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

Schwab Fdmtl Intl Sm Co Idx

Factor regression results for Schwab Fdmtl Intl Sm Co Idx
Ticker SFILX
Time Period Feb 2008 - Feb 2019
Coefficient of Determination (R2) 96.4%
Adjusted R2 96.3%
Regression F statistic 685.80 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.154 with p-value 0.798)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 19.077 with p-value 0.002)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.04 0.024 43.180 0.000 0.995...1.091
Size (SMB) 0.42 0.060 7.053 0.000 0.304...0.541
Value (HML) 0.17 0.074 2.249 0.026 0.020...0.315
Profitability (RMW) 0.27 0.108 2.499 0.014 0.056...0.482
Investment (CMA) 0.02 0.079 0.292 0.771 -0.133...0.179
Alpha (α) 2.34bps 0.001 0.233 0.816 -0.18%...0.22%
Annualized Alpha (α) 0.28%  
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.
  • 5-factor model: Ra = Rrf + Bmkt × ( Rmkt - Rrf ) + Bsmb × SMB + Bhml × HML + Brmw × RMW + Bcma × CMA + α
  • Symbols:
    Ra
    Asset return
    Rrf
    Risk free return
    Bmkt
    Market loading factor (exposure to market risk, different from CAPM beta)
    Rmkt
    Market return
    Bsmb
    Size loading factor (the level of exposure to size risk)
    SMB
    Small Minus Big: The size premium
    Bhml
    Value loading factor (the level of exposure to value risk)
    HML
    High Minus Low: The value premium
    Brmw
    Profitability loading factor
    RMW
    Robust Minus Weak: The profitability premium
    Bcma
    Investment loading factor
    CMA
    Conservative Minus Aggressive: The conservative investment premium
    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) 33.92 15.71 1.63 34.86 11.80  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML RMW CMA Total R2
Schwab Fdmtl Intl Sm Co Idx SFILX Feb 2008 Feb 2019 0.28% 35.39 6.64 0.27 9.38 0.27 54.30 96.4%
Regression residuals
MonthSFILX
Feb 2008-0.0262
Mar 20080.0186
Apr 2008-0.0201
May 2008-0.0041
Jun 2008-0.0114
Jul 20080.0079
Aug 20080.0103
Sep 20080.0167
Oct 20080.0016
Nov 20080.0178
Dec 20080.0200
Jan 2009-0.0070
Feb 2009-0.0083
Mar 20090.0187
Apr 20090.0481
May 20090.0123
Jun 2009-0.0030
Jul 2009-0.0074
Aug 20090.0207
Sep 2009-0.0022
Oct 2009-0.0175
Nov 2009-0.0009
Dec 2009-0.0021
Jan 2010-0.0031
Feb 20100.0031
Mar 20100.0003
Apr 2010-0.0005
May 2010-0.0013
Jun 20100.0104
Jul 20100.0013
Aug 2010-0.0020
Sep 20100.0028
Oct 2010-0.0085
Nov 20100.0038
Dec 20100.0071
Jan 2011-0.0111
Feb 2011-0.0104
Mar 20110.0075
Apr 2011-0.0103
May 20110.0003
Jun 20110.0066
Jul 20110.0035
Aug 20110.0093
Sep 2011-0.0103
Oct 2011-0.0099
Nov 20110.0220
Dec 2011-0.0203
Jan 20120.0085
Feb 2012-0.0087
Mar 2012-0.0020
Apr 2012-0.0107
May 20120.0002
Jun 2012-0.0016
Jul 2012-0.0138
Aug 20120.0004
Sep 2012-0.0028
Oct 2012-0.0005
Nov 20120.0015
Dec 20120.0061
Jan 2013-0.0191
Feb 20130.0092
Mar 20130.0104
Apr 2013-0.0013
May 2013-0.0205
Jun 20130.0198
Jul 2013-0.0038
Aug 2013-0.0085
Sep 20130.0073
Oct 2013-0.0071
Nov 2013-0.0032
Dec 20130.0012
Jan 2014-0.0089
Feb 2014-0.0010
Mar 2014-0.0092
Apr 2014-0.0043
May 20140.0033
Jun 2014-0.0021
Jul 2014-0.0023
Aug 20140.0032
Sep 2014-0.0032
Oct 20140.0162
Nov 2014-0.0111
Dec 20140.0097
Jan 20150.0078
Feb 20150.0093
Mar 2015-0.0006
Apr 2015-0.0144
May 20150.0027
Jun 20150.0013
Jul 20150.0020
Aug 20150.0099
Sep 20150.0032
Oct 2015-0.0031
Nov 20150.0069
Dec 2015-0.0045
Jan 20160.0120
Feb 2016-0.0041
Mar 2016-0.0055
Apr 2016-0.0097
May 20160.0167
Jun 2016-0.0004
Jul 2016-0.0002
Aug 2016-0.0063
Sep 20160.0063
Oct 2016-0.0028
Nov 20160.0050
Dec 2016-0.0079
Jan 2017-0.0047
Feb 20170.0022
Mar 2017-0.0080
Apr 20170.0026
May 2017-0.0114
Jun 20170.0008
Jul 2017-0.0029
Aug 2017-0.0027
Sep 20170.0004
Oct 20170.0023
Nov 2017-0.0004
Dec 2017-0.0021
Jan 2018-0.0064
Feb 2018-0.0069
Mar 20180.0082
Apr 2018-0.0019
May 2018-0.0025
Jun 2018-0.0018
Jul 2018-0.0039
Aug 2018-0.0004
Sep 2018-0.0042
Oct 2018-0.0024
Nov 2018-0.0005
Dec 2018-0.0089
Jan 20190.0080
Feb 2019-0.0001