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

Schwab Fdmtl Intl Sm Co Idx

Factor regression results for Schwab Fdmtl Intl Sm Co Idx
Ticker SFILX
Time Period Feb 2008 - Feb 2019
Regression Basis 133 monthly samples
Coefficient of Determination (R2) 96.4%
Adjusted R2 96.3%
Regression F statistic 689.58 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.152 with p-value 0.795)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 17.555 with p-value 0.004)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.04 0.024 43.897 0.000 0.996...1.090
Size (SMB) 0.43 0.060 7.177 0.000 0.312...0.550
Value (HML) 0.16 0.074 2.201 0.030 0.017...0.310
Profitability (RMW) 0.27 0.106 2.563 0.012 0.062...0.484
Investment (CMA) 0.02 0.079 0.260 0.795 -0.136...0.177
Alpha (α) 2.32bps 0.001 0.232 0.817 -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 14.89 1.60 35.41 11.92  
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 6.42 0.26 9.66 0.25 54.30 96.4%
Regression residuals
MonthSFILX
Feb 2008-0.0257
Mar 20080.0189
Apr 2008-0.0198
May 2008-0.0043
Jun 2008-0.0111
Jul 20080.0079
Aug 20080.0103
Sep 20080.0165
Oct 20080.0009
Nov 20080.0195
Dec 20080.0200
Jan 2009-0.0064
Feb 2009-0.0087
Mar 20090.0177
Apr 20090.0483
May 20090.0126
Jun 2009-0.0031
Jul 2009-0.0073
Aug 20090.0212
Sep 2009-0.0025
Oct 2009-0.0180
Nov 2009-0.0007
Dec 2009-0.0020
Jan 2010-0.0030
Feb 20100.0028
Mar 20100.0008
Apr 2010-0.0020
May 2010-0.0016
Jun 20100.0098
Jul 20100.0010
Aug 2010-0.0017
Sep 20100.0020
Oct 2010-0.0085
Nov 20100.0042
Dec 20100.0070
Jan 2011-0.0105
Feb 2011-0.0097
Mar 20110.0073
Apr 2011-0.0108
May 20110.0001
Jun 20110.0074
Jul 20110.0035
Aug 20110.0088
Sep 2011-0.0094
Oct 2011-0.0100
Nov 20110.0218
Dec 2011-0.0197
Jan 20120.0083
Feb 2012-0.0091
Mar 2012-0.0016
Apr 2012-0.0115
May 20120.0000
Jun 2012-0.0011
Jul 2012-0.0142
Aug 20120.0003
Sep 2012-0.0029
Oct 2012-0.0003
Nov 20120.0016
Dec 20120.0064
Jan 2013-0.0193
Feb 20130.0090
Mar 20130.0098
Apr 2013-0.0009
May 2013-0.0202
Jun 20130.0198
Jul 2013-0.0035
Aug 2013-0.0086
Sep 20130.0067
Oct 2013-0.0068
Nov 2013-0.0031
Dec 20130.0015
Jan 2014-0.0089
Feb 2014-0.0009
Mar 2014-0.0093
Apr 2014-0.0043
May 20140.0034
Jun 2014-0.0024
Jul 2014-0.0024
Aug 20140.0034
Sep 2014-0.0030
Oct 20140.0161
Nov 2014-0.0110
Dec 20140.0094
Jan 20150.0078
Feb 20150.0094
Mar 2015-0.0006
Apr 2015-0.0143
May 20150.0026
Jun 20150.0011
Jul 20150.0022
Aug 20150.0096
Sep 20150.0031
Oct 2015-0.0030
Nov 20150.0068
Dec 2015-0.0048
Jan 20160.0120
Feb 2016-0.0039
Mar 2016-0.0058
Apr 2016-0.0095
May 20160.0164
Jun 2016-0.0008
Jul 2016-0.0005
Aug 2016-0.0061
Sep 20160.0060
Oct 2016-0.0025
Nov 20160.0055
Dec 2016-0.0077
Jan 2017-0.0045
Feb 20170.0019
Mar 2017-0.0081
Apr 20170.0026
May 2017-0.0117
Jun 20170.0008
Jul 2017-0.0025
Aug 2017-0.0030
Sep 20170.0005
Oct 20170.0025
Nov 2017-0.0001
Dec 2017-0.0021
Jan 2018-0.0062
Feb 2018-0.0072
Mar 20180.0082
Apr 2018-0.0015
May 2018-0.0029
Jun 2018-0.0014
Jul 2018-0.0035
Aug 2018-0.0004
Sep 2018-0.0041
Oct 2018-0.0026
Nov 2018-0.0006
Dec 2018-0.0086
Jan 20190.0072
Feb 2019-0.0002