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 7
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Asset 9
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Factor Analysis Results

iShares Edge MSCI USA Momentum Fctr ETF

Factor regression results for iShares Edge MSCI USA Momentum Fctr ETF
Ticker MTUM
Time Period May 2013 - Sep 2018
Coefficient of Determination (R2) 91.5%
Adjusted R2 90.9%
Regression F statistic 160.68 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.271 with p-value 0.876)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 5.155 with p-value 0.272)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.041 23.531 0.000 0.879...1.042
Size (SMB) -0.17 0.047 -3.659 0.001 -0.265...-0.078
Value (HML) -0.28 0.057 -4.835 0.000 -0.390...-0.162
Momentum (MOM) 0.25 0.043 5.872 0.000 0.167...0.339
Alpha (α) 16.63bps 0.001 1.363 0.178 -0.08%...0.41%
Annualized Alpha (α) 2.00%  
Notes on results:
  • Time frame for factor analysis is the full available data range unless a specific date interval is specified.
  • 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
    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
  • Resources:

Factor Performance Attribution in Basis Points

Factor regression results
Monthly Factor Premiums (BPS) 112.58 6.60 -25.23 37.12  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
iShares Edge MSCI USA Momentum Fctr ETF MTUM May 2013 Sep 2018 2.00% 108.14 -1.13 6.96 9.38 139.98 91.5%
Regression residuals
MonthMTUM
May 2013-0.0110
Jun 20130.0016
Jul 20130.0041
Aug 2013-0.0185
Sep 2013-0.0135
Oct 20130.0140
Nov 20130.0016
Dec 2013-0.0037
Jan 2014-0.0015
Feb 20140.0151
Mar 2014-0.0207
Apr 2014-0.0041
May 20140.0124
Jun 2014-0.0045
Jul 20140.0009
Aug 20140.0006
Sep 2014-0.0007
Oct 2014-0.0004
Nov 2014-0.0032
Dec 2014-0.0018
Jan 20150.0010
Feb 2015-0.0032
Mar 2015-0.0051
Apr 20150.0010
May 20150.0014
Jun 20150.0046
Jul 2015-0.0231
Aug 20150.0099
Sep 2015-0.0075
Oct 20150.0037
Nov 2015-0.0027
Dec 2015-0.0030
Jan 20160.0122
Feb 2016-0.0036
Mar 20160.0020
Apr 20160.0091
May 2016-0.0047
Jun 20160.0145
Jul 2016-0.0040
Aug 2016-0.0025
Sep 20160.0015
Oct 20160.0005
Nov 2016-0.0116
Dec 20160.0026
Jan 20170.0037
Feb 2017-0.0026
Mar 20170.0126
Apr 20170.0078
May 20170.0168
Jun 20170.0018
Jul 20170.0071
Aug 2017-0.0074
Sep 20170.0205
Oct 20170.0119
Nov 2017-0.0039
Dec 2017-0.0092
Jan 20180.0069
Feb 20180.0048
Mar 2018-0.0052
Apr 20180.0021
May 2018-0.0034
Jun 2018-0.0069
Jul 2018-0.0149
Aug 2018-0.0003
Sep 2018-0.0020