.5%

DFA US Small Cap I

Factor regression results for DFA US Small Cap I
Ticker DFSTX
Time Period Jun 2000 - Mar 2019
Coefficient of Determination (R2) 97.2%
Adjusted R2 97.1%
Regression F statistic 1,898.93 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.912 with p-value 0.248)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 5.778 with p-value 0.216)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
AQR-MKT-RF 1.12 0.025 44.315 0.000 1.068...1.168
AQR-SMB 0.93 0.036 25.682 0.000 0.862...1.006
AQR-HML 0.27 0.044 6.108 0.000 0.183...0.357
AQR-QMJ 0.27 0.048 5.602 0.000 0.173...0.360
Alpha -13.98bps 0.001 -1.929 0.055 -0.28%...0.00%
Annualized Alpha -1.68%  

iShares Core S&P Small-Cap ETF

Factor regression results for iShares Core S&P Small-Cap ETF
Ticker IJR
Time Period Jun 2000 - Mar 2019
Coefficient of Determination (R2) 94.5%
Adjusted R2 94.4%
Regression F statistic 945.60 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.375 with p-value 0.998)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 4.098 with p-value 0.393)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
AQR-MKT-RF 1.13 0.031 36.714 0.000 1.066...1.187
AQR-SMB 0.87 0.054 16.038 0.000 0.759...0.972
AQR-HML 0.33 0.041 8.189 0.000 0.253...0.413
AQR-QMJ 0.43 0.043 9.879 0.000 0.343...0.514
Alpha -18.49bps 0.001 -2.138 0.034 -0.36%...-0.01%
Annualized Alpha -2.22%  
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.
  • Symbols:
    MKT-RF
    Market factor (excess return over the risk free rate)
    SMB
    Size factor (Small Minus Big)
    HML
    Value factor (High Minus Low)
    MOM
    Momentum factor (Up Minus Down)
    RMW
    Profitability factor (Robust Minus Weak)
    CMA
    Conservative investment factor (Conservative Minus Aggressive)
    ST-REV
    Short-term reversal factor
    LT-REV
    Long-term reversal factor
    QMJ
    Quality factor (Quality Minus Junk)
    BAB
    Bet Against Beta factor
    TRM
    Term factor (fixed income)
    CDT
    Credit factor (fixed income)
    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) 47.13 22.76 14.34 46.38  
Name Ticker Start Date End Date Annual Alpha AQR-MKT-RF AQR-SMB AQR-HML AQR-QMJ Total R2
DFA US Small Cap I DFSTX Jun 2000 Mar 2019 -1.68% 52.69 21.26 3.88 12.35 76.20 97.2%
iShares Core S&P Small-Cap ETF IJR Jun 2000 Mar 2019 -2.22% 53.11 19.70 4.78 19.89 78.98 94.5%
Regression residuals
MonthDFSTXIJR
Jun 20000.0009-0.0263
Jul 2000-0.0032-0.0143
Aug 20000.01820.0345
Sep 20000.01830.0007
Oct 20000.00260.0329
Nov 2000-0.0012-0.0371
Dec 20000.03660.0814
Jan 2001-0.0117-0.0309
Feb 20010.0053-0.0065
Mar 20010.02340.0106
Apr 2001-0.0149-0.0066
May 2001-0.0048-0.0273
Jun 20010.03100.0036
Jul 2001-0.00890.0111
Aug 2001-0.00120.0039
Sep 2001-0.0064-0.0162
Oct 2001-0.0110-0.0111
Nov 2001-0.0101-0.0182
Dec 2001-0.0049-0.0005
Jan 2002-0.0263-0.0124
Feb 2002-0.0022-0.0041
Mar 20020.0014-0.0007
Apr 2002-0.00750.0171
May 2002-0.0120-0.0189
Jun 2002-0.0124-0.0182
Jul 2002-0.0273-0.0324
Aug 20020.00940.0115
Sep 2002-0.00180.0117
Oct 20020.0025-0.0045
Nov 20020.02070.0031
Dec 2002-0.0218-0.0084
Jan 2003-0.0105-0.0127
Feb 2003-0.0098-0.0153
Mar 2003-0.0020-0.0065
Apr 20030.02220.0165
May 20030.0148-0.0063
Jun 2003-0.0090-0.0063
Jul 20030.0016-0.0030
Aug 20030.00250.0051
Sep 2003-0.0249-0.0354
Oct 2003-0.0089-0.0074
Nov 2003-0.0109-0.0081
Dec 2003-0.0025-0.0130
Jan 2004-0.0035-0.0104
Feb 2004-0.00310.0058
Mar 2004-0.00480.0052
Apr 20040.00850.0045
May 2004-0.00340.0087
Jun 20040.00040.0119
Jul 2004-0.0186-0.0112
Aug 2004-0.0077-0.0043
Sep 20040.00620.0108
Oct 2004-0.00080.0011
Nov 2004-0.00330.0012
Dec 2004-0.0063-0.0206
Jan 2005-0.00480.0076
Feb 2005-0.00590.0017
Mar 2005-0.0034-0.0043
Apr 2005-0.00310.0000
May 20050.00820.0060
Jun 2005-0.0027-0.0029
Jul 20050.00730.0038
Aug 20050.00410.0026
Sep 20050.00450.0061
Oct 20050.0044-0.0025
Nov 20050.00190.0067
Dec 2005-0.0017-0.0071
Jan 20060.00810.0053
Feb 20060.00660.0060
Mar 2006-0.00200.0056
Apr 2006-0.0012-0.0030
May 2006-0.0061-0.0008
Jun 2006-0.0038-0.0021
Jul 2006-0.0102-0.0122
Aug 20060.0003-0.0076
Sep 2006-0.0034-0.0055
Oct 20060.00290.0009
Nov 2006-0.0066-0.0037
Dec 2006-0.0011-0.0084
Jan 2007-0.00440.0013
Feb 2007-0.0009-0.0003
Mar 20070.00150.0076
Apr 2007-0.00390.0005
May 2007-0.00270.0017
Jun 2007-0.0005-0.0059
Jul 20070.00570.0124
Aug 20070.01110.0152
Sep 2007-0.00250.0015
Oct 2007-0.0006-0.0015
Nov 20070.00540.0026
Dec 20070.0021-0.0086
Jan 2008-0.00250.0124
Feb 2008-0.00620.0001
Mar 20080.01190.0050
Apr 2008-0.00110.0125
May 2008-0.0013-0.0061
Jun 20080.00090.0134
Jul 20080.01630.0038
Aug 2008-0.0077-0.0044
Sep 20080.01120.0185
Oct 20080.01730.0124
Nov 20080.0093-0.0011
Dec 2008-0.00120.0044
Jan 2009-0.0333-0.0362
Feb 2009-0.0005-0.0015
Mar 20090.0131-0.0196
Apr 20090.01410.0227
May 2009-0.0242-0.0311
Jun 20090.0037-0.0061
Jul 2009-0.0008-0.0033
Aug 2009-0.0001-0.0058
Sep 2009-0.0109-0.0181
Oct 2009-0.0116-0.0061
Nov 2009-0.0078-0.0087
Dec 20090.00390.0072
Jan 20100.00250.0033
Feb 2010-0.0024-0.0099
Mar 2010-0.00140.0003
Apr 20100.00530.0028
May 20100.01470.0203
Jun 20100.00450.0112
Jul 20100.0017-0.0043
Aug 2010-0.0017-0.0030
Sep 20100.0075-0.0068
Oct 2010-0.0054-0.0030
Nov 20100.00770.0076
Dec 2010-0.00080.0014
Jan 2011-0.0029-0.0031
Feb 20110.0036-0.0054
Mar 20110.00970.0107
Apr 2011-0.00090.0002
May 20110.00010.0078
Jun 20110.0064-0.0003
Jul 20110.00130.0048
Aug 2011-0.0071-0.0049
Sep 2011-0.0061-0.0088
Oct 20110.01390.0185
Nov 2011-0.00130.0041
Dec 2011-0.00190.0024
Jan 2012-0.00140.0063
Feb 2012-0.0038-0.0105
Mar 20120.00050.0022
Apr 2012-0.0006-0.0010
May 20120.00250.0002
Jun 2012-0.0060-0.0050
Jul 2012-0.0000-0.0014
Aug 20120.00060.0058
Sep 2012-0.0010-0.0087
Oct 20120.01200.0027
Nov 20120.00170.0023
Dec 20120.00410.0072
Jan 2013-0.0020-0.0036
Feb 20130.00060.0042
Mar 20130.0030-0.0023
Apr 2013-0.00330.0035
May 20130.0064-0.0003
Jun 20130.0008-0.0000
Jul 20130.0002-0.0009
Aug 20130.00050.0112
Sep 20130.00230.0056
Oct 2013-0.0034-0.0043
Nov 20130.00640.0031
Dec 2013-0.0039-0.0080
Jan 2014-0.00040.0112
Feb 2014-0.0033-0.0032
Mar 2014-0.0035-0.0067
Apr 2014-0.0002-0.0016
May 2014-0.0024-0.0072
Jun 2014-0.00400.0013
Jul 2014-0.0051-0.0045
Aug 20140.0029-0.0005
Sep 20140.01010.0058
Oct 20140.01390.0204
Nov 20140.0037-0.0063
Dec 20140.01160.0185
Jan 20150.00380.0128
Feb 2015-0.0027-0.0070
Mar 20150.01650.0173
Apr 2015-0.0227-0.0228
May 20150.01120.0098
Jun 20150.01560.0151
Jul 20150.01910.0210
Aug 20150.0023-0.0019
Sep 20150.02060.0133
Oct 2015-0.0086-0.0082
Nov 20150.01170.0149
Dec 20150.00180.0061
Jan 20160.0130-0.0000
Feb 2016-0.0046-0.0074
Mar 2016-0.0153-0.0074
Apr 2016-0.0215-0.0127
May 20160.01000.0139
Jun 2016-0.0123-0.0017
Jul 2016-0.0075-0.0047
Aug 20160.0002-0.0004
Sep 2016-0.00460.0043
Oct 20160.0117-0.0064
Nov 20160.02000.0236
Dec 2016-0.0028-0.0013
Jan 2017-0.0094-0.0110
Feb 2017-0.00130.0018
Mar 2017-0.0045-0.0026
Apr 20170.00150.0002
May 2017-0.0027-0.0017
Jun 2017-0.00190.0053
Jul 20170.00190.0044
Aug 2017-0.0052-0.0058
Sep 20170.01000.0201
Oct 20170.0025-0.0028
Nov 2017-0.0040-0.0026
Dec 2017-0.0054-0.0054
Jan 2018-0.0037-0.0023
Feb 20180.00210.0087
Mar 20180.00150.0152
Apr 2018-0.0058-0.0006
May 2018-0.00680.0112
Jun 2018-0.0038-0.0015
Jul 20180.00500.0127
Aug 20180.00200.0155
Sep 2018-0.0045-0.0123
Oct 2018-0.0029-0.0191
Nov 20180.00500.0085
Dec 20180.00390.0028
Jan 2019-0.00730.0002
Feb 2019-0.0030-0.0028
Mar 2019-0.0064-0.0081