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

Factor Analysis Summary

Factor regression results
Name Ticker Start Date End Date Rm-Rf SMB HML MOM Alpha Annual Alpha R2
DFA US Targeted Value I DFFVX Oct 2011 Mar 2018 1.07 0.68 0.50 -0.00 -0.12% -1.40% 97.3%
Vanguard Small Cap Value Index Admiral VSIAX Oct 2011 Mar 2018 1.01 0.54 0.28 -0.01 -0.02% -0.21% 96.7%
iShares S&P Small-Cap 600 Value ETF IJS Oct 2011 Mar 2018 1.00 0.81 0.39 -0.02 0.07% 0.79% 96.4%

DFA US Targeted Value I

Factor regression results for DFA US Targeted Value I
Ticker DFFVX
Time Period Oct 2011 - Mar 2018
Regression Basis 78 monthly samples
Coefficient of Determination (R2) 97.3%
Adjusted R2 97.2%
Regression F statistic 658.33 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.635 with p-value 0.055)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 2.356 with p-value 0.671)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.07 0.028 37.608 0.000 1.009...1.122
Size (SMB) 0.68 0.038 17.883 0.000 0.604...0.755
Value (HML) 0.50 0.043 11.577 0.000 0.412...0.583
Momentum (MOM) -0.00 0.031 -0.129 0.898 -0.066...0.058
Alpha (α) -11.64bps 0.001 -1.274 0.207 -0.30%...0.07%
Annualized Alpha (α) -1.40%  

Vanguard Small Cap Value Index Admiral

Factor regression results for Vanguard Small Cap Value Index Admiral
Ticker VSIAX
Time Period Oct 2011 - Mar 2018
Regression Basis 78 monthly samples
Coefficient of Determination (R2) 96.7%
Adjusted R2 96.6%
Regression F statistic 542.97 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.666 with p-value 0.073)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.448 with p-value 0.836)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.028 36.384 0.000 0.952...1.063
Size (SMB) 0.54 0.037 14.575 0.000 0.467...0.615
Value (HML) 0.28 0.042 6.649 0.000 0.196...0.363
Momentum (MOM) -0.01 0.030 -0.197 0.845 -0.066...0.055
Alpha (α) -1.78bps 0.001 -0.200 0.842 -0.20%...0.16%
Annualized Alpha (α) -0.21%  

iShares S&P Small-Cap 600 Value ETF

Factor regression results for iShares S&P Small-Cap 600 Value ETF
Ticker IJS
Time Period Oct 2011 - Mar 2018
Regression Basis 78 monthly samples
Coefficient of Determination (R2) 96.4%
Adjusted R2 96.3%
Regression F statistic 495.60 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.642 with p-value 0.059)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 2.024 with p-value 0.731)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.00 0.032 31.000 0.000 0.933...1.061
Size (SMB) 0.81 0.043 18.776 0.000 0.724...0.896
Value (HML) 0.39 0.049 8.027 0.000 0.294...0.489
Momentum (MOM) -0.02 0.035 -0.503 0.617 -0.088...0.053
Alpha (α) 6.56bps 0.001 0.632 0.529 -0.14%...0.27%
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.
  • 4-factor model: Ra = Rrf + Bmkt × ( Rmkt - Rrf ) + Bsmb × SMB + Bhml × HML + Bmom × MOM + 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
    Bmom
    Momentum loading factor (the level of exposure to momentum)
    MOM
    Up Minus Down: The momentum 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) 132.08 0.41 5.50 32.22  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
DFA US Targeted Value I DFFVX Oct 2011 Mar 2018 -1.40% 140.74 0.28 2.74 -0.13 131.99 97.3%
Vanguard Small Cap Value Index Admiral VSIAX Oct 2011 Mar 2018 -0.21% 133.05 0.22 1.54 -0.19 132.83 96.7%
iShares S&P Small-Cap 600 Value ETF IJS Oct 2011 Mar 2018 0.79% 131.69 0.33 2.15 -0.57 140.17 96.4%
Regression residuals
MonthDFFVXVSIAXIJS
Oct 20110.01490.01140.0123
Nov 20110.01040.00330.0118
Dec 2011-0.00060.00140.0112
Jan 2012-0.00130.00900.0136
Feb 20120.0018-0.0098-0.0138
Mar 2012-0.0135-0.0068-0.0011
Apr 2012-0.00000.0042-0.0045
May 2012-0.00440.0014-0.0073
Jun 2012-0.0070-0.0013-0.0021
Jul 20120.00700.00350.0074
Aug 20120.0104-0.00210.0058
Sep 2012-0.0072-0.0054-0.0068
Oct 20120.00300.0073-0.0083
Nov 20120.01040.00060.0071
Dec 2012-0.00450.0034-0.0036
Jan 20130.00260.0043-0.0099
Feb 20130.00740.00710.0066
Mar 20130.00300.0017-0.0048
Apr 2013-0.0118-0.00460.0023
May 2013-0.0035-0.0132-0.0097
Jun 2013-0.0003-0.00510.0012
Jul 2013-0.0042-0.0013-0.0083
Aug 20130.0048-0.00860.0006
Sep 20130.00310.00320.0092
Oct 20130.00410.00230.0003
Nov 20130.0031-0.00850.0000
Dec 20130.00230.0025-0.0105
Jan 2014-0.00620.0070-0.0011
Feb 20140.00300.0029-0.0015
Mar 20140.00390.00500.0032
Apr 20140.00810.01010.0075
May 20140.00290.00650.0014
Jun 2014-0.00160.0024-0.0102
Jul 20140.0021-0.00330.0034
Aug 20140.00740.00860.0012
Sep 2014-0.0055-0.0119-0.0045
Oct 2014-0.01470.00620.0181
Nov 2014-0.00200.00490.0076
Dec 2014-0.0134-0.0018-0.0030
Jan 20150.01220.0115-0.0040
Feb 20150.0131-0.0020-0.0006
Mar 20150.00840.0089-0.0014
Apr 2015-0.0044-0.0078-0.0092
May 20150.0023-0.0007-0.0073
Jun 2015-0.0016-0.0116-0.0005
Jul 20150.00810.00910.0086
Aug 20150.00810.0031-0.0014
Sep 20150.00080.00850.0126
Oct 2015-0.0063-0.00120.0032
Nov 2015-0.0033-0.0101-0.0086
Dec 2015-0.0048-0.00420.0037
Jan 20160.00720.00610.0175
Feb 20160.01280.01340.0155
Mar 2016-0.00020.01060.0114
Apr 2016-0.0091-0.0016-0.0081
May 2016-0.00020.0031-0.0045
Jun 2016-0.00880.00240.0092
Jul 2016-0.0042-0.0043-0.0072
Aug 2016-0.0141-0.0137-0.0176
Sep 20160.0013-0.0063-0.0053
Oct 20160.00240.00240.0013
Nov 20160.00750.00090.0067
Dec 2016-0.0089-0.0008-0.0020
Jan 20170.00260.0003-0.0133
Feb 2017-0.00470.0003-0.0000
Mar 2017-0.0024-0.0070-0.0066
Apr 2017-0.0119-0.0057-0.0052
May 2017-0.0081-0.01010.0012
Jun 20170.00460.0004-0.0024
Jul 20170.0009-0.00140.0004
Aug 2017-0.0067-0.0011-0.0074
Sep 20170.0003-0.01010.0103
Oct 2017-0.0029-0.0037-0.0014
Nov 20170.00310.00310.0103
Dec 20170.0029-0.0002-0.0063
Jan 2018-0.0113-0.0169-0.0135
Feb 2018-0.0040-0.0095-0.0025
Mar 20180.00470.00960.0035