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 Edge MSCI USA Momentum Fctr ETF MTUM Jan 2014 May 2019 0.95 -0.22 -0.32 0.30 -0.10 -0.15 0.22% 2.67% 92.9%
iShares Edge MSCI USA Quality Factor ETF QUAL Jan 2014 May 2019 0.99 -0.12 -0.12 0.02 0.15 -0.03 -0.06% -0.76% 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% -1.37% 97.5%
iShares Edge MSCI Min Vol USA ETF USMV Jan 2014 May 2019 0.78 -0.19 -0.01 0.05 0.10 0.29 0.03% 0.34% 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% 1.57% 97.9%

iShares Edge MSCI USA Momentum Fctr ETF

Factor regression results for iShares Edge MSCI USA Momentum Fctr ETF
Ticker MTUM
Time Period Jan 2014 - May 2019
Coefficient of Determination (R2) 92.9%
Adjusted R2 92.2%
Regression F statistic 127.06 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.146 with p-value 0.730)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 11.084 with p-value 0.086)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.95 0.043 22.238 0.000 0.866...1.037
Size (SMB) -0.22 0.064 -3.454 0.001 -0.348...-0.093
Value (HML) -0.32 0.076 -4.234 0.000 -0.477...-0.171
Momentum (MOM) 0.30 0.052 5.731 0.000 0.195...0.403
Quality (QMJ) -0.10 0.068 -1.442 0.155 -0.235...0.038
Bet Against Beta (BAB) -0.15 0.088 -1.761 0.083 -0.330...0.021
Alpha (α) 22.25bps 0.001 1.588 0.118 -0.06%...0.50%
Annualized Alpha (α) 2.67%  

iShares Edge MSCI USA Quality Factor ETF

Factor regression results for iShares Edge MSCI USA Quality Factor ETF
Ticker QUAL
Time Period Jan 2014 - May 2019
Coefficient of Determination (R2) 96.3%
Adjusted R2 95.9%
Regression F statistic 249.24 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.102 with p-value 0.669)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.820 with p-value 0.936)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.99 0.030 32.653 0.000 0.926...1.047
Size (SMB) -0.12 0.045 -2.754 0.008 -0.214...-0.034
Value (HML) -0.12 0.054 -2.237 0.029 -0.229...-0.013
Momentum (MOM) 0.02 0.037 0.516 0.608 -0.055...0.093
Quality (QMJ) 0.15 0.048 3.068 0.003 0.051...0.244
Bet Against Beta (BAB) -0.03 0.062 -0.450 0.654 -0.152...0.096
Alpha (α) -6.32bps 0.001 -0.639 0.526 -0.26%...0.13%
Annualized Alpha (α) -0.76%  

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
Coefficient of Determination (R2) 97.5%
Adjusted R2 97.2%
Regression F statistic 371.64 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.122 with p-value 0.698)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 11.121 with p-value 0.085)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.14 0.036 31.602 0.000 1.071...1.216
Size (SMB) 1.15 0.054 21.311 0.000 1.042...1.259
Value (HML) 0.43 0.065 6.659 0.000 0.301...0.560
Momentum (MOM) 0.03 0.044 0.724 0.472 -0.056...0.120
Quality (QMJ) 0.58 0.058 10.085 0.000 0.467...0.698
Bet Against Beta (BAB) 0.06 0.074 0.862 0.392 -0.084...0.212
Alpha (α) -11.40bps 0.001 -0.962 0.340 -0.35%...0.12%
Annualized Alpha (α) -1.37%  

iShares Edge MSCI Min Vol USA ETF

Factor regression results for iShares Edge MSCI Min Vol USA ETF
Ticker USMV
Time Period Jan 2014 - May 2019
Coefficient of Determination (R2) 85.5%
Adjusted R2 84.0%
Regression F statistic 57.01 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.867 with p-value 0.302)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 9.199 with p-value 0.163)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.78 0.047 16.605 0.000 0.682...0.869
Size (SMB) -0.19 0.070 -2.713 0.009 -0.329...-0.050
Value (HML) -0.01 0.083 -0.151 0.881 -0.180...0.154
Momentum (MOM) 0.05 0.057 0.808 0.422 -0.068...0.160
Quality (QMJ) 0.10 0.075 1.387 0.171 -0.046...0.253
Bet Against Beta (BAB) 0.29 0.096 3.013 0.004 0.097...0.479
Alpha (α) 2.87bps 0.002 0.188 0.852 -0.28%...0.33%
Annualized Alpha (α) 0.34%  

Schwab US Large-Cap Growth ETF

Factor regression results for Schwab US Large-Cap Growth ETF
Ticker SCHG
Time Period Jan 2014 - May 2019
Coefficient of Determination (R2) 97.9%
Adjusted R2 97.7%
Regression F statistic 448.38 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.244 with p-value 0.845)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.204 with p-value 0.977)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.01 0.025 40.556 0.000 0.959...1.058
Size (SMB) -0.14 0.037 -3.878 0.000 -0.218...-0.070
Value (HML) -0.34 0.044 -7.563 0.000 -0.425...-0.247
Momentum (MOM) 0.01 0.030 0.340 0.735 -0.050...0.071
Quality (QMJ) -0.09 0.040 -2.196 0.032 -0.167...-0.008
Bet Against Beta (BAB) -0.07 0.051 -1.469 0.147 -0.177...0.027
Alpha (α) 13.07bps 0.001 1.605 0.114 -0.03%...0.29%
Annualized Alpha (α) 1.57%  
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 -27.47 -56.78 45.01 59.59 79.84  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM QMJ BAB Total R2
iShares Edge MSCI USA Momentum Fctr ETF MTUM Jan 2014 May 2019 2.67% 64.02 6.06 18.38 13.46 -5.87 -12.31 105.98 92.9%
iShares Edge MSCI USA Quality Factor ETF QUAL Jan 2014 May 2019 -0.76% 66.37 3.41 6.86 0.86 8.81 -2.22 77.76 96.3%
iShares S&P Small-Cap 600 Value ETF IJS Jan 2014 May 2019 -1.37% 76.94 -31.60 -24.44 1.44 34.69 5.10 50.73 97.5%
iShares Edge MSCI Min Vol USA ETF USMV Jan 2014 May 2019 0.34% 52.18 5.19 0.71 2.07 6.16 23.00 92.18 85.5%
Schwab US Large-Cap Growth ETF SCHG Jan 2014 May 2019 1.57% 67.85 3.95 19.08 0.46 -5.19 -5.97 93.26 97.9%
Regression residuals
MonthMTUMQUALIJSUSMVSCHG
Jan 2014-0.0006-0.00590.0158-0.00850.0011
Feb 20140.01380.0036-0.00160.00820.0003
Mar 2014-0.0221-0.0068-0.0044-0.00140.0005
Apr 2014-0.00320.00450.01180.0066-0.0016
May 20140.01350.0016-0.0007-0.01100.0101
Jun 2014-0.0075-0.0162-0.0140-0.0023-0.0059
Jul 20140.00250.00800.0078-0.00920.0075
Aug 20140.00140.0032-0.00070.0030-0.0025
Sep 20140.00140.00470.0046-0.0078-0.0019
Oct 20140.0017-0.00160.01100.01830.0024
Nov 20140.0044-0.00810.00300.0030-0.0004
Dec 2014-0.00620.00240.00890.00340.0003
Jan 2015-0.00150.0105-0.00370.00760.0084
Feb 2015-0.00130.0016-0.00950.0002-0.0014
Mar 2015-0.0111-0.00470.0048-0.0022-0.0004
Apr 20150.0031-0.0025-0.0119-0.0044-0.0077
May 2015-0.00100.0015-0.0003-0.0097-0.0016
Jun 20150.0050-0.0031-0.0006-0.01490.0027
Jul 2015-0.02010.00460.00740.00230.0000
Aug 20150.00670.0065-0.00100.00660.0069
Sep 2015-0.00490.00850.0068-0.0115-0.0005
Oct 20150.00420.01180.00050.00290.0041
Nov 2015-0.00800.00060.0063-0.0078-0.0043
Dec 2015-0.0013-0.00180.00740.0063-0.0100
Jan 20160.0130-0.0021-0.00110.0139-0.0064
Feb 20160.00210.0037-0.00290.01210.0028
Mar 20160.00550.00300.00360.01790.0040
Apr 20160.01060.0011-0.00370.0062-0.0029
May 2016-0.0057-0.00830.0031-0.0061-0.0044
Jun 20160.01970.0032-0.00700.0314-0.0088
Jul 2016-0.0023-0.0055-0.0105-0.01750.0086
Aug 2016-0.0072-0.0023-0.0057-0.01350.0019
Sep 20160.00150.00340.0063-0.00230.0017
Oct 20160.0022-0.00370.0028-0.02360.0013
Nov 2016-0.0181-0.00330.0153-0.01410.0013
Dec 20160.00680.0036-0.0115-0.0021-0.0005
Jan 20170.0044-0.0067-0.0121-0.00340.0077
Feb 2017-0.00070.00790.00360.0097-0.0033
Mar 20170.0163-0.0041-0.0102-0.0039-0.0012
Apr 20170.0109-0.0083-0.0070-0.00190.0062
May 20170.0195-0.00380.0018-0.00290.0009
Jun 2017-0.00460.00040.0008-0.0068-0.0088
Jul 20170.0049-0.00960.00520.00100.0031
Aug 2017-0.00670.0003-0.00450.00240.0001
Sep 20170.01590.00880.0172-0.0060-0.0081
Oct 20170.00890.0032-0.0060-0.00490.0050
Nov 20170.00150.0049-0.0052-0.00000.0014
Dec 2017-0.00520.0045-0.0003-0.0073-0.0020
Jan 20180.0072-0.0125-0.0081-0.01330.0069
Feb 2018-0.00100.00380.0060-0.01050.0014
Mar 2018-0.00320.0124-0.00200.01110.0022
Apr 20180.0061-0.01250.00400.00130.0039
May 2018-0.00160.0023-0.0050-0.00680.0059
Jun 20180.0007-0.0057-0.00810.00650.0055
Jul 2018-0.01540.00150.01020.0037-0.0098
Aug 2018-0.0027-0.0014-0.00350.00630.0016
Sep 20180.00090.0071-0.00670.00810.0012
Oct 2018-0.0139-0.0055-0.01340.00200.0019
Nov 2018-0.0089-0.01380.00110.0134-0.0151
Dec 2018-0.00320.00130.0067-0.00200.0014
Jan 2019-0.00200.00370.0153-0.0004-0.0023
Feb 2019-0.00850.0092-0.00950.0151-0.0121
Mar 2019-0.01520.0074-0.00480.0087-0.0003
Apr 2019-0.0099-0.00400.0045-0.01270.0065
May 20190.0084-0.0063-0.00640.0136-0.0045