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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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 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 Alpha Annual Alpha R2
AQR Small Cap Multi-Style I QSMLX Apr 2013 Oct 2020 0.99 0.75 0.28 -0.12% -1.38% 96.8%
Vanguard Small-Cap Value ETF VBR Apr 2013 Oct 2020 1.01 0.53 0.42 -0.11% -1.33% 97.4%
SPDR S&P 600 Small Cap Value ETF SLYV Apr 2013 Oct 2020 1.00 0.80 0.53 0.00% 0.02% 97.7%

AQR Small Cap Multi-Style I

Factor regression results for AQR Small Cap Multi-Style I
Ticker QSMLX
Time Period Apr 2013 - Oct 2020
Regression Basis 91 monthly samples
Coefficient of Determination (R2) 96.8%
Adjusted R2 96.7%
Regression F statistic 887.85 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.322 with p-value 0.941)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 2.687 with p-value 0.442)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.99 0.026 37.837 0.000 0.937...1.041
Size (SMB) 0.75 0.043 17.460 0.000 0.666...0.837
Value (HML) 0.28 0.035 7.836 0.000 0.206...0.346
Alpha (α) -11.52bps 0.001 -1.088 0.280 -0.33%...0.10%
Annualized Alpha (α) -1.38%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Apr 2013 - Oct 2020
Regression Basis 91 monthly samples
Coefficient of Determination (R2) 97.4%
Adjusted R2 97.3%
Regression F statistic 1,074.07 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.675 with p-value 0.060)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 14.692 with p-value 0.002)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.023 43.092 0.000 0.962...1.055
Size (SMB) 0.53 0.039 13.873 0.000 0.458...0.611
Value (HML) 0.42 0.032 13.260 0.000 0.356...0.481
Alpha (α) -11.05bps 0.001 -1.165 0.247 -0.30%...0.08%
Annualized Alpha (α) -1.33%  

SPDR S&P 600 Small Cap Value ETF

Factor regression results for SPDR S&P 600 Small Cap Value ETF
Ticker SLYV
Time Period Apr 2013 - Oct 2020
Regression Basis 91 monthly samples
Coefficient of Determination (R2) 97.7%
Adjusted R2 97.6%
Regression F statistic 1,206.98 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.351 with p-value 0.001)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 2.879 with p-value 0.411)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.00 0.024 41.326 0.000 0.955...1.052
Size (SMB) 0.80 0.040 19.951 0.000 0.718...0.877
Value (HML) 0.53 0.033 16.046 0.000 0.460...0.590
Alpha (α) 0.21bps 0.001 0.021 0.983 -0.19%...0.20%
Annualized Alpha (α) 0.02%  
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) 101.69 -8.65 -62.97  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML Total R2
AQR Small Cap Multi-Style I QSMLX Apr 2013 Oct 2020 -1.38% 100.57 -6.50 -17.39 65.16 96.8%
Vanguard Small-Cap Value ETF VBR Apr 2013 Oct 2020 -1.33% 102.60 -4.62 -26.37 60.56 97.4%
SPDR S&P 600 Small Cap Value ETF SLYV Apr 2013 Oct 2020 0.02% 102.03 -6.90 -33.08 62.26 97.7%
Regression residuals
MonthQSMLXVBRSLYV
Apr 20130.0124-0.00300.0025
May 20130.0031-0.0158-0.0122
Jun 20130.0147-0.0056-0.0052
Jul 20130.01120.0001-0.0004
Aug 2013-0.0089-0.00370.0050
Sep 20130.00810.00560.0122
Oct 2013-0.00170.00130.0002
Nov 20130.0095-0.0088-0.0011
Dec 2013-0.00690.0035-0.0091
Jan 2014-0.01510.0106-0.0006
Feb 20140.00360.0037-0.0017
Mar 20140.0073-0.0008-0.0031
Apr 20140.00080.00960.0065
May 2014-0.00450.00740.0033
Jun 2014-0.00150.0044-0.0077
Jul 2014-0.0044-0.00330.0032
Aug 20140.01120.00990.0028
Sep 2014-0.0025-0.0087-0.0040
Oct 20140.00740.00890.0228
Nov 2014-0.00350.00960.0094
Dec 20140.0020-0.0030-0.0085
Jan 20150.00480.01710.0034
Feb 20150.00180.00080.0045
Mar 20150.00940.0111-0.0006
Apr 2015-0.0165-0.0094-0.0108
May 2015-0.00090.0011-0.0060
Jun 20150.0045-0.01050.0017
Jul 20150.01790.01550.0095
Aug 2015-0.00140.0001-0.0000
Sep 20150.01750.00810.0108
Oct 2015-0.00140.00070.0027
Nov 2015-0.0090-0.0088-0.0057
Dec 2015-0.0035-0.00040.0068
Jan 20160.01160.00510.0160
Feb 20160.00550.01460.0191
Mar 2016-0.00940.01120.0123
Apr 2016-0.0206-0.0047-0.0121
May 20160.01310.0057-0.0019
Jun 2016-0.00250.00550.0077
Jul 20160.0084-0.0014-0.0002
Aug 2016-0.0136-0.0166-0.0196
Sep 2016-0.0026-0.0045-0.0043
Oct 2016-0.0057-0.0012-0.0046
Nov 20160.0032-0.0092-0.0003
Dec 20160.0118-0.0040-0.0079
Jan 2017-0.00630.0048-0.0076
Feb 20170.00400.00290.0023
Mar 20170.0001-0.0007-0.0005
Apr 20170.0027-0.0016-0.0014
May 2017-0.0140-0.00490.0078
Jun 2017-0.0011-0.0004-0.0024
Jul 20170.00500.00100.0011
Aug 2017-0.00430.0022-0.0065
Sep 2017-0.0040-0.01250.0090
Oct 2017-0.0002-0.0038-0.0026
Nov 2017-0.00310.00390.0111
Dec 2017-0.01240.0004-0.0071
Jan 20180.0053-0.0152-0.0116
Feb 2018-0.0109-0.0079-0.0034
Mar 20180.00410.01070.0049
Apr 2018-0.0163-0.00720.0014
May 2018-0.00570.00310.0047
Jun 2018-0.00110.00160.0052
Jul 20180.00100.00160.0070
Aug 2018-0.0003-0.00060.0070
Sep 2018-0.00760.0013-0.0051
Oct 20180.0089-0.0027-0.0057
Nov 2018-0.01550.0086-0.0075
Dec 20180.00530.00290.0010
Jan 2019-0.00300.01240.0149
Feb 20190.00930.00510.0033
Mar 2019-0.00940.0029-0.0045
Apr 2019-0.0029-0.00080.0037
May 2019-0.00740.0034-0.0104
Jun 20190.00290.00020.0084
Jul 20190.01400.00450.0129
Aug 20190.01070.00480.0182
Sep 2019-0.01290.00160.0122
Oct 20190.01950.00360.0066
Nov 2019-0.0028-0.0111-0.0095
Dec 2019-0.0195-0.0123-0.0161
Jan 20200.00120.0101-0.0059
Feb 2020-0.0020-0.0086-0.0081
Mar 2020-0.0138-0.0296-0.0080
Apr 2020-0.0114-0.0146-0.0140
May 2020-0.00030.0002-0.0246
Jun 20200.0017-0.00840.0016
Jul 20200.0183-0.0071-0.0073
Aug 2020-0.0120-0.0160-0.0085
Sep 20200.01830.0109-0.0030
Oct 20200.00280.01360.0023