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 Allocation

Portfolio Allocation
Ticker Name Allocation
VEA Vanguard FTSE Developed Markets ETF 50.00%
DISVX DFA International Small Cap Value I 50.00%
Save portfolio »

Portfolio Regression Results

Factor regression results for the portfolio
Time Period Aug 2007 - Dec 2020
Regression Basis 161 monthly samples
Coefficient of Determination (R2) 97.8%
Adjusted R2 97.8%
Regression F statistic 1,410.73 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.689 with p-value 1.000)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 11.128 with p-value 0.049)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.08 0.017 64.122 0.000 1.047...1.114
Size (SMB) 0.15 0.042 3.617 0.000 0.068...0.233
Value (HML) 0.18 0.052 3.436 0.001 0.076...0.282
Profitability (RMW) 0.13 0.076 1.722 0.087 -0.019...0.281
Investment (CMA) 0.12 0.062 1.861 0.065 -0.007...0.239
Alpha (α) -6.99bps 0.001 -0.971 0.333 -0.21%...0.07%
Annualized Alpha (α) -0.84%  

Equity Assets

Equity Assets
WeightRm-Rft(Rm-Rf)SMBt(SMB)HMLt(HML)RMWt(RMW)CMAt(CMA)Annual Alphat(Alpha)R^2
Intl Developed Ex US100.00%1.0864.120.153.620.183.440.131.720.121.86-0.84%-0.9797.85%
Vanguard FTSE Developed Markets ETF50.00%1.0563.94-0.24-6.05-0.02-0.400.192.500.203.25-1.22%-1.4597.79%
DFA International Small Cap Value I50.00%1.1147.170.559.360.385.180.080.720.040.40-0.46%-0.3896.29%
Factor regressions from August 2007 to December 2020. Statistically significant values in bold.
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) 36.66 7.11 -16.49 37.36 -0.35  
Name Start Date End Date Annual Alpha Rm-Rf SMB HML RMW CMA Total R2
Portfolio Aug 2007 Dec 2020 -0.84% 39.61 1.07 -2.95 4.89 -0.04 35.59 97.8%
Regression residuals
MonthPortfolio
Aug 20070.58%
Sep 2007-1.65%
Oct 2007-0.15%
Nov 2007-1.02%
Dec 2007-1.10%
Jan 20082.19%
Feb 2008-1.74%
Mar 20081.72%
Apr 2008-1.61%
May 2008-0.19%
Jun 2008-0.70%
Jul 2008-0.18%
Aug 20080.97%
Sep 20081.49%
Oct 20080.54%
Nov 2008-0.53%
Dec 20081.74%
Jan 2009-1.29%
Feb 20090.58%
Mar 20091.62%
Apr 20091.08%
May 2009-0.93%
Jun 2009-0.87%
Jul 2009-0.19%
Aug 20091.16%
Sep 2009-0.85%
Oct 2009-1.38%
Nov 20090.37%
Dec 2009-0.54%
Jan 20100.13%
Feb 20100.50%
Mar 2010-0.10%
Apr 2010-0.79%
May 2010-0.47%
Jun 2010-0.19%
Jul 20100.74%
Aug 2010-0.10%
Sep 2010-0.40%
Oct 2010-0.55%
Nov 20100.74%
Dec 20101.06%
Jan 2011-0.86%
Feb 2011-0.26%
Mar 20110.72%
Apr 2011-0.53%
May 2011-0.09%
Jun 2011-0.47%
Jul 2011-0.75%
Aug 20110.20%
Sep 2011-1.17%
Oct 20110.57%
Nov 20112.41%
Dec 2011-1.28%
Jan 20121.50%
Feb 2012-0.01%
Mar 20120.11%
Apr 2012-1.06%
May 2012-0.24%
Jun 2012-0.21%
Jul 2012-0.39%
Aug 20120.41%
Sep 2012-0.12%
Oct 20120.17%
Nov 20120.32%
Dec 20120.98%
Jan 2013-1.64%
Feb 20130.67%
Mar 20130.84%
Apr 2013-0.94%
May 2013-0.62%
Jun 20130.96%
Jul 20130.48%
Aug 2013-0.48%
Sep 20130.95%
Oct 2013-0.15%
Nov 2013-0.19%
Dec 20130.88%
Jan 2014-0.63%
Feb 20140.81%
Mar 20140.04%
Apr 2014-0.43%
May 2014-0.13%
Jun 2014-0.46%
Jul 2014-0.82%
Aug 20140.76%
Sep 2014-0.19%
Oct 20141.25%
Nov 2014-0.66%
Dec 20140.62%
Jan 20150.48%
Feb 20151.05%
Mar 2015-0.17%
Apr 2015-0.93%
May 20151.30%
Jun 20150.25%
Jul 20150.06%
Aug 20150.80%
Sep 20151.01%
Oct 2015-1.08%
Nov 20150.81%
Dec 2015-0.08%
Jan 20160.64%
Feb 2016-1.05%
Mar 2016-0.10%
Apr 2016-1.05%
May 20160.84%
Jun 2016-0.71%
Jul 20160.01%
Aug 20160.14%
Sep 20160.19%
Oct 2016-0.61%
Nov 20161.04%
Dec 2016-0.40%
Jan 2017-0.18%
Feb 20170.29%
Mar 2017-0.55%
Apr 2017-0.44%
May 2017-0.97%
Jun 20170.54%
Jul 2017-0.49%
Aug 2017-0.24%
Sep 20170.33%
Oct 2017-0.24%
Nov 2017-0.31%
Dec 20170.12%
Jan 2018-0.59%
Feb 2018-0.62%
Mar 20180.70%
Apr 2018-0.34%
May 20180.09%
Jun 2018-0.16%
Jul 20180.10%
Aug 20180.23%
Sep 2018-0.42%
Oct 2018-0.37%
Nov 2018-0.43%
Dec 2018-0.92%
Jan 20190.71%
Feb 20190.40%
Mar 2019-0.52%
Apr 20190.31%
May 2019-1.47%
Jun 20190.34%
Jul 2019-0.10%
Aug 20190.92%
Sep 20190.15%
Oct 2019-0.05%
Nov 20190.23%
Dec 20190.49%
Jan 2020-0.93%
Feb 20201.52%
Mar 2020-2.36%
Apr 20202.00%
May 20200.56%
Jun 2020-0.32%
Jul 20200.63%
Aug 2020-0.51%
Sep 20200.44%
Oct 2020-0.05%
Nov 2020-1.10%
Dec 20200.59%