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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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% -1.69% 97.2%
iShares Core S&P Small-Cap ETF IJR Jun 2000 Mar 2019 1.13 0.87 0.33 0.43 -0.19% -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
Regression Basis 226 monthly samples
Coefficient of Determination (R2) 97.2%
Adjusted R2 97.1%
Regression F statistic 1,908.17 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.912 with p-value 0.247)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 5.722 with p-value 0.221)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
AQR-MKT-RF Market 1.12 0.025 44.289 0.000 1.068...1.168
AQR-SMB Size 0.93 0.036 25.673 0.000 0.863...1.006
AQR-HML Value 0.27 0.044 6.088 0.000 0.182...0.357
AQR-QMJ Quality 0.27 0.047 5.613 0.000 0.173...0.360
Alpha Alpha -14.05bps 0.001 -1.935 0.054 -0.28%...0.00%
Annualized Alpha Annualized Alpha -1.69%  

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
Regression Basis 226 monthly samples
Coefficient of Determination (R2) 94.5%
Adjusted R2 94.4%
Regression F statistic 948.00 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.378 with p-value 0.998)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 4.056 with p-value 0.398)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
AQR-MKT-RF Market 1.13 0.030 37.744 0.000 1.068...1.186
AQR-SMB Size 0.87 0.054 16.058 0.000 0.759...0.971
AQR-HML Value 0.33 0.041 8.136 0.000 0.252...0.413
AQR-QMJ Quality 0.43 0.043 9.949 0.000 0.344...0.514
Alpha Alpha -18.51bps 0.001 -2.072 0.039 -0.36%...-0.01%
Annualized Alpha 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) 47.09 22.92 14.35 46.27  
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 -1.69% 52.65 21.42 3.86 12.33 76.20 97.2%
iShares Core S&P Small-Cap ETF IJR Jun 2000 Mar 2019 -2.22% 53.06 19.83 4.77 19.84 78.98 94.5%
Regression residuals
MonthDFSTXIJR
Jun 20000.0009-0.0263
Jul 2000-0.0031-0.0141
Aug 20000.01810.0345
Sep 20000.01770.0001
Oct 20000.00290.0332
Nov 2000-0.0013-0.0371
Dec 20000.03690.0817
Jan 2001-0.0116-0.0307
Feb 20010.0051-0.0068
Mar 20010.02330.0105
Apr 2001-0.0147-0.0064
May 2001-0.0046-0.0271
Jun 20010.03120.0038
Jul 2001-0.00900.0109
Aug 2001-0.00100.0040
Sep 2001-0.0058-0.0155
Oct 2001-0.0111-0.0111
Nov 2001-0.0101-0.0181
Dec 2001-0.0050-0.0007
Jan 2002-0.0262-0.0123
Feb 2002-0.0022-0.0041
Mar 20020.0012-0.0009
Apr 2002-0.00770.0169
May 2002-0.0120-0.0190
Jun 2002-0.0118-0.0176
Jul 2002-0.0273-0.0324
Aug 20020.00810.0102
Sep 2002-0.00200.0116
Oct 20020.0025-0.0045
Nov 20020.02080.0032
Dec 2002-0.0222-0.0086
Jan 2003-0.0103-0.0124
Feb 2003-0.0099-0.0153
Mar 2003-0.0018-0.0062
Apr 20030.02210.0163
May 20030.0145-0.0065
Jun 2003-0.0088-0.0061
Jul 20030.0017-0.0029
Aug 20030.00240.0050
Sep 2003-0.0249-0.0354
Oct 2003-0.0083-0.0069
Nov 2003-0.0108-0.0081
Dec 2003-0.0026-0.0132
Jan 2004-0.0037-0.0106
Feb 2004-0.00280.0061
Mar 2004-0.00480.0053
Apr 20040.00830.0043
May 2004-0.00340.0087
Jun 20040.00050.0121
Jul 2004-0.0186-0.0112
Aug 2004-0.0078-0.0044
Sep 20040.00620.0107
Oct 2004-0.00090.0010
Nov 2004-0.00330.0011
Dec 2004-0.0060-0.0204
Jan 2005-0.00480.0076
Feb 2005-0.00580.0019
Mar 2005-0.0034-0.0044
Apr 2005-0.00320.0000
May 20050.00830.0061
Jun 2005-0.0028-0.0030
Jul 20050.00730.0038
Aug 20050.00390.0024
Sep 20050.00520.0070
Oct 20050.0041-0.0028
Nov 20050.00200.0067
Dec 2005-0.0017-0.0071
Jan 20060.00850.0058
Feb 20060.00650.0060
Mar 2006-0.00180.0059
Apr 2006-0.0014-0.0032
May 2006-0.0062-0.0009
Jun 2006-0.0038-0.0021
Jul 2006-0.0102-0.0122
Aug 20060.0004-0.0075
Sep 2006-0.0034-0.0055
Oct 20060.00290.0009
Nov 2006-0.0067-0.0038
Dec 2006-0.0011-0.0084
Jan 2007-0.00430.0014
Feb 2007-0.0008-0.0003
Mar 20070.00140.0075
Apr 2007-0.00390.0005
May 2007-0.00280.0017
Jun 2007-0.0005-0.0059
Jul 20070.00570.0123
Aug 20070.01110.0153
Sep 2007-0.00250.0014
Oct 2007-0.0005-0.0014
Nov 20070.00540.0025
Dec 20070.0019-0.0088
Jan 2008-0.00240.0126
Feb 2008-0.0065-0.0003
Mar 20080.01200.0051
Apr 2008-0.00120.0125
May 2008-0.0013-0.0061
Jun 20080.00080.0132
Jul 20080.01630.0038
Aug 2008-0.0077-0.0043
Sep 20080.01150.0187
Oct 20080.01720.0121
Nov 20080.0093-0.0011
Dec 2008-0.00120.0043
Jan 2009-0.0334-0.0364
Feb 2009-0.0008-0.0020
Mar 20090.0132-0.0196
Apr 20090.01390.0226
May 2009-0.0245-0.0314
Jun 20090.0035-0.0063
Jul 2009-0.0009-0.0033
Aug 2009-0.0005-0.0064
Sep 2009-0.0104-0.0177
Oct 2009-0.0121-0.0066
Nov 2009-0.0073-0.0083
Dec 20090.00380.0071
Jan 20100.00250.0033
Feb 2010-0.0026-0.0101
Mar 2010-0.00130.0005
Apr 20100.00550.0030
May 20100.01440.0200
Jun 20100.00450.0112
Jul 20100.0017-0.0042
Aug 2010-0.0018-0.0031
Sep 20100.0075-0.0068
Oct 2010-0.0051-0.0028
Nov 20100.00750.0073
Dec 2010-0.00060.0015
Jan 2011-0.0028-0.0030
Feb 20110.0036-0.0054
Mar 20110.00970.0107
Apr 2011-0.00080.0003
May 20110.00010.0078
Jun 20110.0064-0.0003
Jul 20110.00150.0050
Aug 2011-0.0067-0.0045
Sep 2011-0.0062-0.0090
Oct 20110.01390.0185
Nov 2011-0.00120.0043
Dec 2011-0.00180.0025
Jan 2012-0.00150.0063
Feb 2012-0.0039-0.0108
Mar 20120.00070.0025
Apr 2012-0.0004-0.0007
May 20120.00290.0007
Jun 2012-0.0059-0.0049
Jul 2012-0.0003-0.0017
Aug 20120.00080.0060
Sep 2012-0.0012-0.0089
Oct 20120.01210.0028
Nov 20120.00180.0025
Dec 20120.00390.0070
Jan 2013-0.0020-0.0036
Feb 20130.00040.0040
Mar 20130.0027-0.0027
Apr 2013-0.00360.0032
May 20130.0066-0.0001
Jun 20130.00090.0000
Jul 20130.0004-0.0007
Aug 20130.00060.0113
Sep 20130.00230.0056
Oct 2013-0.0031-0.0040
Nov 20130.00630.0030
Dec 2013-0.0038-0.0080
Jan 2014-0.00060.0110
Feb 2014-0.0033-0.0032
Mar 2014-0.0034-0.0067
Apr 2014-0.0001-0.0015
May 2014-0.0025-0.0073
Jun 2014-0.00400.0013
Jul 2014-0.0051-0.0045
Aug 20140.0028-0.0008
Sep 20140.01000.0057
Oct 20140.01400.0204
Nov 20140.0036-0.0064
Dec 20140.01140.0183
Jan 20150.00380.0128
Feb 2015-0.0027-0.0070
Mar 20150.01640.0172
Apr 2015-0.0227-0.0228
May 20150.01120.0098
Jun 20150.01550.0151
Jul 20150.01900.0210
Aug 20150.0025-0.0018
Sep 20150.02060.0133
Oct 2015-0.0088-0.0085
Nov 20150.01150.0148
Dec 20150.00200.0062
Jan 20160.0129-0.0002
Feb 2016-0.0046-0.0074
Mar 2016-0.0151-0.0072
Apr 2016-0.0215-0.0126
May 20160.01000.0140
Jun 2016-0.0122-0.0017
Jul 2016-0.0073-0.0045
Aug 2016-0.0002-0.0010
Sep 2016-0.00480.0040
Oct 20160.0117-0.0064
Nov 20160.01940.0230
Dec 2016-0.0026-0.0011
Jan 2017-0.0098-0.0113
Feb 2017-0.00140.0016
Mar 2017-0.0050-0.0030
Apr 20170.0012-0.0001
May 2017-0.0025-0.0015
Jun 2017-0.00180.0054
Jul 20170.00220.0048
Aug 2017-0.0050-0.0054
Sep 20170.00970.0197
Oct 20170.0026-0.0026
Nov 2017-0.0039-0.0025
Dec 2017-0.0053-0.0053
Jan 2018-0.0034-0.0020
Feb 20180.00290.0095
Mar 20180.00090.0144
Apr 2018-0.0056-0.0006
May 2018-0.00660.0115
Jun 2018-0.0040-0.0017
Jul 20180.00490.0123
Aug 20180.00220.0157
Sep 2018-0.0043-0.0120
Oct 2018-0.0027-0.0189
Nov 20180.00520.0089
Dec 20180.00440.0036
Jan 2019-0.0076-0.0003
Feb 2019-0.0031-0.0028
Mar 2019-0.0063-0.0081