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 Alpha Annual Alpha R2
Vanguard US Value Factor ETF VFVA Mar 2018 Dec 2019 1.20 0.43 0.79 0.06% 0.73% 97.7%
DFA Tax-Managed US Marketwide Value II DFMVX Mar 2018 Dec 2019 1.04 0.01 0.36 -0.00% -0.05% 98.8%
DFA Tax-Managed US Targeted Value DTMVX Mar 2018 Dec 2019 1.10 0.67 0.60 -0.07% -0.85% 98.9%

Vanguard US Value Factor ETF

Factor regression results for Vanguard US Value Factor ETF
Ticker VFVA
Time Period Mar 2018 - Dec 2019
Coefficient of Determination (R2) 97.7%
Adjusted R2 97.4%
Regression F statistic 259.29 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.527 with p-value 0.910)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.686 with p-value 0.640)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.20 0.057 21.144 0.000 1.083...1.322
Size (SMB) 0.43 0.104 4.159 0.001 0.214...0.652
Value (HML) 0.79 0.084 9.494 0.000 0.619...0.971
Alpha (α) 6.11bps 0.002 0.261 0.797 -0.43%...0.55%
Annualized Alpha (α) 0.73%  

DFA Tax-Managed US Marketwide Value II

Factor regression results for DFA Tax-Managed US Marketwide Value II
Ticker DFMVX
Time Period Mar 2018 - Dec 2019
Coefficient of Determination (R2) 98.8%
Adjusted R2 98.5%
Regression F statistic 475.27 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.065 with p-value 0.584)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 0.336 with p-value 0.953)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.04 0.032 32.563 0.000 0.973...1.108
Size (SMB) 0.01 0.059 0.092 0.928 -0.118...0.128
Value (HML) 0.36 0.047 7.567 0.000 0.257...0.455
Alpha (α) -0.38bps 0.001 -0.029 0.977 -0.28%...0.27%
Annualized Alpha (α) -0.05%  

DFA Tax-Managed US Targeted Value

Factor regression results for DFA Tax-Managed US Targeted Value
Ticker DTMVX
Time Period Mar 2018 - Dec 2019
Coefficient of Determination (R2) 98.9%
Adjusted R2 98.7%
Regression F statistic 533.74 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.498 with p-value 0.119)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.608 with p-value 0.307)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.10 0.038 28.792 0.000 1.017...1.177
Size (SMB) 0.67 0.070 9.611 0.000 0.524...0.817
Value (HML) 0.60 0.056 10.737 0.000 0.484...0.720
Alpha (α) -7.05bps 0.002 -0.450 0.658 -0.40%...0.26%
Annualized Alpha (α) -0.85%  
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.
  • 3-factor model: Ra = Rrf + Bmkt × ( Rmkt - Rrf ) + Bsmb × SMB + Bhml × HML + 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
    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) 81.05 -19.45 -78.18  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML Total R2
Vanguard US Value Factor ETF VFVA Mar 2018 Dec 2019 0.73% 97.44 -8.43 -62.15 32.98 97.7%
DFA Tax-Managed US Marketwide Value II DFMVX Mar 2018 Dec 2019 -0.05% 84.32 -0.10 -27.83 56.00 98.8%
DFA Tax-Managed US Targeted Value DTMVX Mar 2018 Dec 2019 -0.85% 88.87 -13.04 -47.08 21.70 98.9%
Regression residuals
MonthVFVADFMVXDTMVX
Mar 20180.00480.00280.0066
Apr 20180.0020-0.0017-0.0111
May 2018-0.0131-0.00770.0008
Jun 20180.01480.0010-0.0022
Jul 2018-0.01150.0053-0.0024
Aug 2018-0.0029-0.00390.0004
Sep 20180.00310.0045-0.0063
Oct 20180.01080.0032-0.0021
Nov 2018-0.02010.0019-0.0036
Dec 20180.0022-0.00550.0073
Jan 20190.02200.00540.0016
Feb 20190.00020.00320.0049
Mar 20190.0020-0.0060-0.0001
Apr 2019-0.0032-0.00960.0034
May 2019-0.01050.0066-0.0060
Jun 20190.00350.00330.0065
Jul 2019-0.0012-0.00140.0089
Aug 20190.0067-0.00300.0032
Sep 20190.0013-0.00110.0077
Oct 2019-0.00060.01050.0041
Nov 2019-0.0029-0.0008-0.0079
Dec 2019-0.0073-0.0072-0.0136