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.

Portfolio Assets
Allocation
Asset 1
%
Asset 2
%
Asset 3
%
Asset 4
%
Asset 5
%
Asset 6
%
Asset 7
%
Asset 8
%
Asset 9
%
Asset 10
%
Total
%

Factor Analysis Results

Factor Analysis Summary

Factor regression results
Name Ticker Start Date End Date Rm-Rf SMB HML MOM Alpha Annual Alpha R2
SPDR S&P 400 Mid Cap Value ETF MDYV Jan 2011 Dec 2014 1.06 0.37 0.23 0.00 -0.04% -0.49% 95.7%
iShares Core S&P US Value ETF IUSV Jan 2011 Dec 2014 0.96 0.00 0.30 0.02 0.02% 0.23% 98.3%
SPDR Portfolio S&P 500 Value ETF SPYV Jan 2011 Dec 2014 1.02 -0.12 0.32 -0.06 -0.06% -0.73% 97.8%
SPDR S&P 600 Small Cap Value ETF SLYV Jan 2011 Dec 2014 1.03 0.80 0.19 -0.11 0.13% 1.56% 97.6%
Vanguard Mega Cap Value ETF MGV Jan 2011 Dec 2014 0.95 -0.20 0.33 0.03 -0.00% -0.06% 96.5%
Schwab US Large-Cap Value ETF SCHV Jan 2011 Dec 2014 0.93 -0.20 0.24 0.10 -0.02% -0.27% 96.6%
iShares Morningstar Small-Cap Value ETF JKL Jan 2011 Dec 2014 1.06 0.49 0.25 -0.01 -0.02% -0.28% 96.7%
iShares S&P Mid-Cap 400 Value ETF IJJ Jan 2011 Dec 2014 1.06 0.41 0.20 0.01 -0.04% -0.44% 95.1%
Vanguard Small-Cap Value ETF VBR Jan 2011 Dec 2014 1.04 0.56 0.24 -0.02 0.02% 0.20% 98.4%
Vanguard Russell 1000 Value ETF VONV Jan 2011 Dec 2014 0.97 -0.06 0.33 0.05 0.01% 0.09% 98.1%

SPDR S&P 400 Mid Cap Value ETF

Factor regression results for SPDR S&P 400 Mid Cap Value ETF
Ticker MDYV
Time Period Jan 2011 - Dec 2014
Coefficient of Determination (R2) 95.7%
Adjusted R2 95.3%
Regression F statistic 237.19 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.202 with p-value 0.767)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 0.458 with p-value 0.977)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.047 22.741 0.000 0.966...1.154
Size (SMB) 0.37 0.076 4.877 0.000 0.217...0.523
Value (HML) 0.23 0.083 2.726 0.009 0.059...0.395
Momentum (MOM) 0.00 0.061 0.081 0.935 -0.117...0.127
Alpha (α) -4.12bps 0.001 -0.276 0.784 -0.34%...0.26%
Annualized Alpha (α) -0.49%  

iShares Core S&P US Value ETF

Factor regression results for iShares Core S&P US Value ETF
Ticker IUSV
Time Period Jan 2011 - Dec 2014
Coefficient of Determination (R2) 98.3%
Adjusted R2 98.2%
Regression F statistic 625.13 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.923 with p-value 0.404)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 5.022 with p-value 0.285)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.024 40.362 0.000 0.915...1.011
Size (SMB) 0.00 0.039 0.056 0.955 -0.076...0.080
Value (HML) 0.30 0.043 7.125 0.000 0.218...0.390
Momentum (MOM) 0.02 0.031 0.738 0.464 -0.040...0.085
Alpha (α) 1.93bps 0.001 0.252 0.802 -0.14%...0.17%
Annualized Alpha (α) 0.23%  

SPDR Portfolio S&P 500 Value ETF

Factor regression results for SPDR Portfolio S&P 500 Value ETF
Ticker SPYV
Time Period Jan 2011 - Dec 2014
Coefficient of Determination (R2) 97.8%
Adjusted R2 97.6%
Regression F statistic 486.97 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.390 with p-value 0.918)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 5.614 with p-value 0.230)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.02 0.028 36.124 0.000 0.960...1.073
Size (SMB) -0.12 0.046 -2.555 0.014 -0.209...-0.025
Value (HML) 0.32 0.050 6.422 0.000 0.221...0.424
Momentum (MOM) -0.06 0.037 -1.759 0.086 -0.138...0.009
Alpha (α) -6.07bps 0.001 -0.672 0.505 -0.24%...0.12%
Annualized Alpha (α) -0.73%  

SPDR S&P 600 Small Cap Value ETF

Factor regression results for SPDR S&P 600 Small Cap Value ETF
Ticker SLYV
Time Period Jan 2011 - Dec 2014
Coefficient of Determination (R2) 97.6%
Adjusted R2 97.4%
Regression F statistic 439.09 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.720 with p-value 0.170)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 2.393 with p-value 0.664)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.03 0.038 26.714 0.000 0.948...1.103
Size (SMB) 0.80 0.062 12.827 0.000 0.675...0.927
Value (HML) 0.19 0.069 2.769 0.008 0.052...0.328
Momentum (MOM) -0.11 0.050 -2.155 0.037 -0.208...-0.007
Alpha (α) 12.98bps 0.001 1.054 0.298 -0.12%...0.38%
Annualized Alpha (α) 1.56%  

Vanguard Mega Cap Value ETF

Factor regression results for Vanguard Mega Cap Value ETF
Ticker MGV
Time Period Jan 2011 - Dec 2014
Coefficient of Determination (R2) 96.5%
Adjusted R2 96.2%
Regression F statistic 298.13 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.153 with p-value 0.710)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.450 with p-value 0.835)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.95 0.032 29.212 0.000 0.883...1.014
Size (SMB) -0.20 0.053 -3.758 0.001 -0.305...-0.092
Value (HML) 0.33 0.058 5.614 0.000 0.209...0.443
Momentum (MOM) 0.03 0.042 0.778 0.441 -0.052...0.118
Alpha (α) -0.46bps 0.001 -0.044 0.965 -0.21%...0.21%
Annualized Alpha (α) -0.06%  

Schwab US Large-Cap Value ETF

Factor regression results for Schwab US Large-Cap Value ETF
Ticker SCHV
Time Period Jan 2011 - Dec 2014
Coefficient of Determination (R2) 96.6%
Adjusted R2 96.2%
Regression F statistic 302.02 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.195 with p-value 0.758)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 4.481 with p-value 0.345)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.93 0.031 30.159 0.000 0.872...0.996
Size (SMB) -0.20 0.050 -3.917 0.000 -0.299...-0.096
Value (HML) 0.24 0.055 4.363 0.000 0.130...0.353
Momentum (MOM) 0.10 0.040 2.529 0.015 0.021...0.183
Alpha (α) -2.24bps 0.001 -0.225 0.823 -0.22%...0.18%
Annualized Alpha (α) -0.27%  

iShares Morningstar Small-Cap Value ETF

Factor regression results for iShares Morningstar Small-Cap Value ETF
Ticker JKL
Time Period Jan 2011 - Dec 2014
Coefficient of Determination (R2) 96.7%
Adjusted R2 96.4%
Regression F statistic 318.87 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.605 with p-value 0.087)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.589 with p-value 0.811)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.042 25.377 0.000 0.976...1.145
Size (SMB) 0.49 0.068 7.138 0.000 0.348...0.623
Value (HML) 0.25 0.075 3.411 0.001 0.104...0.405
Momentum (MOM) -0.01 0.054 -0.094 0.925 -0.114...0.104
Alpha (α) -2.33bps 0.001 -0.173 0.863 -0.29%...0.25%
Annualized Alpha (α) -0.28%  

iShares S&P Mid-Cap 400 Value ETF

Factor regression results for iShares S&P Mid-Cap 400 Value ETF
Ticker IJJ
Time Period Jan 2011 - Dec 2014
Coefficient of Determination (R2) 95.1%
Adjusted R2 94.7%
Regression F statistic 210.33 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.037 with p-value 0.560)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.335 with p-value 0.855)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.050 21.259 0.000 0.961...1.163
Size (SMB) 0.41 0.081 5.009 0.000 0.243...0.571
Value (HML) 0.20 0.089 2.253 0.029 0.021...0.381
Momentum (MOM) 0.01 0.065 0.204 0.839 -0.118...0.144
Alpha (α) -3.68bps 0.002 -0.229 0.820 -0.36%...0.29%
Annualized Alpha (α) -0.44%  

Vanguard Small-Cap Value ETF

Factor regression results for Vanguard Small-Cap Value ETF
Ticker VBR
Time Period Jan 2011 - Dec 2014
Coefficient of Determination (R2) 98.4%
Adjusted R2 98.3%
Regression F statistic 660.95 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.797 with p-value 0.248)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 5.175 with p-value 0.270)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.04 0.029 35.604 0.000 0.984...1.103
Size (SMB) 0.56 0.048 11.744 0.000 0.464...0.656
Value (HML) 0.24 0.052 4.622 0.000 0.136...0.348
Momentum (MOM) -0.02 0.038 -0.529 0.599 -0.097...0.057
Alpha (α) 1.63bps 0.001 0.173 0.863 -0.17%...0.21%
Annualized Alpha (α) 0.20%  

Vanguard Russell 1000 Value ETF

Factor regression results for Vanguard Russell 1000 Value ETF
Ticker VONV
Time Period Jan 2011 - Dec 2014
Coefficient of Determination (R2) 98.1%
Adjusted R2 97.9%
Regression F statistic 560.03 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.970 with p-value 0.468)
Heteroskedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.027 with p-value 0.553)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.97 0.025 38.827 0.000 0.923...1.024
Size (SMB) -0.06 0.041 -1.417 0.164 -0.140...0.024
Value (HML) 0.33 0.045 7.304 0.000 0.237...0.417
Momentum (MOM) 0.05 0.033 1.546 0.130 -0.015...0.116
Alpha (α) 0.72bps 0.001 0.089 0.929 -0.16%...0.17%
Annualized Alpha (α) 0.09%  
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
    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) 124.42 -14.17 -1.19 31.98  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
SPDR S&P 400 Mid Cap Value ETF MDYV Jan 2011 Dec 2014 -0.49% 131.91 -5.24 -0.27 0.16 122.43 95.7%
iShares Core S&P US Value ETF IUSV Jan 2011 Dec 2014 0.23% 119.81 -0.03 -0.36 0.73 122.08 98.3%
SPDR Portfolio S&P 500 Value ETF SPYV Jan 2011 Dec 2014 -0.73% 126.44 1.66 -0.38 -2.05 119.59 97.8%
SPDR S&P 600 Small Cap Value ETF SLYV Jan 2011 Dec 2014 1.56% 127.55 -11.35 -0.23 -3.43 125.53 97.6%
Vanguard Mega Cap Value ETF MGV Jan 2011 Dec 2014 -0.06% 118.01 2.81 -0.39 1.05 121.03 96.5%
Schwab US Large-Cap Value ETF SCHV Jan 2011 Dec 2014 -0.27% 116.20 2.80 -0.29 3.25 119.72 96.6%
iShares Morningstar Small-Cap Value ETF JKL Jan 2011 Dec 2014 -0.28% 131.96 -6.88 -0.30 -0.16 122.29 96.7%
iShares S&P Mid-Cap 400 Value ETF IJJ Jan 2011 Dec 2014 -0.44% 132.16 -5.77 -0.24 0.42 122.90 95.1%
Vanguard Small-Cap Value ETF VBR Jan 2011 Dec 2014 0.20% 129.84 -7.93 -0.29 -0.64 122.60 98.4%
Vanguard Russell 1000 Value ETF VONV Jan 2011 Dec 2014 0.09% 121.12 0.82 -0.39 1.61 123.88 98.1%
Regression residuals
MonthMDYVIUSVSPYVSLYVMGVSCHVJKLIJJVBRVONV
Jan 20110.0072-0.00090.0054-0.00720.0038-0.00160.00200.0134-0.0033-0.0055
Feb 2011-0.0034-0.00180.0015-0.00920.00630.0029-0.0072-0.0037-0.00040.0006
Mar 20110.00870.00560.00670.00350.00100.0030-0.00140.0060-0.00030.0068
Apr 2011-0.00590.0038-0.0000-0.00860.01000.0080-0.0028-0.00470.00100.0048
May 2011-0.00190.00820.0002-0.00230.00200.00420.00710.00470.00080.0039
Jun 20110.0061-0.00350.00080.0067-0.0029-0.0018-0.0022-0.0044-0.00060.0011
Jul 2011-0.0074-0.0084-0.00960.0081-0.0094-0.0081-0.0009-0.00680.0015-0.0023
Aug 20110.00520.00120.00180.00570.00150.00610.00480.00670.0033-0.0033
Sep 2011-0.00220.00110.00560.00130.00480.01080.0028-0.0124-0.00480.0034
Oct 20110.00990.00610.01420.01010.00480.00080.01430.00820.00670.0053
Nov 2011-0.0110-0.0016-0.00860.0115-0.0089-0.00430.00310.00910.0039-0.0034
Dec 20110.00970.00590.00610.01660.01220.01420.01020.00040.00040.0087
Jan 2012-0.0023-0.0045-0.00130.0034-0.0062-0.0059-0.00240.00460.0059-0.0042
Feb 20120.0033-0.0048-0.0049-0.0157-0.0067-0.0068-0.0078-0.0001-0.0113-0.0072
Mar 2012-0.0066-0.0045-0.00020.0014-0.00250.0012-0.0089-0.0115-0.0069-0.0022
Apr 20120.0045-0.0016-0.0014-0.0022-0.0053-0.00200.00150.00770.0035-0.0062
May 2012-0.00430.00180.0060-0.00840.0037-0.00180.00870.00010.00390.0028
Jun 2012-0.00850.00630.0036-0.00020.01310.01160.0004-0.0128-0.00160.0049
Jul 20120.00220.00590.00200.01220.00150.0010-0.00670.00020.00310.0056
Aug 2012-0.0054-0.0077-0.00940.0011-0.0153-0.0125-0.0058-0.0027-0.0030-0.0037
Sep 2012-0.01180.0002-0.0017-0.00310.00440.0027-0.0043-0.0135-0.0075-0.0017
Oct 20120.00540.0003-0.0014-0.0049-0.0057-0.00120.01640.01100.0084-0.0007
Nov 20120.0108-0.0061-0.00330.0042-0.0117-0.0066-0.00180.00980.0008-0.0058
Dec 20120.00520.0015-0.0027-0.0050-0.00090.00050.00260.00550.0034-0.0028
Jan 20130.01070.00820.0080-0.00410.00830.00890.01050.01240.00140.0124
Feb 20130.0079-0.0017-0.00150.0051-0.00170.00280.00410.00400.0052-0.0023
Mar 20130.00690.00130.0000-0.00610.00280.00190.00530.00740.00010.0008
Apr 2013-0.0114-0.0027-0.00210.00290.00060.0017-0.0100-0.0077-0.0034-0.0031
May 2013-0.0106-0.0086-0.0027-0.0075-0.0045-0.0116-0.0197-0.0192-0.0143-0.0091
Jun 2013-0.00280.0013-0.0022-0.00590.00600.0027-0.0127-0.0052-0.00670.0033
Jul 2013-0.0051-0.00010.00480.00100.0004-0.00030.0014-0.0040-0.00210.0005
Aug 2013-0.0103-0.0046-0.0059-0.0044-0.0024-0.0085-0.0113-0.0061-0.0085-0.0062
Sep 2013-0.0007-0.0068-0.00390.0089-0.0078-0.0019-0.0076-0.00220.0005-0.0062
Oct 20130.00390.0011-0.00170.0021-0.0014-0.00120.00120.00180.00110.0022
Nov 2013-0.0290-0.00300.0017-0.00180.0045-0.0015-0.0048-0.0287-0.0108-0.0034
Dec 2013-0.0022-0.0029-0.0110-0.0112-0.00620.00060.00100.00040.0015-0.0035
Jan 20140.02250.00180.0058-0.00590.0026-0.00630.00730.01940.00720.0025
Feb 2014-0.0060-0.0011-0.0083-0.0031-0.0058-0.0006-0.0004-0.00560.0006-0.0025
Mar 20140.00380.00350.00330.00850.00490.00280.00450.00640.00610.0054
Apr 20140.01210.00640.00230.00530.00020.00380.00800.01570.01080.0056
May 20140.0029-0.0062-0.00730.0023-0.0073-0.00900.00060.00260.0060-0.0059
Jun 20140.00580.0050-0.0019-0.01100.00130.0047-0.00270.00480.00050.0033
Jul 2014-0.00520.00010.00240.00200.0002-0.0078-0.0011-0.0051-0.00310.0018
Aug 20140.0065-0.0041-0.0063-0.0003-0.0040-0.0022-0.00020.00800.0063-0.0036
Sep 2014-0.01200.00040.0067-0.00830.0052-0.0011-0.0162-0.0150-0.01050.0004
Oct 20140.00010.00450.00130.01490.00590.00690.01460.00140.00240.0049
Nov 20140.00450.00270.0057-0.00060.00360.00100.0117-0.00040.00340.0036
Dec 2014-0.00010.00290.0033-0.00130.0011-0.0001-0.00530.0001-0.00060.0002