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 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% -0.45% 95.7%
iShares Core S&P US Value ETF IUSV Jan 2011 Dec 2014 0.96 0.00 0.30 0.02 0.02% 0.22% 98.3%
SPDR Portfolio S&P 500 Value ETF SPYV Jan 2011 Dec 2014 1.02 -0.12 0.32 -0.06 -0.06% -0.75% 97.8%
SPDR S&P 600 Small Cap Value ETF SLYV Jan 2011 Dec 2014 1.02 0.80 0.19 -0.11 0.13% 1.61% 97.6%
Vanguard Mega Cap Value ETF MGV Jan 2011 Dec 2014 0.95 -0.20 0.33 0.04 -0.01% -0.10% 96.5%
Schwab US Large-Cap Value ETF SCHV Jan 2011 Dec 2014 0.93 -0.20 0.24 0.10 -0.03% -0.30% 96.6%
iShares Morningstar Small-Cap Value ETF JKL Jan 2011 Dec 2014 1.06 0.49 0.25 -0.01 -0.02% -0.24% 96.7%
iShares S&P Mid-Cap 400 Value ETF IJJ Jan 2011 Dec 2014 1.06 0.41 0.20 0.01 -0.03% -0.39% 95.1%
Vanguard Small-Cap Value ETF VBR Jan 2011 Dec 2014 1.04 0.56 0.24 -0.02 0.02% 0.24% 98.4%
Vanguard Russell 1000 Value ETF VONV Jan 2011 Dec 2014 0.97 -0.06 0.33 0.05 0.01% 0.07% 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 237.85 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.210 with p-value 0.775)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 0.454 with p-value 0.978)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.047 22.757 0.000 0.965...1.153
Size (SMB) 0.37 0.076 4.904 0.000 0.219...0.524
Value (HML) 0.23 0.083 2.718 0.009 0.058...0.392
Momentum (MOM) 0.00 0.060 0.047 0.962 -0.119...0.125
Alpha (α) -3.78bps 0.001 -0.253 0.802 -0.34%...0.26%
Annualized Alpha (α) -0.45%  

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 625.47 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.930 with p-value 0.413)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 4.810 with p-value 0.307)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.024 40.400 0.000 0.915...1.012
Size (SMB) 0.00 0.039 0.059 0.953 -0.076...0.081
Value (HML) 0.30 0.042 7.135 0.000 0.217...0.389
Momentum (MOM) 0.02 0.031 0.776 0.442 -0.038...0.086
Alpha (α) 1.81bps 0.001 0.237 0.814 -0.14%...0.17%
Annualized Alpha (α) 0.22%  

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 485.92 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.390 with p-value 0.918)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 5.626 with p-value 0.229)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.02 0.028 36.127 0.000 0.960...1.074
Size (SMB) -0.12 0.046 -2.554 0.014 -0.209...-0.025
Value (HML) 0.32 0.050 6.428 0.000 0.221...0.423
Momentum (MOM) -0.06 0.037 -1.733 0.090 -0.137...0.010
Alpha (α) -6.25bps 0.001 -0.690 0.494 -0.24%...0.12%
Annualized Alpha (α) -0.75%  

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 436.97 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.729 with p-value 0.178)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 2.408 with p-value 0.661)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.02 0.038 26.646 0.000 0.947...1.102
Size (SMB) 0.80 0.063 12.789 0.000 0.674...0.927
Value (HML) 0.19 0.068 2.766 0.008 0.051...0.328
Momentum (MOM) -0.11 0.050 -2.158 0.037 -0.208...-0.007
Alpha (α) 13.45bps 0.001 1.088 0.283 -0.11%...0.38%
Annualized Alpha (α) 1.61%  

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 299.55 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.154 with p-value 0.711)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.331 with p-value 0.856)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.95 0.032 29.315 0.000 0.884...1.015
Size (SMB) -0.20 0.053 -3.776 0.000 -0.305...-0.093
Value (HML) 0.33 0.058 5.650 0.000 0.210...0.442
Momentum (MOM) 0.04 0.042 0.841 0.405 -0.049...0.120
Alpha (α) -0.79bps 0.001 -0.076 0.940 -0.22%...0.20%
Annualized Alpha (α) -0.10%  

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 96.3%
Regression F statistic 304.27 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.193 with p-value 0.756)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 4.264 with p-value 0.371)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.93 0.031 30.288 0.000 0.872...0.997
Size (SMB) -0.20 0.050 -3.932 0.000 -0.299...-0.096
Value (HML) 0.24 0.055 4.398 0.000 0.131...0.352
Momentum (MOM) 0.10 0.040 2.589 0.013 0.023...0.184
Alpha (α) -2.52bps 0.001 -0.254 0.801 -0.23%...0.17%
Annualized Alpha (α) -0.30%  

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 319.61 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.613 with p-value 0.091)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.570 with p-value 0.814)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.042 25.396 0.000 0.976...1.144
Size (SMB) 0.49 0.068 7.156 0.000 0.349...0.623
Value (HML) 0.25 0.074 3.412 0.001 0.104...0.403
Momentum (MOM) -0.01 0.054 -0.113 0.911 -0.115...0.103
Alpha (α) -2.00bps 0.001 -0.149 0.882 -0.29%...0.25%
Annualized Alpha (α) -0.24%  

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 210.87 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.044 with p-value 0.569)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.297 with p-value 0.862)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.06 0.050 21.266 0.000 0.960...1.162
Size (SMB) 0.41 0.081 5.041 0.000 0.246...0.573
Value (HML) 0.20 0.089 2.231 0.031 0.019...0.377
Momentum (MOM) 0.01 0.065 0.154 0.878 -0.121...0.141
Alpha (α) -3.24bps 0.002 -0.202 0.841 -0.36%...0.29%
Annualized Alpha (α) -0.39%  

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 664.67 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.812 with p-value 0.264)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 5.059 with p-value 0.281)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.04 0.029 35.686 0.000 0.984...1.102
Size (SMB) 0.56 0.048 11.791 0.000 0.465...0.657
Value (HML) 0.24 0.052 4.630 0.000 0.136...0.346
Momentum (MOM) -0.02 0.038 -0.562 0.577 -0.098...0.055
Alpha (α) 2.01bps 0.001 0.214 0.831 -0.17%...0.21%
Annualized Alpha (α) 0.24%  

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 98.0%
Regression F statistic 563.66 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.968 with p-value 0.465)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.082 with p-value 0.544)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.97 0.025 38.977 0.000 0.924...1.024
Size (SMB) -0.06 0.041 -1.427 0.161 -0.140...0.024
Value (HML) 0.33 0.044 7.345 0.000 0.237...0.417
Momentum (MOM) 0.05 0.032 1.577 0.122 -0.014...0.116
Alpha (α) 0.56bps 0.001 0.070 0.945 -0.16%...0.17%
Annualized Alpha (α) 0.07%  
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
    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) 124.42 -14.60 -1.15 32.58  
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 -0.45% 131.80 -5.43 -0.26 0.09 122.43 95.7%
iShares Core S&P US Value ETF IUSV Jan 2011 Dec 2014 0.22% 119.87 -0.03 -0.35 0.78 122.08 98.3%
SPDR Portfolio S&P 500 Value ETF SPYV Jan 2011 Dec 2014 -0.75% 126.56 1.71 -0.37 -2.06 119.59 97.8%
SPDR S&P 600 Small Cap Value ETF SLYV Jan 2011 Dec 2014 1.61% 127.50 -11.69 -0.22 -3.51 125.53 97.6%
Vanguard Mega Cap Value ETF MGV Jan 2011 Dec 2014 -0.10% 118.13 2.91 -0.37 1.15 121.03 96.5%
Schwab US Large-Cap Value ETF SCHV Jan 2011 Dec 2014 -0.30% 116.26 2.88 -0.28 3.38 119.72 96.6%
iShares Morningstar Small-Cap Value ETF JKL Jan 2011 Dec 2014 -0.24% 131.88 -7.10 -0.29 -0.20 122.29 96.7%
iShares S&P Mid-Cap 400 Value ETF IJJ Jan 2011 Dec 2014 -0.39% 132.02 -5.98 -0.23 0.33 122.90 95.1%
Vanguard Small-Cap Value ETF VBR Jan 2011 Dec 2014 0.24% 129.75 -8.19 -0.28 -0.69 122.60 98.4%
Vanguard Russell 1000 Value ETF VONV Jan 2011 Dec 2014 0.07% 121.18 0.85 -0.37 1.67 123.88 98.1%
Regression residuals
MonthMDYVIUSVSPYVSLYVMGVSCHVJKLIJJVBRVONV
Jan 20110.0073-0.00080.0055-0.00720.0038-0.00160.00210.0136-0.0033-0.0054
Feb 2011-0.0035-0.00190.0014-0.00940.00620.0028-0.0072-0.0037-0.00050.0005
Mar 20110.00870.00560.00670.00340.00100.0029-0.00140.0060-0.00030.0068
Apr 2011-0.00600.0038-0.0001-0.00870.01000.0080-0.0029-0.00480.00090.0048
May 2011-0.00200.00820.0003-0.00250.00220.00430.00700.00460.00070.0040
Jun 20110.0060-0.00350.00080.0065-0.0029-0.0018-0.0023-0.0045-0.00070.0011
Jul 2011-0.0074-0.0085-0.00970.0083-0.0095-0.0081-0.0007-0.00670.0017-0.0023
Aug 20110.00520.00130.00200.00560.00170.00630.00480.00660.0033-0.0032
Sep 2011-0.00230.00110.00550.00140.00470.01080.0028-0.0125-0.00480.0033
Oct 20110.00980.00610.01410.01000.00480.00090.01420.00820.00670.0054
Nov 2011-0.0109-0.0016-0.00870.0115-0.0090-0.00430.00310.00920.0039-0.0035
Dec 20110.00970.00580.00610.01640.01210.01420.01010.00040.00030.0087
Jan 2012-0.0025-0.0043-0.00120.0034-0.0059-0.0057-0.00250.00430.0058-0.0040
Feb 20120.0033-0.0048-0.0049-0.0157-0.0067-0.0068-0.0077-0.0001-0.0112-0.0072
Mar 2012-0.0066-0.0046-0.00040.0014-0.00270.0010-0.0089-0.0114-0.0069-0.0024
Apr 20120.0046-0.0016-0.0014-0.0021-0.0053-0.00210.00160.00780.0036-0.0062
May 2012-0.00420.00170.0059-0.00840.0035-0.00200.00870.00020.00390.0027
Jun 2012-0.00850.00620.00380.00020.01300.01120.0005-0.0128-0.00150.0047
Jul 20120.00240.00590.00200.01240.00140.0009-0.00650.00040.00330.0055
Aug 2012-0.0054-0.0076-0.00930.0012-0.0152-0.0125-0.0057-0.0027-0.0029-0.0037
Sep 2012-0.01170.0003-0.0017-0.00290.00440.0028-0.0042-0.0135-0.0074-0.0016
Oct 20120.00550.0003-0.0014-0.0048-0.0057-0.00120.01640.01110.0084-0.0007
Nov 20120.0108-0.0060-0.00320.0041-0.0117-0.0065-0.00190.00970.0007-0.0057
Dec 20120.00500.0015-0.0027-0.0052-0.00090.00060.00240.00540.0033-0.0028
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 20130.00680.00130.0001-0.00630.00290.00190.00520.0073-0.00010.0009
Apr 2013-0.0114-0.0027-0.00210.00290.00060.0018-0.0100-0.0077-0.0034-0.0031
May 2013-0.0106-0.0086-0.0026-0.0074-0.0044-0.0116-0.0197-0.0192-0.0142-0.0091
Jun 2013-0.00260.0013-0.0023-0.00560.00590.0026-0.0125-0.0051-0.00650.0033
Jul 2013-0.0050-0.00020.00480.00100.0003-0.00040.0014-0.0039-0.00210.0005
Aug 2013-0.0104-0.0046-0.0059-0.0046-0.0023-0.0084-0.0115-0.0063-0.0087-0.0062
Sep 2013-0.0007-0.0069-0.00400.0089-0.0078-0.0020-0.0076-0.00220.0006-0.0062
Oct 20130.00400.0011-0.00180.0022-0.0015-0.00130.00130.00200.00120.0022
Nov 2013-0.0289-0.00300.0017-0.00170.0045-0.0015-0.0047-0.0286-0.0108-0.0034
Dec 2013-0.0022-0.0029-0.0111-0.0113-0.00620.00070.00100.00040.0015-0.0035
Jan 20140.02250.00180.0058-0.00590.0026-0.00620.00730.01940.00720.0025
Feb 2014-0.0060-0.0012-0.0083-0.0033-0.0058-0.0006-0.0005-0.00560.0005-0.0026
Mar 20140.00370.00360.00330.00840.00500.00290.00450.00640.00610.0054
Apr 20140.01200.00640.00240.00510.00030.00390.00800.01560.01070.0056
May 20140.0029-0.0062-0.00730.0023-0.0074-0.00900.00060.00260.0060-0.0059
Jun 20140.00570.0050-0.0019-0.01120.00140.0048-0.00280.00470.00040.0033
Jul 2014-0.00510.00010.00240.00200.0002-0.0078-0.0011-0.0051-0.00300.0018
Aug 20140.0065-0.0041-0.0063-0.0004-0.0040-0.0021-0.00020.00800.0063-0.0035
Sep 2014-0.01200.00040.0067-0.00840.0052-0.0011-0.0162-0.0150-0.01050.0004
Oct 20140.00010.00450.00130.01510.00590.00690.01470.00140.00250.0050
Nov 20140.00450.00270.0057-0.00060.00360.00100.0117-0.00040.00340.0036
Dec 2014-0.00020.00290.0034-0.00140.0011-0.0002-0.00540.0001-0.00070.0002