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 QMJ BAB Alpha Annual Alpha R2
iShares MSCI USA Momentum Factor ETF MTUM Jan 2014 May 2019 0.95 -0.22 -0.32 0.30 -0.10 -0.15 0.22% 2.64% 92.9%
iShares MSCI USA Quality Factor ETF QUAL Jan 2014 May 2019 0.99 -0.12 -0.12 0.02 0.15 -0.03 -0.06% -0.74% 96.3%
iShares S&P Small-Cap 600 Value ETF IJS Jan 2014 May 2019 1.14 1.15 0.43 0.03 0.58 0.06 -0.11% -1.31% 97.5%
iShares MSCI USA Min Vol Factor ETF USMV Jan 2014 May 2019 0.77 -0.19 -0.01 0.05 0.10 0.29 0.03% 0.37% 85.5%
Schwab US Large-Cap Growth ETF SCHG Jan 2014 May 2019 1.01 -0.14 -0.34 0.01 -0.09 -0.07 0.13% 1.55% 97.9%

iShares MSCI USA Momentum Factor ETF

Factor regression results for iShares MSCI USA Momentum Factor ETF
Ticker MTUM
Time Period Jan 2014 - May 2019
Regression Basis 65 monthly samples
Coefficient of Determination (R2) 92.9%
Adjusted R2 92.2%
Regression F statistic 126.61 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.147 with p-value 0.732)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 11.090 with p-value 0.086)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.95 0.043 22.244 0.000 0.866...1.037
Size (SMB) -0.22 0.064 -3.433 0.001 -0.347...-0.091
Value (HML) -0.32 0.077 -4.220 0.000 -0.477...-0.170
Momentum (MOM) 0.30 0.052 5.699 0.000 0.193...0.403
Quality (QMJ) -0.10 0.068 -1.422 0.160 -0.234...0.040
Bet Against Beta (BAB) -0.15 0.088 -1.735 0.088 -0.327...0.023
Alpha (α) 21.97bps 0.001 1.568 0.122 -0.06%...0.50%
Annualized Alpha (α) 2.64%  

iShares MSCI USA Quality Factor ETF

Factor regression results for iShares MSCI USA Quality Factor ETF
Ticker QUAL
Time Period Jan 2014 - May 2019
Regression Basis 65 monthly samples
Coefficient of Determination (R2) 96.3%
Adjusted R2 95.9%
Regression F statistic 249.56 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.107 with p-value 0.676)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.756 with p-value 0.941)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.99 0.030 32.716 0.000 0.926...1.046
Size (SMB) -0.12 0.045 -2.767 0.008 -0.214...-0.034
Value (HML) -0.12 0.054 -2.236 0.029 -0.229...-0.013
Momentum (MOM) 0.02 0.037 0.549 0.585 -0.054...0.094
Quality (QMJ) 0.15 0.048 3.076 0.003 0.052...0.244
Bet Against Beta (BAB) -0.03 0.062 -0.478 0.635 -0.153...0.094
Alpha (α) -6.14bps 0.001 -0.622 0.536 -0.26%...0.14%
Annualized Alpha (α) -0.74%  

iShares S&P Small-Cap 600 Value ETF

Factor regression results for iShares S&P Small-Cap 600 Value ETF
Ticker IJS
Time Period Jan 2014 - May 2019
Regression Basis 65 monthly samples
Coefficient of Determination (R2) 97.5%
Adjusted R2 97.3%
Regression F statistic 379.17 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.114 with p-value 0.686)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 11.206 with p-value 0.082)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.14 0.036 31.928 0.000 1.071...1.214
Size (SMB) 1.15 0.053 21.530 0.000 1.042...1.256
Value (HML) 0.43 0.064 6.719 0.000 0.302...0.559
Momentum (MOM) 0.03 0.044 0.793 0.431 -0.053...0.122
Quality (QMJ) 0.58 0.057 10.226 0.000 0.469...0.698
Bet Against Beta (BAB) 0.06 0.073 0.819 0.416 -0.087...0.207
Alpha (α) -10.95bps 0.001 -0.935 0.354 -0.34%...0.13%
Annualized Alpha (α) -1.31%  

iShares MSCI USA Min Vol Factor ETF

Factor regression results for iShares MSCI USA Min Vol Factor ETF
Ticker USMV
Time Period Jan 2014 - May 2019
Regression Basis 65 monthly samples
Coefficient of Determination (R2) 85.5%
Adjusted R2 84.0%
Regression F statistic 57.03 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.869 with p-value 0.306)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 9.237 with p-value 0.161)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.77 0.047 16.617 0.000 0.681...0.868
Size (SMB) -0.19 0.070 -2.740 0.008 -0.330...-0.051
Value (HML) -0.01 0.083 -0.150 0.881 -0.180...0.155
Momentum (MOM) 0.05 0.057 0.815 0.419 -0.068...0.161
Quality (QMJ) 0.10 0.074 1.359 0.180 -0.048...0.250
Bet Against Beta (BAB) 0.29 0.095 3.012 0.004 0.096...0.478
Alpha (α) 3.08bps 0.002 0.202 0.841 -0.27%...0.34%
Annualized Alpha (α) 0.37%  

Schwab US Large-Cap Growth ETF

Factor regression results for Schwab US Large-Cap Growth ETF
Ticker SCHG
Time Period Jan 2014 - May 2019
Regression Basis 65 monthly samples
Coefficient of Determination (R2) 97.9%
Adjusted R2 97.7%
Regression F statistic 449.55 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.243 with p-value 0.844)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.207 with p-value 0.977)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.025 40.677 0.000 0.959...1.058
Size (SMB) -0.14 0.037 -3.884 0.000 -0.218...-0.070
Value (HML) -0.34 0.044 -7.575 0.000 -0.425...-0.247
Momentum (MOM) 0.01 0.030 0.306 0.761 -0.051...0.070
Quality (QMJ) -0.09 0.040 -2.244 0.029 -0.168...-0.010
Bet Against Beta (BAB) -0.07 0.051 -1.402 0.166 -0.173...0.030
Alpha (α) 12.88bps 0.001 1.587 0.118 -0.03%...0.29%
Annualized Alpha (α) 1.55%  
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
    Bqmj
    Quality loading factor
    QMJ
    Quality Minus Junk factor
    Bbab
    Bet Against Beta loading factor
    BAB
    Betting Against Beta factor
    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) 67.28 -27.48 -56.72 45.22 59.00 79.91  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM QMJ BAB Total R2
iShares MSCI USA Momentum Factor ETF MTUM Jan 2014 May 2019 2.64% 64.04 6.02 18.33 13.49 -5.73 -12.14 105.98 92.9%
iShares MSCI USA Quality Factor ETF QUAL Jan 2014 May 2019 -0.74% 66.35 3.42 6.84 0.92 8.73 -2.36 77.76 96.3%
iShares S&P Small-Cap 600 Value ETF IJS Jan 2014 May 2019 -1.31% 76.86 -31.57 -24.41 1.57 34.44 4.80 50.73 97.5%
iShares MSCI USA Min Vol Factor ETF USMV Jan 2014 May 2019 0.37% 52.13 5.24 0.71 2.10 5.96 22.97 92.18 85.5%
Schwab US Large-Cap Growth ETF SCHG Jan 2014 May 2019 1.55% 67.86 3.95 19.07 0.42 -5.24 -5.69 93.26 97.9%
Regression residuals
MonthMTUMQUALIJSUSMVSCHG
Jan 2014-0.0005-0.00590.0158-0.00860.0010
Feb 20140.01380.0036-0.00160.00820.0003
Mar 2014-0.0222-0.0068-0.0044-0.00140.0005
Apr 2014-0.00310.00460.01180.0065-0.0016
May 20140.01350.0016-0.0008-0.01100.0100
Jun 2014-0.0075-0.0163-0.0140-0.0024-0.0059
Jul 20140.00260.00800.0077-0.00930.0075
Aug 20140.00130.0032-0.00070.0030-0.0026
Sep 20140.00140.00470.0045-0.0078-0.0019
Oct 20140.0015-0.00160.01100.01830.0024
Nov 20140.0045-0.00810.00300.0029-0.0004
Dec 2014-0.00630.00230.00890.00370.0003
Jan 2015-0.00140.0105-0.00390.00740.0084
Feb 2015-0.00130.0016-0.00950.0002-0.0013
Mar 2015-0.0111-0.00470.0047-0.0023-0.0004
Apr 20150.0029-0.0026-0.0117-0.0041-0.0078
May 2015-0.00100.0014-0.0004-0.0097-0.0016
Jun 20150.0050-0.0031-0.0007-0.01490.0027
Jul 2015-0.02010.00450.00720.0023-0.0000
Aug 20150.00670.0064-0.00120.00650.0071
Sep 2015-0.00490.00850.0065-0.0116-0.0005
Oct 20150.00420.01180.00050.00290.0041
Nov 2015-0.00800.00060.0062-0.0077-0.0043
Dec 2015-0.0013-0.00190.00720.0063-0.0100
Jan 20160.0130-0.0022-0.00140.0139-0.0062
Feb 20160.00210.0038-0.00280.01220.0029
Mar 20160.00570.00300.00370.01770.0041
Apr 20160.01070.0011-0.00360.0061-0.0029
May 2016-0.0056-0.00830.0030-0.0061-0.0044
Jun 20160.01970.0031-0.00710.0314-0.0088
Jul 2016-0.0024-0.0055-0.0103-0.01740.0085
Aug 2016-0.0071-0.0023-0.0057-0.01360.0020
Sep 20160.00150.00340.0063-0.00240.0016
Oct 20160.0022-0.00370.0027-0.02360.0013
Nov 2016-0.0181-0.00330.0154-0.01400.0013
Dec 20160.00660.0037-0.0114-0.0020-0.0006
Jan 20170.0044-0.0067-0.0120-0.00350.0077
Feb 2017-0.00070.00790.00370.0098-0.0033
Mar 20170.0163-0.0040-0.0102-0.0039-0.0012
Apr 20170.0108-0.0083-0.0070-0.00180.0062
May 20170.0195-0.00390.0017-0.00290.0009
Jun 2017-0.00460.00040.0008-0.0068-0.0088
Jul 20170.0049-0.00960.00530.00100.0031
Aug 2017-0.00670.0004-0.00390.00250.0001
Sep 20170.01600.00860.0166-0.0061-0.0080
Oct 20170.00890.0032-0.0059-0.00480.0050
Nov 20170.00140.0048-0.00530.00000.0014
Dec 2017-0.00540.0045-0.0002-0.0074-0.0021
Jan 20180.0072-0.0125-0.0080-0.01330.0069
Feb 2018-0.00090.00370.0058-0.01040.0015
Mar 2018-0.00330.0125-0.00190.01120.0021
Apr 20180.0062-0.01260.00360.00120.0039
May 2018-0.00160.0024-0.0049-0.00680.0059
Jun 20180.0007-0.0056-0.00780.00650.0054
Jul 2018-0.01530.00150.01000.0037-0.0097
Aug 2018-0.0028-0.0014-0.00320.00650.0016
Sep 20180.00090.0071-0.00650.00810.0012
Oct 2018-0.0140-0.0055-0.01330.00200.0018
Nov 2018-0.0087-0.01390.00070.0133-0.0150
Dec 2018-0.00320.00140.0069-0.00200.0014
Jan 2019-0.00190.00370.0151-0.0005-0.0023
Feb 2019-0.00850.0091-0.00970.0151-0.0121
Mar 2019-0.01550.0074-0.00450.0088-0.0004
Apr 2019-0.0097-0.00400.0045-0.01270.0065
May 20190.0086-0.0062-0.00580.0137-0.0046