Factor Regression Analysis

Factor Regression Overview

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:

  • The capital asset pricing model (CAPM) with market factor (MKT)
  • The Fama-French three factor model with market, size, and value factors (MKT, SMB, HML)
  • The Carhart four-factor model with market, size, value, and momentum factors (MKT, SMB, HML, MOM)
  • The Fama-French five factor model with market, size, value, profitability, and investment factors (MKT, SMB, HML, RMW, CMA)
  • The q-factor model with market, size, investment, return on equity, and expected growth factors (MKT, ME, I/A, ROE, EG)

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.

Additionally you can freely construct the factor model using any combination of existing factors or other time series under the custom factor returns model.

Regression Model

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

Factor Analysis Results

Factor Regression Summary

Name Ticker Start Date End Date Rm-Rf SMB HML MOM Alpha Annual Alpha R2
iShares S&P Small-Cap 600 Value ETF IJS Apr 2006 Apr 2023 0.96 0.83 0.49 -0.02 0.04% 0.46% 97.4%
iShares Russell 2000 Value ETF IWN Apr 2006 Apr 2023 0.96 0.79 0.50 0.01 -0.10% -1.17% 98.2%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Apr 2023 1.10 1.05 0.79 -0.41 0.08% 0.97% 91.5%
Vanguard Small-Cap Value ETF VBR Apr 2006 Apr 2023 1.00 0.54 0.42 -0.05 -0.01% -0.09% 97.6%
Statistically significant factor exposures in bold

iShares S&P Small-Cap 600 Value ETF

Ticker IJS
Time Period Apr 2006 - Apr 2023
Regression Basis 205 monthly samples
Coefficient of Determination (R2) 97.4%
Adjusted R2 97.4%
Regression F statistic 1,879.18 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.760 with p-value 0.040)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 21.632 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.017 57.138 0.000 0.931...0.997
Size (SMB) 0.83 0.030 27.428 0.000 0.766...0.885
Value (HML) 0.49 0.022 22.182 0.000 0.450...0.538
Momentum (MOM) -0.02 0.017 -1.300 0.195 -0.056...0.012
Alpha (α) 3.83bps 0.001 0.543 0.588 -0.10%...0.18%
Annualized Alpha (α) 0.46%  

iShares Russell 2000 Value ETF

Ticker IWN
Time Period Apr 2006 - Apr 2023
Regression Basis 205 monthly samples
Coefficient of Determination (R2) 98.2%
Adjusted R2 98.1%
Regression F statistic 2,698.26 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.013 with p-value 0.528)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 5.010 with p-value 0.286)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.014 69.694 0.000 0.938...0.992
Size (SMB) 0.79 0.025 31.820 0.000 0.738...0.835
Value (HML) 0.50 0.018 27.549 0.000 0.467...0.539
Momentum (MOM) 0.01 0.014 0.369 0.713 -0.023...0.033
Alpha (α) -9.76bps 0.001 -1.686 0.093 -0.21%...0.02%
Annualized Alpha (α) -1.17%  

Invesco S&P SmallCap 600 Pure Value ETF

Ticker RZV
Time Period Apr 2006 - Apr 2023
Regression Basis 205 monthly samples
Coefficient of Determination (R2) 91.5%
Adjusted R2 91.3%
Regression F statistic 539.23 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.846 with p-value 0.128)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 51.167 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.10 0.044 25.132 0.000 1.015...1.188
Size (SMB) 1.05 0.078 13.389 0.000 0.893...1.202
Value (HML) 0.79 0.058 13.598 0.000 0.673...0.901
Momentum (MOM) -0.41 0.045 -9.166 0.000 -0.497...-0.321
Alpha (α) 8.05bps 0.002 0.439 0.661 -0.28%...0.44%
Annualized Alpha (α) 0.97%  

Vanguard Small-Cap Value ETF

Ticker VBR
Time Period Apr 2006 - Apr 2023
Regression Basis 205 monthly samples
Coefficient of Determination (R2) 97.6%
Adjusted R2 97.6%
Regression F statistic 2,070.31 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.205 with p-value 0.926)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 7.658 with p-value 0.105)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.00 0.015 65.247 0.000 0.973...1.033
Size (SMB) 0.54 0.027 19.778 0.000 0.489...0.597
Value (HML) 0.42 0.020 20.752 0.000 0.381...0.461
Momentum (MOM) -0.05 0.016 -3.249 0.001 -0.082...-0.020
Alpha (α) -0.73bps 0.001 -0.114 0.910 -0.13%...0.12%
Annualized Alpha (α) -0.09%  
Notes and Disclosures
  • IMPORTANT: The projections or other information generated by Portfolio Visualizer regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results and are not guarantees of future results. Results may vary with each use and over time.
  • 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. All use is subject to terms of service.
  • Investing involves risk, including possible loss of principal. Past performance is not a guarantee of future results.
  • Asset allocation and diversification strategies do not guarantee a profit or protect against a loss.
  • Hypothetical returns do not reflect trading costs, transaction fees, commissions, or actual taxes due on investment returns.
  • 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.
  • Refer to the related documentation sections for more details on terms and definitions, methodology, and data sources.
  • The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
  • Refer to the documentation 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 Returns

Monthly Factor Premiums (BPS) 75.03 -1.80 -14.51 0.89  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
iShares S&P Small-Cap 600 Value ETF IJS Apr 2006 Apr 2023 0.46% 72.32 -1.49 -7.17 -0.02 67.48 97.4%
iShares Russell 2000 Value ETF IWN Apr 2006 Apr 2023 -1.17% 72.39 -1.42 -7.31 0.00 53.92 98.2%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Apr 2023 0.97% 82.67 -1.89 -11.42 -0.36 77.05 91.5%
Vanguard Small-Cap Value ETF VBR Apr 2006 Apr 2023 -0.09% 75.26 -0.98 -6.11 -0.05 67.40 97.6%

Risk and Return Attribution

NameStart DateEnd DateCumulative ReturnAnnualized ReturnAnnualized Standard DeviationCumulative ReturnReturn ContributionRisk Contribution
MarketSMBHMLMOMAlphaMarketSMBHMLMOMAlphaMarketSMBHMLMOMAlpha
iShares S&P Small-Cap 600 Value ETFApr 2006Apr 2023225.03%7.14%21.07%267.92%-20.00%-36.50%-0.64%14.24%78.96%-5.89%-10.76%-0.19%4.20%65.50%19.82%11.29%0.79%2.61%
iShares Russell 2000 Value ETFApr 2006Apr 2023149.80%5.51%20.64%230.40%-16.00%-31.86%0.13%-32.87%74.02%-5.14%-10.24%0.04%-10.56%67.44%19.02%11.90%-0.19%1.83%
Invesco S&P SmallCap 600 Pure Value ETFApr 2006Apr 2023169.72%5.98%30.29%259.82%-27.88%-60.36%-17.43%15.57%68.18%-7.32%-15.84%-4.57%4.09%47.37%16.26%14.64%13.21%8.52%
Vanguard Small-Cap Value ETFApr 2006Apr 2023234.64%7.33%20.13%283.66%-11.78%-31.05%-1.47%-4.71%85.26%-3.54%-9.33%-0.44%-1.42%74.23%11.81%9.62%1.96%2.37%

iShares S&P Small-Cap 600 Value ETF Cumulative Return

iShares Russell 2000 Value ETF Cumulative Return

Invesco S&P SmallCap 600 Pure Value ETF Cumulative Return

Vanguard Small-Cap Value ETF Cumulative Return

Residuals

MonthIJSIWNRZVVBR
Apr 2006-0.89%-0.70%-0.91%-1.31%
May 2006-0.41%0.24%-2.74%-0.19%
Jun 2006-0.12%0.74%1.79%0.89%
Jul 2006-0.84%1.07%-0.09%0.12%
Aug 20060.38%0.87%-2.56%-0.18%
Sep 20060.03%-0.32%-0.37%-0.70%
Oct 20060.66%0.58%0.15%0.17%
Nov 2006-0.40%0.00%-0.91%0.67%
Dec 2006-1.34%-0.54%-0.01%-1.33%
Jan 20070.55%0.02%1.11%0.36%
Feb 2007-0.39%-0.53%-0.10%0.35%
Mar 20070.18%0.69%-0.67%-0.02%
Apr 20070.49%-0.60%0.84%-0.44%
May 20071.18%0.69%-0.73%0.31%
Jun 2007-0.88%-0.86%-0.75%-0.65%
Jul 20070.95%-1.37%2.34%-1.22%
Aug 20071.01%1.70%-2.08%1.19%
Sep 2007-0.11%0.00%-0.33%-0.29%
Oct 20070.48%0.52%0.50%0.95%
Nov 20070.03%-0.19%-0.15%-0.32%
Dec 20070.14%-0.52%2.92%-0.20%
Jan 20080.60%1.03%5.81%0.79%
Feb 20080.35%0.51%-2.23%1.25%
Mar 20080.87%0.18%4.09%0.09%
Apr 2008-0.14%1.25%-5.32%1.21%
May 20080.24%-0.39%-1.12%1.27%
Jun 20080.13%-0.93%3.01%-1.94%
Jul 2008-1.52%0.58%-2.78%0.73%
Aug 2008-0.73%0.10%-4.59%-0.88%
Sep 20082.00%3.65%4.01%1.99%
Oct 20080.09%-1.17%2.38%-1.97%
Nov 20081.34%1.76%2.33%2.87%
Dec 20081.81%0.96%-4.82%0.52%
Jan 2009-0.70%-0.23%-5.44%0.36%
Feb 20090.15%-0.63%-1.81%-0.76%
Mar 2009-3.12%-1.56%2.50%-2.25%
Apr 20091.17%-1.13%16.28%2.42%
May 2009-2.72%-0.65%-2.37%-0.77%
Jun 20090.36%-1.20%9.00%-0.53%
Jul 2009-0.55%0.03%2.91%-0.43%
Aug 2009-2.85%-1.00%-4.93%-0.25%
Sep 2009-2.40%-1.58%-0.60%-0.69%
Oct 20092.10%1.80%-5.72%0.77%
Nov 2009-0.35%-0.59%-2.12%-0.56%
Dec 20090.56%0.41%-1.03%1.11%
Jan 20100.00%0.06%1.47%-0.29%
Feb 2010-1.05%-1.23%2.29%-0.20%
Mar 2010-0.56%0.21%0.58%0.32%
Apr 2010-0.73%-0.33%-1.09%0.52%
May 20100.14%0.62%-0.57%0.93%
Jun 20100.81%0.43%-2.72%0.25%
Jul 20100.01%0.47%0.40%0.62%
Aug 20100.05%0.50%-0.93%0.54%
Sep 20100.01%0.06%0.00%0.12%
Oct 20100.54%0.52%2.27%0.20%
Nov 2010-0.73%-0.37%1.41%0.17%
Dec 2010-0.15%-0.58%-2.09%-1.27%
Jan 2011-0.56%-0.41%-2.94%-0.40%
Feb 2011-1.05%-0.03%-0.80%-0.07%
Mar 20110.59%-0.10%1.03%0.57%
Apr 2011-0.27%0.42%-0.59%0.67%
May 20110.95%1.16%2.93%0.34%
Jun 20110.41%-0.41%0.26%0.02%
Jul 20110.95%0.64%2.42%0.12%
Aug 20111.43%0.35%1.15%0.45%
Sep 20110.24%0.05%0.90%-0.63%
Oct 20111.57%0.99%0.13%1.16%
Nov 20111.30%0.50%1.12%0.62%
Dec 20110.99%0.42%0.67%-0.19%
Jan 20121.62%0.88%-0.35%0.82%
Feb 2012-1.28%-1.47%-1.55%-1.07%
Mar 2012-0.14%0.12%-1.46%-0.76%
Apr 2012-0.32%0.09%0.24%0.61%
May 2012-0.65%0.42%0.21%0.63%
Jun 2012-0.13%0.50%0.22%-0.10%
Jul 20120.88%0.26%0.91%0.46%
Aug 20120.48%0.06%1.90%-0.50%
Sep 2012-0.78%-0.42%0.01%-0.95%
Oct 2012-1.13%-0.62%-4.18%0.19%
Nov 20120.75%-0.23%4.43%0.25%
Dec 2012-0.67%0.24%-3.20%-0.28%
Jan 2013-0.84%-0.05%-2.15%0.20%
Feb 20130.55%0.01%0.57%0.50%
Mar 2013-0.35%-0.25%-1.80%0.26%
Apr 20130.32%0.27%-0.95%-0.36%
May 2013-1.22%-2.32%1.59%-1.84%
Jun 2013-0.12%-0.29%-0.93%-0.77%
Jul 2013-0.70%-0.57%-1.74%0.03%
Aug 20130.26%-0.61%0.74%-0.46%
Sep 20131.19%0.54%2.67%0.61%
Oct 20130.09%-0.13%-0.80%0.06%
Nov 2013-0.01%-0.33%2.09%-1.01%
Dec 2013-1.07%-0.22%-1.08%0.18%
Jan 2014-0.04%-0.25%0.15%1.02%
Feb 20140.00%0.02%0.54%0.34%
Mar 2014-0.09%-0.12%-2.52%-0.35%
Apr 20140.66%0.49%-0.47%0.65%
May 20140.23%0.24%0.14%0.70%
Jun 2014-0.89%-0.05%-1.36%0.37%
Jul 20140.39%-0.73%1.20%-0.42%
Aug 20140.25%0.25%-0.03%0.89%
Sep 2014-0.34%-1.05%0.42%-0.95%
Oct 20142.09%2.24%0.93%0.81%
Nov 20141.23%0.43%1.84%1.00%
Dec 2014-0.57%-0.31%-2.18%-0.39%
Jan 2015-0.05%1.05%-0.08%1.83%
Feb 20150.26%-0.70%2.13%-0.17%
Mar 2015-0.20%0.69%0.20%1.08%
Apr 2015-0.99%-1.12%-0.72%-1.37%
May 2015-0.66%-0.64%-0.02%0.29%
Jun 2015-0.08%-0.12%0.42%-1.05%
Jul 20151.50%1.10%3.19%2.04%
Aug 2015-0.52%-0.61%-0.27%-0.23%
Sep 20151.16%1.33%0.94%0.96%
Oct 20150.76%-0.14%0.15%-0.10%
Nov 2015-0.81%-0.10%-1.00%-0.89%
Dec 20150.65%0.27%1.76%0.07%
Jan 20161.49%0.74%-1.14%0.47%
Feb 20161.69%0.50%2.41%1.19%
Mar 20161.27%0.42%0.39%0.74%
Apr 2016-1.16%-0.86%-2.23%-0.90%
May 2016-0.32%1.13%-5.57%0.48%
Jun 20161.15%0.81%2.26%0.69%
Jul 2016-0.33%0.31%-0.60%-0.33%
Aug 2016-2.00%-0.46%-4.71%-1.91%
Sep 2016-0.58%-0.49%0.94%-0.59%
Oct 2016-0.22%0.30%-0.01%-0.21%
Nov 2016-0.22%0.01%-2.11%-1.43%
Dec 2016-0.44%0.67%-2.52%-0.53%
Jan 2017-0.87%-0.37%-2.30%0.41%
Feb 20170.29%0.46%-1.47%0.12%
Mar 2017-0.21%-0.15%-2.05%-0.18%
Apr 2017-0.17%-0.14%-1.08%-0.22%
May 20170.60%-0.17%-0.92%-0.48%
Jun 2017-0.47%0.18%-0.73%-0.23%
Jul 20170.20%0.23%-2.04%0.06%
Aug 2017-0.52%-0.25%2.26%0.25%
Sep 20170.78%-0.33%0.43%-1.45%
Oct 2017-0.12%-0.73%1.92%-0.30%
Nov 20171.13%0.41%1.22%0.27%
Dec 2017-0.49%-0.95%-1.66%-0.02%
Jan 2018-0.85%-1.05%-0.57%-1.30%
Feb 2018-0.25%-1.14%1.23%-0.67%
Mar 20180.23%0.31%-0.68%0.92%
Apr 20180.12%0.36%-0.12%-0.84%
May 20180.45%0.68%2.31%0.41%
Jun 20180.31%0.19%0.36%-0.02%
Jul 20180.92%0.19%-1.73%0.08%
Aug 20180.78%0.10%3.02%0.14%
Sep 2018-0.58%0.06%-0.06%0.07%
Oct 2018-0.57%0.44%0.35%-0.49%
Nov 2018-0.88%0.26%-5.19%0.66%
Dec 2018-0.48%-0.22%0.79%0.17%
Jan 20191.56%0.70%0.68%0.72%
Feb 20190.28%0.26%-0.45%0.46%
Mar 2019-0.62%0.45%0.45%0.28%
Apr 20190.56%0.06%-2.75%-0.38%
May 2019-1.13%0.56%-0.95%0.71%
Jun 20190.84%-0.51%0.13%-0.24%
Jul 20191.35%0.41%2.12%0.37%
Aug 20191.61%1.07%3.98%0.65%
Sep 20191.30%1.00%1.63%-0.29%
Oct 20190.53%1.18%0.72%0.19%
Nov 2019-0.90%-1.13%-1.52%-1.24%
Dec 2019-1.53%-0.76%-2.39%-1.36%
Jan 2020-0.59%0.38%-4.08%1.23%
Feb 2020-1.49%-0.74%-3.77%-1.14%
Mar 2020-1.94%-1.39%1.93%-2.86%
Apr 2020-0.84%-1.82%5.52%-1.65%
May 2020-2.49%-1.66%-1.37%-0.06%
Jun 2020-0.02%-0.47%1.55%-1.00%
Jul 2020-0.27%-0.91%2.97%-0.28%
Aug 2020-0.68%-0.25%4.76%-1.64%
Sep 2020-0.37%0.21%1.83%1.19%
Oct 2020-0.13%0.25%-4.47%0.94%
Nov 20201.02%1.54%-3.48%0.23%
Dec 2020-0.36%0.54%-5.74%0.01%
Jan 2021-1.20%-2.13%-2.52%-2.94%
Feb 20212.66%1.76%1.03%1.47%
Mar 20210.77%0.75%0.10%0.09%
Apr 20210.04%0.15%-0.55%1.27%
May 20210.30%-0.39%2.23%-0.85%
Jun 2021-0.89%-0.79%1.73%-1.28%
Jul 2021-1.50%-0.59%-1.58%-0.11%
Aug 2021-0.53%0.22%1.96%-0.40%
Sep 2021-0.36%-0.65%-0.26%-0.62%
Oct 2021-1.34%-0.41%0.76%-0.47%
Nov 20210.17%-0.70%0.80%-0.51%
Dec 20210.78%0.82%-2.58%1.18%
Jan 20220.13%-1.46%-1.00%-0.41%
Feb 20221.14%0.54%-0.43%1.52%
Mar 2022-0.21%1.30%3.56%0.35%
Apr 20220.91%-0.61%3.63%1.56%
May 2022-0.00%-0.47%-0.77%-0.23%
Jun 20220.30%-0.37%0.64%-0.50%
Jul 2022-1.19%0.29%-3.62%0.16%
Aug 2022-1.99%-0.76%-0.57%0.08%
Sep 2022-0.93%-0.76%0.53%-0.14%
Oct 20222.62%0.88%3.90%0.68%
Nov 20221.13%0.19%1.54%1.83%
Dec 2022-0.67%-0.80%1.95%0.48%
Jan 20232.65%1.17%-1.24%0.23%
Feb 2023-0.23%-0.59%0.32%-0.32%
Mar 2023-0.29%-1.04%-0.44%-1.84%
Apr 2023-0.56%-0.73%0.43%-0.01%

iShares S&P Small-Cap 600 Value ETF

iShares Russell 2000 Value ETF

Invesco S&P SmallCap 600 Pure Value ETF

Vanguard Small-Cap Value ETF

iShares S&P Small-Cap 600 Value ETF

iShares Russell 2000 Value ETF

Invesco S&P SmallCap 600 Pure Value ETF

Vanguard Small-Cap Value ETF