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
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Asset 2
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Asset 3
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Asset 4
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Asset 5
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Asset 6
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Asset 7
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Asset 8
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Asset 9
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Asset 10
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Factor Analysis Results

Factor Analysis Summary

Factor regression results
Name Ticker Start Date End Date Rm-Rf SMB HML RMW CMA Alpha Annual Alpha R2
Vanguard Small-Cap Value ETF VBR Jan 2013 Oct 2020 0.99 0.55 0.34 0.07 -0.06 -0.08% -0.95% 97.6%
Vanguard S&P Small-Cap 600 Value ETF VIOV Jan 2013 Oct 2020 0.98 0.85 0.36 0.17 0.08 0.01% 0.07% 98.0%

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Jan 2013 - Oct 2020
Regression Basis 94 monthly samples
Coefficient of Determination (R2) 97.6%
Adjusted R2 97.5%
Regression F statistic 726.19 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.719 with p-value 0.087)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 9.041 with p-value 0.107)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.99 0.024 41.378 0.000 0.940...1.035
Size (SMB) 0.55 0.040 13.694 0.000 0.474...0.635
Value (HML) 0.34 0.039 8.909 0.000 0.267...0.421
Profitability (RMW) 0.07 0.062 1.138 0.258 -0.053...0.195
Investment (CMA) -0.06 0.070 -0.811 0.420 -0.196...0.082
Alpha (α) -7.94bps 0.001 -0.886 0.378 -0.26%...0.10%
Annualized Alpha (α) -0.95%  

Vanguard S&P Small-Cap 600 Value ETF

Factor regression results for Vanguard S&P Small-Cap 600 Value ETF
Ticker VIOV
Time Period Jan 2013 - Oct 2020
Regression Basis 94 monthly samples
Coefficient of Determination (R2) 98.0%
Adjusted R2 97.9%
Regression F statistic 857.64 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.673 with p-value 0.018)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 10.711 with p-value 0.057)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.98 0.024 40.705 0.000 0.933...1.029
Size (SMB) 0.85 0.041 20.684 0.000 0.765...0.927
Value (HML) 0.36 0.039 9.126 0.000 0.278...0.433
Profitability (RMW) 0.17 0.063 2.690 0.009 0.044...0.294
Investment (CMA) 0.08 0.071 1.130 0.262 -0.061...0.220
Alpha (α) 0.57bps 0.001 0.063 0.950 -0.17%...0.19%
Annualized Alpha (α) 0.07%  
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) 110.03 -18.29 -60.13 10.21 -25.30  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML RMW CMA Total R2
Vanguard Small-Cap Value ETF VBR Jan 2013 Oct 2020 -0.95% 108.66 -10.14 -20.68 0.72 1.44 72.06 97.6%
Vanguard S&P Small-Cap 600 Value ETF VIOV Jan 2013 Oct 2020 0.07% 107.97 -15.47 -21.40 1.73 -2.02 71.38 98.0%
Regression residuals
MonthVBRVIOV
Jan 20130.0062-0.0094
Feb 20130.00670.0087
Mar 20130.0029-0.0066
Apr 2013-0.00270.0006
May 2013-0.0149-0.0028
Jun 2013-0.00730.0006
Jul 20130.0027-0.0088
Aug 2013-0.00650.0059
Sep 20130.00560.0095
Oct 20130.0014-0.0032
Nov 2013-0.0093-0.0026
Dec 20130.0042-0.0058
Jan 20140.01150.0053
Feb 20140.00510.0074
Mar 2014-0.0014-0.0087
Apr 20140.00850.0014
May 20140.00720.0057
Jun 20140.0037-0.0069
Jul 2014-0.00360.0041
Aug 20140.01050.0026
Sep 2014-0.0110-0.0043
Oct 20140.00990.0200
Nov 20140.00820.0143
Dec 2014-0.0028-0.0107
Jan 20150.0133-0.0048
Feb 20150.00180.0070
Mar 20150.0091-0.0038
Apr 2015-0.0077-0.0025
May 20150.0015-0.0035
Jun 2015-0.0136-0.0035
Jul 20150.01410.0098
Aug 20150.00100.0010
Sep 20150.00730.0106
Oct 20150.00300.0048
Nov 2015-0.0072-0.0006
Dec 2015-0.00190.0113
Jan 20160.00580.0032
Feb 20160.01170.0096
Mar 20160.01100.0113
Apr 2016-0.0020-0.0050
May 20160.00640.0020
Jun 20160.00490.0029
Jul 2016-0.0037-0.0049
Aug 2016-0.0164-0.0155
Sep 2016-0.00320.0017
Oct 2016-0.0004-0.0062
Nov 2016-0.00870.0001
Dec 2016-0.0040-0.0044
Jan 20170.0045-0.0083
Feb 20170.00230.0049
Mar 2017-0.0028-0.0047
Apr 2017-0.0044-0.0044
May 2017-0.00620.0052
Jun 2017-0.00010.0039
Jul 20170.00250.0030
Aug 20170.0002-0.0069
Sep 2017-0.01070.0100
Oct 2017-0.00570.0006
Nov 20170.00060.0016
Dec 2017-0.0003-0.0085
Jan 2018-0.0140-0.0069
Feb 2018-0.0118-0.0004
Mar 20180.01180.0012
Apr 2018-0.00400.0071
May 20180.00360.0053
Jun 20180.00070.0013
Jul 20180.00050.0044
Aug 2018-0.00210.0058
Sep 20180.0018-0.0079
Oct 2018-0.0015-0.0046
Nov 20180.0101-0.0045
Dec 20180.0024-0.0005
Jan 20190.01180.0173
Feb 20190.00390.0028
Mar 20190.0018-0.0082
Apr 2019-0.00410.0046
May 20190.0031-0.0141
Jun 2019-0.00090.0057
Jul 20190.00450.0145
Aug 20190.00480.0162
Sep 20190.00050.0091
Oct 20190.00170.0025
Nov 2019-0.0098-0.0053
Dec 2019-0.0114-0.0150
Jan 20200.0126-0.0003
Feb 2020-0.0083-0.0038
Mar 2020-0.0224-0.0052
Apr 2020-0.0161-0.0162
May 2020-0.0024-0.0262
Jun 2020-0.00600.0035
Jul 2020-0.0018-0.0036
Aug 2020-0.0169-0.0111
Sep 20200.0077-0.0043
Oct 20200.01320.0037