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 FF-MKT-RF FF-SMB5 FF-HML FF-MOM FF-RMW Alpha Annual Alpha R2
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Nov 2020 1.12 1.17 0.52 -0.45 0.41 -0.11% -1.31% 92.2%
DFA US Small Cap Value I DFSVX Apr 2006 Nov 2020 1.05 0.85 0.42 -0.00 0.09 -0.15% -1.82% 98.7%

Invesco S&P SmallCap 600 Pure Value ETF

Factor regression results for Invesco S&P SmallCap 600 Pure Value ETF
Ticker RZV
Time Period Apr 2006 - Nov 2020
Regression Basis 176 monthly samples
Coefficient of Determination (R2) 92.2%
Adjusted R2 92.0%
Regression F statistic 401.72 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.796 with p-value 0.080)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 45.976 with p-value 0.000)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
FF-MKT-RF Market 1.12 0.049 22.604 0.000 1.021...1.216
FF-SMB5 Size 1.17 0.091 12.945 0.000 0.995...1.354
FF-HML Value 0.52 0.079 6.655 0.000 0.368...0.678
FF-MOM Momentum -0.45 0.049 -9.290 0.000 -0.550...-0.357
FF-RMW Profitability 0.41 0.130 3.179 0.002 0.156...0.669
Alpha Alpha -10.94bps 0.002 -0.540 0.590 -0.51%...0.29%
Annualized Alpha Annualized Alpha -1.31%  

DFA US Small Cap Value I

Factor regression results for DFA US Small Cap Value I
Ticker DFSVX
Time Period Apr 2006 - Nov 2020
Regression Basis 176 monthly samples
Coefficient of Determination (R2) 98.7%
Adjusted R2 98.6%
Regression F statistic 2,504.84 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.858 with p-value 0.160)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.596 with p-value 0.609)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
FF-MKT-RF Market 1.05 0.015 69.938 0.000 1.017...1.077
FF-SMB5 Size 0.85 0.027 31.074 0.000 0.799...0.907
FF-HML Value 0.42 0.024 17.647 0.000 0.372...0.466
FF-MOM Momentum -0.00 0.015 -0.234 0.815 -0.033...0.026
FF-RMW Profitability 0.09 0.039 2.381 0.018 0.016...0.171
Alpha Alpha -15.17bps 0.001 -2.478 0.014 -0.27%...-0.03%
Annualized Alpha Annualized Alpha -1.82%  
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.
  • Symbols:
    MKT-RF
    Market factor (excess return over the risk free rate)
    SMB
    Size factor (Small Minus Big)
    HML
    Value factor (High Minus Low)
    MOM
    Momentum factor (Up Minus Down)
    RMW
    Profitability factor (Robust Minus Weak)
    CMA
    Conservative investment factor (Conservative Minus Aggressive)
    ST-REV
    Short-term reversal factor
    LT-REV
    Long-term reversal factor
    QMJ
    Quality factor (Quality Minus Junk)
    BAB
    Bet Against Beta factor
    TRM
    Term factor (fixed income)
    CDT
    Credit factor (fixed income)
    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) 80.40 -1.48 -37.18 3.68 26.49  
Name Ticker Start Date End Date Annual Alpha FF-MKT-RF FF-SMB5 FF-HML FF-MOM FF-RMW Total R2
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Nov 2020 -1.31% 89.94 -1.74 -19.44 -1.67 10.93 67.08 92.2%
DFA US Small Cap Value I DFSVX Apr 2006 Nov 2020 -1.82% 84.18 -1.26 -15.59 -0.01 2.48 54.61 98.7%
Regression residuals
MonthRZVDFSVX
Apr 2006-0.0141-0.0047
May 2006-0.02040.0048
Jun 20060.0151-0.0015
Jul 20060.0009-0.0133
Aug 2006-0.01930.0012
Sep 2006-0.00380.0008
Oct 2006-0.00230.0027
Nov 2006-0.00990.0025
Dec 20060.0094-0.0016
Jan 20070.00830.0057
Feb 2007-0.00180.0051
Mar 2007-0.00980.0026
Apr 20070.00310.0010
May 2007-0.0164-0.0024
Jun 2007-0.01150.0003
Jul 20070.0222-0.0001
Aug 2007-0.0145-0.0069
Sep 20070.0013-0.0075
Oct 20070.00140.0029
Nov 2007-0.0039-0.0106
Dec 20070.0288-0.0035
Jan 20080.05400.0125
Feb 2008-0.02260.0110
Mar 20080.04180.0113
Apr 2008-0.0683-0.0205
May 2008-0.0230-0.0003
Jun 20080.0097-0.0158
Jul 2008-0.0242-0.0240
Aug 2008-0.0515-0.0116
Sep 20080.0323-0.0029
Oct 20080.0252-0.0049
Nov 20080.00910.0082
Dec 2008-0.05160.0065
Jan 2009-0.06030.0058
Feb 2009-0.02420.0178
Mar 20090.0340-0.0060
Apr 20090.13320.0093
May 2009-0.0208-0.0009
Jun 20090.0921-0.0065
Jul 20090.03340.0140
Aug 2009-0.0290-0.0106
Sep 2009-0.0170-0.0064
Oct 2009-0.07100.0075
Nov 2009-0.0177-0.0017
Dec 2009-0.0225-0.0019
Jan 20100.02180.0019
Feb 20100.03090.0020
Mar 20100.01130.0003
Apr 2010-0.01150.0060
May 2010-0.0141-0.0068
Jun 2010-0.0289-0.0016
Jul 20100.00480.0162
Aug 2010-0.00860.0020
Sep 2010-0.00800.0132
Oct 20100.01780.0060
Nov 20100.00940.0129
Dec 2010-0.00210.0010
Jan 2011-0.02050.0019
Feb 20110.00240.0099
Mar 2011-0.00230.0003
Apr 2011-0.0115-0.0019
May 20110.0183-0.0042
Jun 2011-0.00820.0003
Jul 20110.01430.0096
Aug 2011-0.0006-0.0076
Sep 20110.0056-0.0085
Oct 20110.00420.0129
Nov 20110.0075-0.0005
Dec 20110.0080-0.0010
Jan 2012-0.00350.0108
Feb 2012-0.01070.0004
Mar 2012-0.0074-0.0081
Apr 20120.00100.0011
May 2012-0.0048-0.0036
Jun 20120.0071-0.0049
Jul 20120.01140.0132
Aug 20120.02870.0094
Sep 20120.0091-0.0048
Oct 2012-0.02710.0046
Nov 20120.04560.0126
Dec 2012-0.0217-0.0029
Jan 2013-0.01490.0019
Feb 20130.01250.0090
Mar 2013-0.01990.0015
Apr 2013-0.0052-0.0087
May 20130.0276-0.0001
Jun 2013-0.0068-0.0040
Jul 2013-0.0104-0.0008
Aug 20130.0034-0.0009
Sep 20130.0273-0.0025
Oct 2013-0.0131-0.0020
Nov 20130.02070.0068
Dec 2013-0.00500.0049
Jan 20140.0179-0.0079
Feb 20140.01040.0082
Mar 2014-0.0272-0.0042
Apr 2014-0.01070.0114
May 20140.00710.0050
Jun 2014-0.0097-0.0031
Jul 20140.01540.0009
Aug 20140.00380.0159
Sep 20140.0026-0.0113
Oct 20140.0074-0.0030
Nov 20140.01170.0022
Dec 2014-0.0157-0.0073
Jan 2015-0.00900.0054
Feb 20150.02450.0031
Mar 20150.00160.0069
Apr 20150.00000.0000
May 20150.00990.0009
Jun 20150.0008-0.0035
Jul 20150.03750.0050
Aug 20150.00330.0093
Sep 20150.01380.0085
Oct 2015-0.0029-0.0083
Nov 20150.00090.0034
Dec 20150.0181-0.0021
Jan 2016-0.00970.0082
Feb 20160.00620.0045
Mar 2016-0.00170.0016
Apr 2016-0.0100-0.0115
May 2016-0.04290.0020
Jun 20160.0168-0.0091
Jul 2016-0.0177-0.0098
Aug 2016-0.0377-0.0128
Sep 20160.01480.0026
Oct 20160.01200.0081
Nov 2016-0.01800.0070
Dec 2016-0.0232-0.0028
Jan 2017-0.0234-0.0011
Feb 2017-0.0147-0.0073
Mar 2017-0.0285-0.0059
Apr 2017-0.0211-0.0031
May 2017-0.0115-0.0043
Jun 20170.0013-0.0063
Jul 2017-0.01110.0051
Aug 20170.0259-0.0016
Sep 20170.01020.0009
Oct 20170.02310.0023
Nov 2017-0.0022-0.0107
Dec 2017-0.0217-0.0033
Jan 20180.0006-0.0096
Feb 20180.0108-0.0074
Mar 2018-0.00490.0045
Apr 20180.01240.0024
May 20180.02510.0101
Jun 2018-0.0041-0.0032
Jul 2018-0.0239-0.0047
Aug 20180.02770.0036
Sep 2018-0.0008-0.0049
Oct 20180.01450.0088
Nov 2018-0.0448-0.0025
Dec 20180.01720.0054
Jan 2019-0.00040.0078
Feb 2019-0.0095-0.0071
Mar 20190.0031-0.0013
Apr 2019-0.0305-0.0016
May 2019-0.0038-0.0203
Jun 2019-0.00480.0044
Jul 20190.02830.0063
Aug 20190.0489-0.0044
Sep 20190.01080.0116
Oct 20190.00490.0035
Nov 2019-0.0119-0.0035
Dec 2019-0.0257-0.0062
Jan 2020-0.0299-0.0020
Feb 2020-0.0246-0.0040
Mar 20200.04720.0068
Apr 20200.0311-0.0040
May 2020-0.0237-0.0248
Jun 20200.0165-0.0051
Jul 20200.03920.0042
Aug 20200.0315-0.0063
Sep 20200.0185-0.0006
Oct 2020-0.03850.0065
Nov 2020-0.0415-0.0149