Fama-French Factor Regression Analysis

This online Fama-French factor regression analysis tool supports regression analysis for individual assets or a portfolio of assets using the capital asset pricing model (CAPM), Fama-French three-factor model, the Carhart four-factor model, or the new Fama-French five-factor model. You can also run market model regression for beta analysis based on selected assets or imported benchmarks. The analysis is based on asset returns for the entered mutual funds and ETFs, and the factor returns published on Kenneth French's web site and AQR's web site. The multiple linear regression indicates how well the returns of the given assets or a portfolio are explained by the Fama-French three-factor model based on market, size and value loading factors. Carhart four-factor model adds momentum as the fourth factor for explaining asset returns, and the Fama-French five-factor model extends the three-factor model with profitability (RMW) and investment (CMA) factors. The tool also supports the use of other factor models including Quality Minus Junk (QMJ) and Bet Against Beta (BAB) factors as described in Asness-Frazzini-Pedersen papers. For bond 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 exposure. 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. You can also view the table of mutual fund and ETF factor regressions.

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Factor Analysis Results

Factor Analysis Summary

Factor regression results
Name Ticker Start Date End Date Rm-Rf SMB HML-DEV MOM QMJ BAB Alpha Annual Alpha R2
Vanguard PRIMECAP Adm VPMAX Dec 2013 Dec 2017 0.97 -0.04 -0.33 -0.17 -0.13 0.14 0.25% 2.98% 90.5%
AQR Style Premia Alternative I QSPIX Dec 2013 Dec 2017 0.15 -0.32 0.38 0.31 0.20 0.25 0.03% 0.30% 47.3%
iShares Edge MSCI USA Momentum Fctr ETF MTUM Dec 2013 Dec 2017 0.98 -0.26 -0.32 0.19 -0.06 -0.21 0.41% 4.87% 89.6%

Vanguard PRIMECAP Adm

Factor regression results for Vanguard PRIMECAP Adm
Ticker VPMAX
Time Period Dec 2013 - Dec 2017
Coefficient of Determination (R2) 90.5%
Adjusted R2 89.2%
Regression F statistic 66.82 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.204 with p-value 0.788)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.067 with p-value 0.983)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.97 0.057 16.951 0.000 0.855...1.086
Size (SMB) -0.04 0.080 -0.559 0.579 -0.205...0.116
Value (HML-DEV) -0.33 0.081 -4.015 0.000 -0.491...-0.162
Momentum (MOM) -0.17 0.073 -2.320 0.025 -0.316...-0.022
Quality (QMJ) -0.13 0.076 -1.665 0.103 -0.281...0.027
Low Beta (BAB) 0.14 0.128 1.076 0.288 -0.121...0.397
Alpha (α) 24.82bps 0.002 1.365 0.180 -0.12%...0.62%
Annualized Alpha (α) 2.98%  

AQR Style Premia Alternative I

Factor regression results for AQR Style Premia Alternative I
Ticker QSPIX
Time Period Dec 2013 - Dec 2017
Coefficient of Determination (R2) 47.3%
Adjusted R2 39.8%
Regression F statistic 6.29 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.184 with p-value 0.768)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 7.669 with p-value 0.263)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.15 0.086 1.765 0.085 -0.022...0.326
Size (SMB) -0.32 0.120 -2.629 0.012 -0.557...-0.073
Value (HML-DEV) 0.38 0.123 3.109 0.003 0.134...0.628
Momentum (MOM) 0.31 0.110 2.854 0.007 0.092...0.535
Quality (QMJ) 0.20 0.115 1.742 0.089 -0.032...0.432
Low Beta (BAB) 0.25 0.193 1.311 0.197 -0.137...0.644
Alpha (α) 2.53bps 0.003 0.092 0.927 -0.53%...0.58%
Annualized Alpha (α) 0.30%  

iShares Edge MSCI USA Momentum Fctr ETF

Factor regression results for iShares Edge MSCI USA Momentum Fctr ETF
Ticker MTUM
Time Period Dec 2013 - Dec 2017
Coefficient of Determination (R2) 89.6%
Adjusted R2 88.1%
Regression F statistic 60.09 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.211 with p-value 0.796)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 9.004 with p-value 0.173)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.98 0.057 16.995 0.000 0.860...1.092
Size (SMB) -0.26 0.080 -3.222 0.002 -0.418...-0.096
Value (HML-DEV) -0.32 0.082 -3.901 0.000 -0.483...-0.154
Momentum (MOM) 0.19 0.073 2.633 0.012 0.045...0.340
Quality (QMJ) -0.06 0.076 -0.743 0.462 -0.211...0.097
Low Beta (BAB) -0.21 0.129 -1.651 0.106 -0.472...0.047
Alpha (α) 40.62bps 0.002 2.226 0.031 0.04%...0.77%
Annualized Alpha (α) 4.87%  
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 × UMD + 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. See QMJ paper by Asness-Frazzini-Pedersen
    Bbab
    Low Beta loading factor
    BAB
    Bet Against Beta factor. See BAB paper by Frazzini-Pedersen
    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) 88.30 -26.73 -30.02 38.63 59.34 91.73  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML-DEV MOM QMJ BAB Total R2
Vanguard PRIMECAP Adm VPMAX Dec 2013 Dec 2017 2.98% 85.67 1.19 9.80 -6.53 -7.53 12.66 120.09 90.5%
AQR Style Premia Alternative I QSPIX Dec 2013 Dec 2017 0.30% 13.44 8.42 -11.43 12.11 11.87 23.25 60.18 47.3%
iShares Edge MSCI USA Momentum Fctr ETF MTUM Dec 2013 Dec 2017 4.87% 86.16 6.88 9.55 7.44 -3.37 -19.50 127.78 89.6%
Regression residuals
MonthVPMAXQSPIXMTUM
Dec 2013-0.0136-0.0062-0.0080
Jan 20140.0101-0.01430.0018
Feb 20140.0092-0.00410.0117
Mar 20140.00090.0125-0.0254
Apr 2014-0.01910.0047-0.0076
May 20140.0133-0.00030.0120
Jun 2014-0.0064-0.0073-0.0081
Jul 20140.00850.0109-0.0002
Aug 2014-0.0077-0.01320.0012
Sep 20140.0117-0.01630.0007
Oct 2014-0.00670.02990.0017
Nov 20140.00050.02630.0003
Dec 2014-0.00090.0005-0.0066
Jan 20150.0016-0.0143-0.0013
Feb 2015-0.0088-0.0294-0.0018
Mar 2015-0.00740.0268-0.0107
Apr 2015-0.0121-0.0051-0.0023
May 2015-0.00100.01670.0015
Jun 2015-0.0130-0.00970.0062
Jul 2015-0.0057-0.0195-0.0138
Aug 20150.00670.00430.0047
Sep 20150.01230.0120-0.0051
Oct 20150.01180.0052-0.0013
Nov 2015-0.0051-0.0138-0.0080
Dec 20150.00790.0157-0.0031
Jan 2016-0.0011-0.00770.0058
Feb 2016-0.0115-0.01380.0004
Mar 20160.0049-0.01040.0086
Apr 2016-0.00230.01070.0128
May 20160.0032-0.0199-0.0080
Jun 2016-0.0254-0.01140.0181
Jul 20160.01250.0066-0.0059
Aug 20160.0092-0.0126-0.0123
Sep 20160.00760.0171-0.0008
Oct 2016-0.0011-0.01210.0007
Nov 20160.00880.0048-0.0211
Dec 20160.0011-0.01990.0080
Jan 20170.00150.00600.0019
Feb 2017-0.00230.0206-0.0006
Mar 2017-0.0076-0.01100.0132
Apr 2017-0.0041-0.00650.0105
May 20170.0050-0.00560.0156
Jun 20170.00380.00350.0001
Jul 2017-0.01240.01710.0036
Aug 2017-0.00050.0077-0.0091
Sep 20170.01740.00750.0183
Oct 20170.00790.00940.0068
Nov 20170.0022-0.00090.0009
Dec 2017-0.00340.0088-0.0062