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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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% -2.21% 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 1,901.21 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.918 with p-value 0.263)
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 44.250 0.000 1.069...1.169
AQR-SMB Size 0.93 0.037 25.569 0.000 0.863...1.007
AQR-HML Value 0.27 0.045 6.035 0.000 0.181...0.356
AQR-QMJ Quality 0.27 0.048 5.622 0.000 0.174...0.362
Alpha Alpha -14.02bps 0.001 -1.931 0.055 -0.28%...0.00%
Annualized Alpha 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
Regression Basis 226 monthly samples
Coefficient of Determination (R2) 94.5%
Adjusted R2 94.4%
Regression F statistic 943.71 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.381 with p-value 0.998)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.962 with p-value 0.411)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
AQR-MKT-RF Market 1.13 0.030 37.761 0.000 1.068...1.186
AQR-SMB Size 0.87 0.054 15.935 0.000 0.759...0.973
AQR-HML Value 0.33 0.041 8.035 0.000 0.250...0.412
AQR-QMJ Quality 0.43 0.043 9.962 0.000 0.344...0.514
Alpha Alpha -18.42bps 0.001 -2.059 0.041 -0.36%...-0.01%
Annualized Alpha Annualized Alpha -2.21%  
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 22.82 14.01 46.42  
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% 52.68 21.33 3.76 12.44 76.20 97.2%
iShares Core S&P Small-Cap ETF IJR Jun 2000 Mar 2019 -2.21% 53.08 19.75 4.64 19.94 78.98 94.5%
Regression residuals
MonthDFSTXIJR
Jun 20000.08%-2.63%
Jul 2000-0.30%-1.40%
Aug 20001.81%3.45%
Sep 20001.77%0.01%
Oct 20000.29%3.34%
Nov 2000-0.12%-3.70%
Dec 20003.70%8.18%
Jan 2001-1.19%-3.11%
Feb 20010.52%-0.67%
Mar 20012.34%1.07%
Apr 2001-1.49%-0.66%
May 2001-0.46%-2.71%
Jun 20013.11%0.38%
Jul 2001-0.90%1.09%
Aug 2001-0.11%0.39%
Sep 2001-0.58%-1.56%
Oct 2001-1.11%-1.12%
Nov 2001-1.01%-1.82%
Dec 2001-0.50%-0.06%
Jan 2002-2.62%-1.22%
Feb 2002-0.22%-0.41%
Mar 20020.12%-0.09%
Apr 2002-0.76%1.69%
May 2002-1.21%-1.90%
Jun 2002-1.18%-1.75%
Jul 2002-2.73%-3.24%
Aug 20020.81%1.02%
Sep 2002-0.20%1.15%
Oct 20020.25%-0.45%
Nov 20022.08%0.32%
Dec 2002-2.22%-0.86%
Jan 2003-1.03%-1.24%
Feb 2003-0.99%-1.54%
Mar 2003-0.18%-0.62%
Apr 20032.21%1.63%
May 20031.46%-0.65%
Jun 2003-0.88%-0.61%
Jul 20030.17%-0.29%
Aug 20030.24%0.50%
Sep 2003-2.49%-3.54%
Oct 2003-0.84%-0.69%
Nov 2003-1.09%-0.82%
Dec 2003-0.26%-1.31%
Jan 2004-0.37%-1.06%
Feb 2004-0.28%0.61%
Mar 2004-0.48%0.52%
Apr 20040.83%0.43%
May 2004-0.34%0.87%
Jun 20040.04%1.21%
Jul 2004-1.86%-1.12%
Aug 2004-0.78%-0.44%
Sep 20040.61%1.07%
Oct 2004-0.09%0.10%
Nov 2004-0.33%0.11%
Dec 2004-0.60%-2.04%
Jan 2005-0.48%0.76%
Feb 2005-0.58%0.19%
Mar 2005-0.34%-0.44%
Apr 2005-0.31%0.00%
May 20050.83%0.61%
Jun 2005-0.28%-0.30%
Jul 20050.72%0.37%
Aug 20050.39%0.24%
Sep 20050.53%0.70%
Oct 20050.41%-0.28%
Nov 20050.19%0.66%
Dec 2005-0.17%-0.71%
Jan 20060.85%0.58%
Feb 20060.65%0.59%
Mar 2006-0.18%0.58%
Apr 2006-0.13%-0.32%
May 2006-0.61%-0.09%
Jun 2006-0.38%-0.21%
Jul 2006-1.02%-1.23%
Aug 20060.04%-0.76%
Sep 2006-0.34%-0.55%
Oct 20060.29%0.09%
Nov 2006-0.67%-0.39%
Dec 2006-0.10%-0.84%
Jan 2007-0.43%0.14%
Feb 2007-0.08%-0.03%
Mar 20070.14%0.75%
Apr 2007-0.39%0.05%
May 2007-0.28%0.16%
Jun 2007-0.05%-0.59%
Jul 20070.56%1.22%
Aug 20071.11%1.52%
Sep 2007-0.25%0.14%
Oct 2007-0.05%-0.15%
Nov 20070.54%0.25%
Dec 20070.19%-0.88%
Jan 2008-0.23%1.26%
Feb 2008-0.65%-0.03%
Mar 20081.19%0.51%
Apr 2008-0.12%1.24%
May 2008-0.14%-0.61%
Jun 20080.07%1.31%
Jul 20081.62%0.38%
Aug 2008-0.78%-0.44%
Sep 20081.14%1.87%
Oct 20081.72%1.21%
Nov 20080.92%-0.12%
Dec 2008-0.12%0.42%
Jan 2009-3.35%-3.66%
Feb 2009-0.09%-0.21%
Mar 20091.32%-1.96%
Apr 20091.39%2.26%
May 2009-2.45%-3.13%
Jun 20090.34%-0.64%
Jul 2009-0.08%-0.33%
Aug 2009-0.04%-0.63%
Sep 2009-1.04%-1.77%
Oct 2009-1.22%-0.66%
Nov 2009-0.74%-0.84%
Dec 20090.37%0.70%
Jan 20100.25%0.33%
Feb 2010-0.26%-1.01%
Mar 2010-0.13%0.05%
Apr 20100.55%0.30%
May 20101.44%2.00%
Jun 20100.44%1.11%
Jul 20100.17%-0.42%
Aug 2010-0.18%-0.31%
Sep 20100.74%-0.69%
Oct 2010-0.52%-0.28%
Nov 20100.75%0.73%
Dec 2010-0.06%0.15%
Jan 2011-0.28%-0.30%
Feb 20110.36%-0.54%
Mar 20110.97%1.07%
Apr 2011-0.09%0.02%
May 20110.01%0.78%
Jun 20110.64%-0.03%
Jul 20110.14%0.48%
Aug 2011-0.69%-0.47%
Sep 2011-0.60%-0.88%
Oct 20111.38%1.85%
Nov 2011-0.14%0.40%
Dec 2011-0.17%0.26%
Jan 2012-0.11%0.67%
Feb 2012-0.42%-1.10%
Mar 20120.04%0.20%
Apr 2012-0.04%-0.08%
May 20120.26%0.04%
Jun 2012-0.56%-0.46%
Jul 2012-0.00%-0.14%
Aug 20120.06%0.58%
Sep 2012-0.11%-0.89%
Oct 20121.22%0.29%
Nov 20120.18%0.24%
Dec 20120.40%0.71%
Jan 2013-0.20%-0.36%
Feb 20130.04%0.40%
Mar 20130.31%-0.22%
Apr 2013-0.39%0.30%
May 20130.63%-0.04%
Jun 20130.08%0.00%
Jul 20130.01%-0.10%
Aug 20130.04%1.11%
Sep 20130.23%0.56%
Oct 2013-0.34%-0.42%
Nov 20130.62%0.30%
Dec 2013-0.39%-0.81%
Jan 2014-0.03%1.13%
Feb 2014-0.33%-0.33%
Mar 2014-0.38%-0.72%
Apr 2014-0.03%-0.16%
May 2014-0.25%-0.74%
Jun 2014-0.41%0.12%
Jul 2014-0.51%-0.46%
Aug 20140.29%-0.06%
Sep 20141.01%0.58%
Oct 20141.40%2.05%
Nov 20140.37%-0.63%
Dec 20141.16%1.85%
Jan 20150.41%1.31%
Feb 2015-0.29%-0.73%
Mar 20151.65%1.73%
Apr 2015-2.27%-2.28%
May 20151.13%0.98%
Jun 20151.53%1.47%
Jul 20151.90%2.09%
Aug 20150.20%-0.22%
Sep 20152.10%1.38%
Oct 2015-0.87%-0.83%
Nov 20151.19%1.51%
Dec 20150.21%0.64%
Jan 20161.30%0.00%
Feb 2016-0.36%-0.60%
Mar 2016-1.48%-0.68%
Apr 2016-2.14%-1.25%
May 20160.98%1.37%
Jun 2016-1.23%-0.17%
Jul 2016-0.74%-0.46%
Aug 2016-0.01%-0.09%
Sep 2016-0.45%0.43%
Oct 20161.16%-0.64%
Nov 20161.99%2.36%
Dec 2016-0.30%-0.17%
Jan 2017-0.98%-1.14%
Feb 2017-0.12%0.18%
Mar 2017-0.48%-0.30%
Apr 20170.13%-0.00%
May 2017-0.25%-0.14%
Jun 2017-0.14%0.58%
Jul 20170.26%0.52%
Aug 2017-0.56%-0.60%
Sep 20171.01%2.01%
Oct 20170.26%-0.26%
Nov 2017-0.38%-0.25%
Dec 2017-0.55%-0.58%
Jan 2018-0.35%-0.21%
Feb 20180.20%0.86%
Mar 20180.14%1.51%
Apr 2018-0.62%-0.11%
May 2018-0.70%1.14%
Jun 2018-0.38%-0.16%
Jul 20180.48%1.23%
Aug 20180.39%1.85%
Sep 2018-0.46%-1.22%
Oct 2018-0.23%-1.84%
Nov 20180.34%0.58%
Dec 20180.42%0.33%
Jan 2019-0.80%-0.07%
Feb 2019-0.28%-0.27%
Mar 2019-0.56%-0.71%