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
Asset 1
%
Asset 2
%
Asset 3
%
Asset 4
%
Asset 5
%
Asset 6
%
Asset 7
%
Asset 8
%
Asset 9
%
Asset 10
%
Total
%

Factor Analysis Results

Portfolio Regression Results

Factor regression results for the portfolio
Portfolio 50.00% Vanguard FTSE Developed Markets ETF (VEA)
50.00% DFA International Small Cap Value I (DISVX)
Time Period Aug 2007 - Oct 2020
Regression Basis 159 monthly samples
Coefficient of Determination (R2) 97.8%
Adjusted R2 97.7%
Regression F statistic 1,340.27 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.692 with p-value 1.000)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 11.206 with p-value 0.047)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.08 0.017 63.406 0.000 1.049...1.116
Size (SMB) 0.14 0.042 3.419 0.001 0.061...0.226
Value (HML) 0.19 0.053 3.550 0.001 0.083...0.293
Profitability (RMW) 0.13 0.077 1.750 0.082 -0.017...0.285
Investment (CMA) 0.11 0.062 1.823 0.070 -0.009...0.236
Alpha (α) -6.60bps 0.001 -0.915 0.362 -0.21%...0.08%
Annualized Alpha (α) -0.79%  
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) 24.75 7.69 -20.22 37.93 -0.33  
Name Start Date End Date Annual Alpha Rm-Rf SMB HML RMW CMA Total R2
Portfolio Aug 2007 Oct 2020 -0.79% 26.80 1.10 -3.80 5.08 -0.04 22.54 97.8%
Regression residuals
MonthPortfolio
Aug 20070.0055
Sep 2007-0.0167
Oct 2007-0.0016
Nov 2007-0.0103
Dec 2007-0.0112
Jan 20080.0221
Feb 2008-0.0174
Mar 20080.0170
Apr 2008-0.0165
May 2008-0.0018
Jun 2008-0.0067
Jul 2008-0.0020
Aug 20080.0096
Sep 20080.0150
Oct 20080.0057
Nov 2008-0.0050
Dec 20080.0174
Jan 2009-0.0123
Feb 20090.0064
Mar 20090.0159
Apr 20090.0100
May 2009-0.0094
Jun 2009-0.0084
Jul 2009-0.0028
Aug 20090.0113
Sep 2009-0.0086
Oct 2009-0.0137
Nov 20090.0035
Dec 2009-0.0058
Jan 20100.0017
Feb 20100.0050
Mar 2010-0.0016
Apr 2010-0.0077
May 2010-0.0043
Jun 2010-0.0017
Jul 20100.0067
Aug 2010-0.0008
Sep 2010-0.0041
Oct 2010-0.0056
Nov 20100.0079
Dec 20100.0106
Jan 2011-0.0091
Feb 2011-0.0026
Mar 20110.0074
Apr 2011-0.0056
May 2011-0.0009
Jun 2011-0.0049
Jul 2011-0.0071
Aug 20110.0023
Sep 2011-0.0118
Oct 20110.0051
Nov 20110.0241
Dec 2011-0.0128
Jan 20120.0148
Feb 2012-0.0003
Mar 20120.0013
Apr 2012-0.0103
May 2012-0.0021
Jun 2012-0.0027
Jul 2012-0.0040
Aug 20120.0038
Sep 2012-0.0013
Oct 20120.0016
Nov 20120.0029
Dec 20120.0095
Jan 2013-0.0167
Feb 20130.0069
Mar 20130.0087
Apr 2013-0.0096
May 2013-0.0064
Jun 20130.0096
Jul 20130.0045
Aug 2013-0.0048
Sep 20130.0095
Oct 2013-0.0019
Nov 2013-0.0019
Dec 20130.0088
Jan 2014-0.0059
Feb 20140.0076
Mar 20140.0003
Apr 2014-0.0048
May 2014-0.0014
Jun 2014-0.0046
Jul 2014-0.0080
Aug 20140.0075
Sep 2014-0.0020
Oct 20140.0126
Nov 2014-0.0066
Dec 20140.0064
Jan 20150.0047
Feb 20150.0102
Mar 2015-0.0015
Apr 2015-0.0094
May 20150.0133
Jun 20150.0026
Jul 20150.0006
Aug 20150.0083
Sep 20150.0105
Oct 2015-0.0113
Nov 20150.0083
Dec 2015-0.0005
Jan 20160.0066
Feb 2016-0.0104
Mar 2016-0.0011
Apr 2016-0.0108
May 20160.0085
Jun 2016-0.0069
Jul 2016-0.0003
Aug 20160.0011
Sep 20160.0021
Oct 2016-0.0064
Nov 20160.0102
Dec 2016-0.0043
Jan 2017-0.0018
Feb 20170.0029
Mar 2017-0.0056
Apr 2017-0.0046
May 2017-0.0097
Jun 20170.0054
Jul 2017-0.0051
Aug 2017-0.0024
Sep 20170.0032
Oct 2017-0.0024
Nov 2017-0.0032
Dec 20170.0014
Jan 2018-0.0061
Feb 2018-0.0060
Mar 20180.0070
Apr 2018-0.0038
May 20180.0013
Jun 2018-0.0017
Jul 20180.0006
Aug 20180.0026
Sep 2018-0.0045
Oct 2018-0.0038
Nov 2018-0.0042
Dec 2018-0.0094
Jan 20190.0069
Feb 20190.0040
Mar 2019-0.0053
Apr 20190.0031
May 2019-0.0144
Jun 20190.0031
Jul 2019-0.0008
Aug 20190.0093
Sep 20190.0012
Oct 2019-0.0007
Nov 20190.0024
Dec 20190.0048
Jan 2020-0.0090
Feb 20200.0150
Mar 2020-0.0231
Apr 20200.0203
May 20200.0059
Jun 2020-0.0034
Jul 20200.0066
Aug 2020-0.0051
Sep 20200.0049
Oct 2020-0.0005