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
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 FF-MKT-RF FF-SMB FF-HML FF-MOM FF-RMW Alpha Annual Alpha R2
iShares S&P Small-Cap 600 Value ETF IJS 02/15/2018 11/30/2020 0.89 0.84 0.46 -0.15 0.28 -0.00% -0.02% 92.0%
iShares Core S&P Small-Cap ETF IJR 02/15/2018 11/30/2020 0.99 0.84 0.36 -0.04 0.21 -0.00% -0.23% 97.9%
Vanguard US Multifactor ETF VFMF 02/15/2018 11/30/2020 0.98 0.45 0.46 0.20 0.17 -0.01% -1.53% 97.4%

iShares S&P Small-Cap 600 Value ETF

Factor regression results for iShares S&P Small-Cap 600 Value ETF
Ticker IJS
Time Period 02/15/2018 - 11/30/2020
Regression Basis 703 daily samples
Coefficient of Determination (R2) 92.0%
Adjusted R2 91.9%
Regression F statistic 1,604.44 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.621 with p-value 1.000)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 4.595 with p-value 0.467)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
FF-MKT-RF Market 0.89 0.014 65.241 0.000 0.861...0.915
FF-SMB Size 0.84 0.033 25.119 0.000 0.770...0.901
FF-HML Value 0.46 0.032 14.706 0.000 0.402...0.526
FF-MOM Momentum -0.15 0.026 -5.905 0.000 -0.201...-0.101
FF-RMW Profitability 0.28 0.053 5.243 0.000 0.174...0.382
Alpha Alpha -0.01bps 0.000 -0.004 0.997 -0.04%...0.04%
Annualized Alpha Annualized Alpha -0.02%  

iShares Core S&P Small-Cap ETF

Factor regression results for iShares Core S&P Small-Cap ETF
Ticker IJR
Time Period 02/15/2018 - 11/30/2020
Regression Basis 703 daily samples
Coefficient of Determination (R2) 97.9%
Adjusted R2 97.9%
Regression F statistic 6,553.06 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.164 with p-value 0.985)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 54.881 with p-value 0.000)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
FF-MKT-RF Market 0.99 0.007 146.863 0.000 0.976...1.003
FF-SMB Size 0.84 0.016 51.077 0.000 0.809...0.874
FF-HML Value 0.36 0.016 22.929 0.000 0.327...0.389
FF-MOM Momentum -0.04 0.013 -3.451 0.001 -0.069...-0.019
FF-RMW Profitability 0.21 0.026 8.047 0.000 0.160...0.263
Alpha Alpha -0.09bps 0.000 -0.090 0.928 -0.02%...0.02%
Annualized Alpha Annualized Alpha -0.23%  

Vanguard US Multifactor ETF

Factor regression results for Vanguard US Multifactor ETF
Ticker VFMF
Time Period 02/15/2018 - 11/30/2020
Regression Basis 703 daily samples
Coefficient of Determination (R2) 97.4%
Adjusted R2 97.4%
Regression F statistic 5,242.35 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.339 with p-value 1.000)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 34.071 with p-value 0.000)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
FF-MKT-RF Market 0.98 0.007 143.880 0.000 0.963...0.990
FF-SMB Size 0.45 0.017 26.915 0.000 0.414...0.479
FF-HML Value 0.46 0.016 29.295 0.000 0.430...0.491
FF-MOM Momentum 0.20 0.013 15.615 0.000 0.174...0.224
FF-RMW Profitability 0.17 0.026 6.453 0.000 0.119...0.223
Alpha Alpha -0.61bps 0.000 -0.602 0.547 -0.03%...0.01%
Annualized Alpha Annualized Alpha -1.53%  
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 daily factor returns.
  • Symbols:
    MKT-RF
    Market factor (excess return over the risk free rate)
    SMB
    Size factor (Small Minus Big)
    HML
    Value factor (High Minus Low)
    MOM
    Momentum factor (Up Minus Down)
    RMW
    Profitability factor (Robust Minus Weak)
    CMA
    Conservative investment factor (Conservative Minus Aggressive)
    ST-REV
    Short-term reversal factor
    LT-REV
    Long-term reversal factor
    QMJ
    Quality factor (Quality Minus Junk)
    BAB
    Bet Against Beta factor
    TRM
    Term factor (fixed income)
    CDT
    Credit factor (fixed income)
    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
Daily Factor Premiums (BPS) 5.83 0.19 -7.19 0.61 0.03  
Name Ticker Start Date End Date Annual Alpha FF-MKT-RF FF-SMB FF-HML FF-MOM FF-RMW Total R2
iShares S&P Small-Cap 600 Value ETF IJS 02/15/2018 11/30/2020 -0.02% 5.18 0.16 -3.33 -0.09 0.01 1.91 92.0%
iShares Core S&P Small-Cap ETF IJR 02/15/2018 11/30/2020 -0.23% 5.77 0.16 -2.57 -0.03 0.01 3.25 97.9%
Vanguard US Multifactor ETF VFMF 02/15/2018 11/30/2020 -1.53% 5.69 0.08 -3.31 0.12 0.01 1.98 97.4%