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
iShares MSCI USA Momentum Factor ETF MTUM May 2013 Jan 2021 1.02 -0.08 -0.16 0.27 0.04% 0.47% 93.2%
Vanguard Growth ETF VUG May 2013 Jan 2021 1.06 -0.12 -0.29 0.01 0.00% 0.05% 97.0%

iShares MSCI USA Momentum Factor ETF

Factor regression results for iShares MSCI USA Momentum Factor ETF
Ticker MTUM
Time Period May 2013 - Jan 2021
Regression Basis 93 monthly samples
Coefficient of Determination (R2) 93.2%
Adjusted R2 92.9%
Regression F statistic 303.60 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.224 with p-value 0.858)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 4.158 with p-value 0.385)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.02 0.030 33.398 0.000 0.955...1.076
Size (SMB) -0.08 0.046 -1.822 0.072 -0.174...0.008
Value (HML) -0.16 0.046 -3.502 0.001 -0.250...-0.069
Momentum (MOM) 0.27 0.038 7.052 0.000 0.193...0.345
Alpha (α) 3.92bps 0.001 0.329 0.743 -0.20%...0.28%
Annualized Alpha (α) 0.47%  

Vanguard Growth ETF

Factor regression results for Vanguard Growth ETF
Ticker VUG
Time Period May 2013 - Jan 2021
Regression Basis 93 monthly samples
Coefficient of Determination (R2) 97.0%
Adjusted R2 96.9%
Regression F statistic 708.99 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.363 with p-value 0.962)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 4.151 with p-value 0.386)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.022 48.523 0.000 1.019...1.106
Size (SMB) -0.12 0.033 -3.753 0.000 -0.189...-0.058
Value (HML) -0.29 0.033 -8.687 0.000 -0.350...-0.220
Momentum (MOM) 0.01 0.027 0.333 0.740 -0.045...0.064
Alpha (α) 0.40bps 0.001 0.046 0.963 -0.17%...0.17%
Annualized Alpha (α) 0.05%  
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) 116.18 13.23 -57.71 27.16  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
iShares MSCI USA Momentum Factor ETF MTUM May 2013 Jan 2021 0.47% 117.97 -1.10 9.21 7.30 137.30 93.2%
Vanguard Growth ETF VUG May 2013 Jan 2021 0.05% 123.43 -1.63 16.46 0.25 138.90 97.0%
Regression residuals
MonthMTUMVUG
May 2013-1.55%-0.27%
Jun 20130.27%-0.76%
Jul 2013-0.03%-0.05%
Aug 2013-1.26%0.30%
Sep 2013-1.59%0.82%
Oct 20131.30%-0.04%
Nov 2013-0.04%-0.72%
Dec 2013-0.29%0.34%
Jan 20140.30%-0.01%
Feb 20141.38%0.58%
Mar 2014-2.36%-0.85%
Apr 20140.00%0.07%
May 20141.43%1.10%
Jun 2014-0.67%-0.20%
Jul 20140.70%0.09%
Aug 20140.01%0.01%
Sep 20140.64%-0.61%
Oct 2014-0.22%0.33%
Nov 20140.18%-0.79%
Dec 2014-0.52%0.04%
Jan 20150.79%0.66%
Feb 2015-0.33%-0.71%
Mar 2015-0.57%-2.51%
Apr 20150.34%2.41%
May 20150.22%-0.23%
Jun 20150.47%0.08%
Jul 2015-1.59%-0.17%
Aug 20151.13%0.97%
Sep 2015-0.40%0.14%
Oct 20150.29%0.46%
Nov 2015-0.44%-0.16%
Dec 20150.47%-1.21%
Jan 20161.68%0.26%
Feb 2016-0.19%-0.37%
Mar 2016-0.19%0.25%
Apr 20160.65%-0.70%
May 2016-0.26%0.08%
Jun 20161.67%-0.99%
Jul 2016-0.54%0.56%
Aug 2016-0.58%0.25%
Sep 20160.30%0.24%
Oct 20160.15%0.14%
Nov 2016-2.71%-0.90%
Dec 2016-0.14%0.23%
Jan 20170.83%0.50%
Feb 20170.08%-0.20%
Mar 20171.62%0.29%
Apr 20170.99%0.55%
May 20172.39%0.23%
Jun 2017-0.05%-0.64%
Jul 20170.84%0.18%
Aug 2017-0.26%0.05%
Sep 20171.32%-0.27%
Oct 20171.32%0.16%
Nov 2017-0.36%-1.07%
Dec 2017-0.72%-0.44%
Jan 20180.88%-0.01%
Feb 20180.89%0.55%
Mar 2018-0.56%0.37%
Apr 20180.13%0.10%
May 2018-0.51%1.15%
Jun 2018-0.37%0.01%
Jul 2018-1.32%-1.14%
Aug 20180.24%-0.17%
Sep 20180.23%-0.49%
Oct 2018-1.64%-0.69%
Nov 2018-0.17%-1.38%
Dec 20180.96%0.68%
Jan 20190.16%0.36%
Feb 2019-0.77%-0.63%
Mar 2019-0.73%0.17%
Apr 2019-1.15%0.67%
May 20192.10%-0.04%
Jun 2019-0.67%-0.94%
Jul 2019-0.49%0.65%
Aug 2019-0.34%0.25%
Sep 20190.03%0.45%
Oct 2019-1.99%-0.26%
Nov 2019-0.35%-0.69%
Dec 2019-0.33%0.54%
Jan 20200.97%0.89%
Feb 20200.43%1.06%
Mar 2020-3.06%-1.20%
Apr 2020-0.71%0.57%
May 2020-0.63%-0.02%
Jun 20201.83%1.95%
Jul 2020-1.34%0.68%
Aug 20201.06%1.10%
Sep 2020-1.38%-1.61%
Oct 2020-0.27%0.94%
Nov 20202.00%-1.50%
Dec 2020-0.48%-0.54%
Jan 20211.46%0.68%